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data-event-name="pinnable-header.vector-toc.pin">move to sidebar</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">hide</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">(Top)</div> </a> </li> <li id="toc-Description_of_the_method" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Description_of_the_method"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Description of the method</span> </div> </a> <button aria-controls="toc-Description_of_the_method-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Description of the method subsection</span> </button> <ul id="toc-Description_of_the_method-sublist" class="vector-toc-list"> <li id="toc-Beatpath_explanation" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Beatpath_explanation"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1</span> <span>Beatpath explanation</span> </div> </a> <ul id="toc-Beatpath_explanation-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Iterative_description" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Iterative_description"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.2</span> <span>Iterative description</span> </div> </a> <ul id="toc-Iterative_description-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Example" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Example"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Example</span> </div> </a> <ul id="toc-Example-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Implementation" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Implementation"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Implementation</span> </div> </a> <ul id="toc-Implementation-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Ties_and_alternative_implementations" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Ties_and_alternative_implementations"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Ties and alternative implementations</span> </div> </a> <ul id="toc-Ties_and_alternative_implementations-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Satisfied_and_failed_criteria" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Satisfied_and_failed_criteria"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Satisfied and failed criteria</span> </div> </a> <button aria-controls="toc-Satisfied_and_failed_criteria-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Satisfied and failed criteria subsection</span> </button> <ul id="toc-Satisfied_and_failed_criteria-sublist" class="vector-toc-list"> <li id="toc-Satisfied_criteria" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Satisfied_criteria"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.1</span> <span>Satisfied criteria</span> </div> </a> <ul id="toc-Satisfied_criteria-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Failed_criteria" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Failed_criteria"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.2</span> <span>Failed criteria</span> </div> </a> <ul id="toc-Failed_criteria-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Comparison_table" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Comparison_table"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.3</span> <span>Comparison table</span> </div> </a> <ul id="toc-Comparison_table-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Difference_from_ranked_pairs" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Difference_from_ranked_pairs"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.4</span> <span>Difference from ranked pairs</span> </div> </a> <ul id="toc-Difference_from_ranked_pairs-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-History" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#History"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>History</span> </div> </a> <ul id="toc-History-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Usage" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Usage"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Usage</span> </div> </a> <button aria-controls="toc-Usage-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Usage subsection</span> </button> <ul id="toc-Usage-sublist" class="vector-toc-list"> <li id="toc-Government" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Government"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.1</span> <span>Government</span> </div> </a> <ul id="toc-Government-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Political_parties" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Political_parties"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.2</span> <span>Political parties</span> </div> </a> <ul id="toc-Political_parties-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Student_government_and_associations" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Student_government_and_associations"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.3</span> <span>Student government and associations</span> </div> </a> <ul id="toc-Student_government_and_associations-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Organizations" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Organizations"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.4</span> <span>Organizations</span> </div> </a> <ul id="toc-Organizations-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Notes" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Notes"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>Notes</span> </div> </a> <ul id="toc-Notes-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> <span class="vector-toc-numb">9</span> <span>External links</span> </div> </a> <ul id="toc-External_links-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Contents" 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mw-first-heading"><span class="mw-page-title-main">Schulze method</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Go to an article in another language. Available in 23 languages" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-23" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">23 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%B7%D8%B1%D9%8A%D9%82%D8%A9_%D8%B4%D9%88%D9%84%D8%B2" title="طريقة شولز – Arabic" lang="ar" hreflang="ar" data-title="طريقة شولز" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/M%C3%A8tode_de_Schulze" title="Mètode de Schulze – Catalan" lang="ca" hreflang="ca" data-title="Mètode de Schulze" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Schulzeho_metoda" title="Schulzeho metoda – Czech" lang="cs" hreflang="cs" data-title="Schulzeho metoda" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Schulze-Methode" title="Schulze-Methode – German" lang="de" hreflang="de" data-title="Schulze-Methode" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%9C%CE%AD%CE%B8%CE%BF%CE%B4%CE%BF%CF%82_%CE%A3%CE%BF%CF%8D%CE%BB%CF%84%CF%83%CE%B5" title="Μέθοδος Σούλτσε – Greek" lang="el" hreflang="el" data-title="Μέθοδος Σούλτσε" data-language-autonym="Ελληνικά" data-language-local-name="Greek" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/M%C3%A9todo_Schulze" title="Método Schulze – Spanish" lang="es" hreflang="es" data-title="Método Schulze" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%B1%D9%88%D8%B4_%D8%B4%D9%88%D9%84%D8%AA%D8%B3%D9%87" title="روش شولتسه – Persian" lang="fa" hreflang="fa" data-title="روش شولتسه" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/M%C3%A9thode_de_Schulze" title="Méthode de Schulze – French" lang="fr" hreflang="fr" data-title="Méthode de Schulze" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%8A%90%EC%B8%A0_%EB%B0%A9%EB%B2%95" title="슐츠 방법 – Korean" lang="ko" hreflang="ko" data-title="슐츠 방법" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Schulzeova_metoda" title="Schulzeova metoda – Croatian" lang="hr" hreflang="hr" data-title="Schulzeova metoda" data-language-autonym="Hrvatski" data-language-local-name="Croatian" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Metode_Schulze" title="Metode Schulze – Indonesian" lang="id" hreflang="id" data-title="Metode Schulze" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesian" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Metodo_Schulze" title="Metodo Schulze – Italian" lang="it" hreflang="it" data-title="Metodo Schulze" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%A9%D7%99%D7%98%D7%AA_%D7%A9%D7%95%D7%9C%D7%A6%D7%94" title="שיטת שולצה – Hebrew" lang="he" hreflang="he" data-title="שיטת שולצה" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Schulze-m%C3%B3dszer" title="Schulze-módszer – Hungarian" lang="hu" hreflang="hu" data-title="Schulze-módszer" data-language-autonym="Magyar" data-language-local-name="Hungarian" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E3%82%B7%E3%83%A5%E3%83%AB%E3%83%84%E6%96%B9%E5%BC%8F" title="シュルツ方式 – Japanese" lang="ja" hreflang="ja" data-title="シュルツ方式" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Metoda_Schulzego" title="Metoda Schulzego – Polish" lang="pl" hreflang="pl" data-title="Metoda Schulzego" data-language-autonym="Polski" data-language-local-name="Polish" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/M%C3%A9todo_de_Schulze" title="Método de Schulze – Portuguese" lang="pt" hreflang="pt" data-title="Método de Schulze" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%9C%D0%B5%D1%82%D0%BE%D0%B4_%D0%A8%D1%83%D0%BB%D1%8C%D1%86%D0%B5" title="Метод Шульце – Russian" lang="ru" hreflang="ru" data-title="Метод Шульце" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Schulze_method" title="Schulze method – Simple English" lang="en-simple" hreflang="en-simple" data-title="Schulze method" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Schulzeova_metoda" title="Schulzeova metoda – Serbo-Croatian" lang="sh" hreflang="sh" data-title="Schulzeova metoda" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="Serbo-Croatian" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Schulzen_vaalitapa" title="Schulzen vaalitapa – Finnish" lang="fi" hreflang="fi" data-title="Schulzen vaalitapa" data-language-autonym="Suomi" data-language-local-name="Finnish" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Schulze-metoden" title="Schulze-metoden – Swedish" lang="sv" hreflang="sv" data-title="Schulze-metoden" data-language-autonym="Svenska" data-language-local-name="Swedish" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%9C%D0%B5%D1%82%D0%BE%D0%B4_%D0%A8%D1%83%D0%BB%D1%8C%D1%86%D0%B5" title="Метод Шульце – Ukrainian" lang="uk" hreflang="uk" data-title="Метод Шульце" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target"><span>Українська</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q113#sitelinks-wikipedia" title="Edit interlanguage links" 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sidebar-collapse nomobile nowraplinks"><tbody><tr><td class="sidebar-pretitle">A joint <a href="/wiki/Portal:Politics" title="Portal:Politics">Politics</a> and <a href="/wiki/Portal:Economics" title="Portal:Economics">Economics</a> series</td></tr><tr><th class="sidebar-title-with-pretitle" style="border-top:1px #fafafa solid; border-bottom:1px #fafafa solid; background:#efefef; background: var(--background-color-interactive, #efefef); color: var(--color-base, #000); padding:0.2em;"><a href="/wiki/Social_choice_theory" title="Social choice theory">Social choice</a> and <a href="/wiki/Electoral_system" title="Electoral system">electoral systems</a></th></tr><tr><td class="sidebar-image"><figure class="mw-halign-center" typeof="mw:File"><a href="/wiki/File:Electoral-systems-gears.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/82/Electoral-systems-gears.svg/128px-Electoral-systems-gears.svg.png" decoding="async" width="128" height="128" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/82/Electoral-systems-gears.svg/192px-Electoral-systems-gears.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/82/Electoral-systems-gears.svg/256px-Electoral-systems-gears.svg.png 2x" data-file-width="1024" data-file-height="1024" /></a><figcaption></figcaption></figure></td></tr><tr><td class="sidebar-above"> <div class="hlist"><ul><li><a href="/wiki/Social_choice_theory" title="Social choice theory">Social choice</a></li><li><a href="/wiki/Mechanism_design" title="Mechanism design">Mechanism design</a></li><li><a href="/wiki/Comparative_politics" title="Comparative politics">Comparative politics</a></li><li><a href="/wiki/Comparison_of_voting_rules" title="Comparison of voting rules">Comparison</a></li><li><a href="/wiki/List_of_electoral_systems" title="List of electoral systems">List</a> (<a href="/wiki/List_of_electoral_systems_by_country" title="List of electoral systems by country">By country</a>)</li></ul></div></td></tr><tr><td class="sidebar-content" style="text-align:left;"> <div class="sidebar-list mw-collapsible"><div class="sidebar-list-title" style="background:#efefef; border-top:1px solid;background: var(--background-color-interactive, #efefef); color: var(--color-base, #000);;color: var(--color-base)"><a href="/wiki/Single-member_district" title="Single-member district">Single-winner methods</a></div><div class="sidebar-list-content mw-collapsible-content"><b>Single vote - <a href="/wiki/Plurality_voting" title="Plurality voting">plurality</a> methods</b> <ul><li><a href="/wiki/First-past-the-post_voting" title="First-past-the-post voting">First preference plurality (FPP)</a></li> <li><a href="/wiki/Two-round_system" title="Two-round system">Two-round</a> (<abbr style="font-size:85%" title=""><a href="/wiki/American_English" title="American English">US</a>:</abbr> <a href="/wiki/Nonpartisan_blanket_primary" title="Nonpartisan blanket primary">Jungle primary</a>) <ul><li><a href="/wiki/Partisan_primary" class="mw-redirect" title="Partisan primary">Partisan primary</a></li></ul></li> <li><a href="/wiki/Instant-runoff_voting" title="Instant-runoff voting">Instant-runoff</a> <ul><li><abbr style="font-size:85%" title=""><a href="/wiki/British_English" title="British English">UK</a>:</abbr> Alternative vote (AV)</li> <li><abbr style="font-size:85%" title=""><a href="/wiki/American_English" title="American English">US</a>:</abbr> Ranked-choice (RCV)</li></ul></li></ul> <hr /> <p><b><a href="/wiki/Condorcet_method" title="Condorcet method">Condorcet methods</a></b> </p> <ul><li><a href="/wiki/Tideman_alternative_method" title="Tideman alternative method">Condorcet-IRV</a></li> <li><a href="/wiki/Round-robin_voting" title="Round-robin voting">Round-robin voting</a> <ul><li><a href="/wiki/Minimax_Condorcet_method" title="Minimax Condorcet method">Minimax</a></li> <li><a class="mw-selflink selflink">Schulze</a></li> <li><a href="/wiki/Ranked_pairs" title="Ranked pairs">Ranked pairs</a></li> <li><a href="/wiki/Maximal_lottery" class="mw-redirect" title="Maximal lottery">Maximal lottery</a></li></ul></li></ul> <hr /> <p><b><a href="/wiki/Positional_voting" title="Positional voting">Positional voting</a></b> </p> <ul><li><a href="/wiki/First-preference_plurality" class="mw-redirect" title="First-preference plurality">Plurality</a> (<abbr style="font-size:85%" title=""><a href="/wiki/Sequential_elimination_method" title="Sequential elimination method">el.</a></abbr> <a href="/wiki/Instant-runoff_voting" title="Instant-runoff voting">IRV</a>)</li> <li><a href="/wiki/Borda_count" title="Borda count">Borda count</a> (<abbr style="font-size:85%" title=""><a href="/wiki/Sequential_elimination_method" title="Sequential elimination method">el.</a></abbr> <a href="/wiki/Baldwin%27s_method" class="mw-redirect" title="Baldwin's method">Baldwin</a>)</li> <li><a href="/wiki/Anti-plurality_voting" title="Anti-plurality voting">Antiplurality</a> (<abbr style="font-size:85%" title=""><a href="/wiki/Sequential_elimination_method" title="Sequential elimination method">el.</a></abbr> <a href="/wiki/Coombs_method" class="mw-redirect" title="Coombs method">Coombs</a>)</li></ul> <hr /> <p><b><a href="/wiki/Rated_voting" title="Rated voting">Cardinal voting</a></b> </p> <ul><li><a href="/wiki/Score_voting" title="Score voting">Score voting</a></li> <li><a href="/wiki/Approval_voting" title="Approval voting">Approval voting</a></li> <li><a href="/wiki/Highest_median_voting_rules" title="Highest median voting rules">Majority judgment</a></li> <li><a href="/wiki/STAR_voting" title="STAR voting">STAR voting</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content" style="text-align:left;"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:#efefef; border-top:1px solid;background: var(--background-color-interactive, #efefef); color: var(--color-base, #000);;color: var(--color-base)"><a href="/wiki/Proportional_representation" title="Proportional representation">Proportional representation</a></div><div class="sidebar-list-content mw-collapsible-content"><b><a href="/wiki/Party-list_proportional_representation" title="Party-list proportional representation">Party-list</a></b> <ul><li><a href="/wiki/Apportionment_(politics)" title="Apportionment (politics)">Apportionment</a> <ul><li><a href="/wiki/Highest_averages_method" title="Highest averages method">Highest averages</a></li> <li><a href="/wiki/Largest_remainder_method" class="mw-redirect" title="Largest remainder method">Largest remainders</a></li> <li><a href="/wiki/National_remnant" title="National remnant">National remnant</a></li> <li><a href="/wiki/Biproportional_apportionment" title="Biproportional apportionment">Biproportional</a></li></ul></li> <li><a href="/wiki/Electoral_list" title="Electoral list">List type</a> <ul><li><a href="/wiki/Closed_list" title="Closed list">Closed list</a></li> <li><a href="/wiki/Open_list" title="Open list">Open list</a></li> <li><a href="/wiki/Panachage" title="Panachage">Panachage</a></li> <li><a href="/wiki/Justified_representation" title="Justified representation">List-free PR</a></li> <li><a href="/wiki/Localized_list" title="Localized list">Localized list</a></li></ul></li></ul> <hr /> <p><b><a href="/wiki/Electoral_quota" title="Electoral quota">Quota-remainder methods</a></b> </p> <ul><li><a href="/wiki/Single_transferable_vote" title="Single transferable vote">Hare STV</a></li> <li><a href="/wiki/Schulze_STV" title="Schulze STV">Schulze STV</a></li> <li><a href="/wiki/CPO-STV" title="CPO-STV">CPO-STV</a></li> <li><a href="/wiki/Quota_Borda_system" title="Quota Borda system">Quota Borda</a></li></ul> <hr /> <p><b><a href="/wiki/Approval-based_committee" class="mw-redirect" title="Approval-based committee">Approval-based committees</a></b> </p> <ul><li><a href="/wiki/Proportional_approval_voting" title="Proportional approval voting">Thiele's method</a></li> <li><a href="/wiki/Phragmen%27s_voting_rules" title="Phragmen's voting rules">Phragmen's method</a></li> <li><a href="/wiki/Expanding_approvals_rule" title="Expanding approvals rule">Expanding approvals rule</a></li> <li><a href="/wiki/Method_of_equal_shares" title="Method of equal shares">Method of equal shares</a></li></ul> <hr /> <p><b><a href="/wiki/Fractional_social_choice" title="Fractional social choice">Fractional social choice</a></b> </p> <ul><li><a href="/wiki/Direct_representation" title="Direct representation">Direct representation</a> <ul><li><a href="/wiki/Interactive_representation" title="Interactive representation">Interactive representation</a></li> <li><a href="/wiki/Liquid_democracy" title="Liquid democracy">Liquid democracy</a></li></ul></li> <li><a href="/wiki/Fractional_approval_voting" title="Fractional approval voting">Fractional approval voting</a></li> <li><a href="/wiki/Maximal_lottery" class="mw-redirect" title="Maximal lottery">Maximal lottery</a></li> <li><a href="/wiki/Random_ballot" title="Random ballot">Random ballot</a></li></ul> <hr /> <p><b><a href="/wiki/Semi-proportional_representation" title="Semi-proportional representation">Semi-proportional representation</a></b> </p> <ul><li><a href="/wiki/Cumulative_voting" title="Cumulative voting">Cumulative</a> <ul><li><a href="/wiki/Single_non-transferable_vote" title="Single non-transferable vote">SNTV</a></li></ul></li> <li><a href="/wiki/Limited_voting" title="Limited voting">Limited voting</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content" style="text-align:left;"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:#efefef; border-top:1px solid;background: var(--background-color-interactive, #efefef); color: var(--color-base, #000);;color: var(--color-base)"><a href="/wiki/Mixed_electoral_system" title="Mixed electoral system">Mixed systems</a></div><div class="sidebar-list-content mw-collapsible-content"><b>By results of combination</b> <ul><li><a href="/wiki/Mixed-member_majoritarian_representation" title="Mixed-member majoritarian representation">Mixed-member majoritarian</a></li> <li><a href="/wiki/Mixed-member_proportional_representation" title="Mixed-member proportional representation">Mixed-member proportional</a></li></ul> <hr /><b>By mechanism of combination</b> <ul><li><b>Non-<a href="/wiki/Compensation_(electoral_systems)" title="Compensation (electoral systems)">compensatory</a></b> <ul><li><a href="/wiki/Parallel_voting" title="Parallel voting">Parallel (superposition)</a></li> <li><a href="/wiki/Coexistence_(electoral_systems)" title="Coexistence (electoral systems)">Coexistence</a></li> <li><a href="/w/index.php?title=Conditional_electoral_system&action=edit&redlink=1" class="new" title="Conditional electoral system (page does not exist)">Conditional</a></li> <li><a href="/wiki/Majority_bonus_system" title="Majority bonus system">Fusion (majority bonus)</a></li></ul></li> <li><b><a href="/wiki/Compensation_(electoral_systems)" title="Compensation (electoral systems)">Compensatory</a></b> <ul><li><a href="/w/index.php?title=Seat_linkage_mixed_system&action=edit&redlink=1" class="new" title="Seat linkage mixed system (page does not exist)">Seat linkage system</a> <ul><li><abbr style="font-size:85%" title=""><a href="/wiki/British_English" title="British English">UK</a>:</abbr> <a href="/wiki/Additional_member_system" class="mw-redirect" title="Additional member system">'AMS'</a></li> <li><abbr style="font-size:85%" title=""><a href="/wiki/New_Zealand_English" title="New Zealand English">NZ</a>:</abbr> <a href="/wiki/Mixed-member_proportional" class="mw-redirect" title="Mixed-member proportional">'MMP'</a></li></ul></li> <li><a href="/wiki/Vote_linkage_mixed_system" class="mw-redirect" title="Vote linkage mixed system">Vote linkage system</a> <ul><li><a href="/wiki/Scorporo" title="Scorporo">Negative vote transfer</a></li> <li><a href="/wiki/Mixed_ballot_transferable_vote" title="Mixed ballot transferable vote">Mixed ballot</a></li></ul></li></ul></li> <li><a href="/wiki/Mixed_electoral_system" title="Mixed electoral system">Supermixed systems</a> <ul><li><a href="/wiki/Dual-member_proportional_representation" class="mw-redirect" title="Dual-member proportional representation">Dual-member proportional</a></li> <li><a href="/wiki/Rural%E2%80%93urban_proportional_representation" title="Rural–urban proportional representation">Rural–urban proportional</a></li> <li><a href="/wiki/Majority_jackpot_system" title="Majority jackpot system">Majority jackpot</a></li></ul></li></ul> <hr /> <p><b>By ballot type</b> </p> <ul><li><a href="/wiki/Mixed_single_vote" title="Mixed single vote">Single vote</a> <ul><li><a href="/wiki/Double_simultaneous_vote" title="Double simultaneous vote">Double simultaneous vote</a></li></ul></li> <li><a href="/wiki/Mixed_electoral_systems" class="mw-redirect" title="Mixed electoral systems">Dual-vote</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content" style="text-align:left;"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:#efefef; border-top:1px solid;background: var(--background-color-interactive, #efefef); color: var(--color-base, #000);;color: var(--color-base)"><a href="/wiki/Pathological_(mathematics)#Voting" title="Pathological (mathematics)">Paradoxes and pathologies</a></div><div class="sidebar-list-content mw-collapsible-content"><b>Spoiler effects</b> <ul><li><a href="/wiki/Spoiler_effect" title="Spoiler effect">Spoiler effect</a></li> <li><a href="/wiki/Independence_of_clones" class="mw-redirect" title="Independence of clones">Cloning paradox</a></li> <li><a href="/wiki/Condorcet_winner_criterion" title="Condorcet winner criterion">Frustrated majorities paradox</a></li> <li><a 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href="/wiki/Turkey-raising" class="mw-redirect" title="Turkey-raising">Turkey-raising</a></li></ul> <hr /> <p><b>Paradoxes of <a href="/wiki/Majority_rule" title="Majority rule">majority rule</a></b> </p> <ul><li><a href="/wiki/Tyranny_of_the_majority" title="Tyranny of the majority">Tyranny of the majority</a></li> <li><a href="/wiki/Discursive_dilemma" title="Discursive dilemma">Discursive dilemma</a></li> <li><a href="/wiki/Condorcet_paradox" title="Condorcet paradox">Conflicting majorities paradox</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content" style="text-align:left;"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:#efefef; border-top:1px solid;background: var(--background-color-interactive, #efefef); color: var(--color-base, #000);;color: var(--color-base)"><a href="/wiki/Social_choice_theory" title="Social choice theory">Social and collective choice</a></div><div class="sidebar-list-content mw-collapsible-content"><b><a href="/wiki/Proof_of_impossibility" title="Proof of impossibility">Impossibility theorems</a></b> <ul><li><a href="/wiki/Arrow%27s_impossibility_theorem" title="Arrow's impossibility theorem">Arrow's theorem</a></li> <li><a href="/wiki/Condorcet_paradox" title="Condorcet paradox">Majority impossibility</a></li> <li><a href="/wiki/Moulin%27s_impossibility_theorem" class="mw-redirect" title="Moulin's impossibility theorem">Moulin's impossibility theorem</a></li> <li><a href="/wiki/McKelvey%E2%80%93Schofield_chaos_theorem" title="McKelvey–Schofield chaos theorem">McKelvey–Schofield chaos theorem</a></li> <li><a href="/wiki/Gibbard%27s_theorem" title="Gibbard's theorem">Gibbard's theorem</a></li></ul> <hr /> <p><b>Positive results</b> </p> <ul><li><a href="/wiki/Median_voter_theorem" title="Median voter theorem">Median voter theorem</a></li> <li><a href="/wiki/Condorcet%27s_jury_theorem" title="Condorcet's jury theorem">Condorcet's jury theorem</a></li> <li><a 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href="mw-data:TemplateStyles:r1129693374"><style data-mw-deduplicate="TemplateStyles:r1239400231">.mw-parser-output .navbar{display:inline;font-size:88%;font-weight:normal}.mw-parser-output .navbar-collapse{float:left;text-align:left}.mw-parser-output .navbar-boxtext{word-spacing:0}.mw-parser-output .navbar ul{display:inline-block;white-space:nowrap;line-height:inherit}.mw-parser-output .navbar-brackets::before{margin-right:-0.125em;content:"[ "}.mw-parser-output .navbar-brackets::after{margin-left:-0.125em;content:" ]"}.mw-parser-output .navbar li{word-spacing:-0.125em}.mw-parser-output .navbar a>span,.mw-parser-output .navbar a>abbr{text-decoration:inherit}.mw-parser-output .navbar-mini abbr{font-variant:small-caps;border-bottom:none;text-decoration:none;cursor:inherit}.mw-parser-output .navbar-ct-full{font-size:114%;margin:0 7em}.mw-parser-output .navbar-ct-mini{font-size:114%;margin:0 4em}html.skin-theme-clientpref-night .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}@media(prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}}@media print{.mw-parser-output .navbar{display:none!important}}</style><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Electoral_systems_sidebar" title="Template:Electoral systems sidebar"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Electoral_systems_sidebar" title="Template talk:Electoral systems sidebar"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Electoral_systems_sidebar" title="Special:EditPage/Template:Electoral systems sidebar"><abbr title="Edit this template">e</abbr></a></li></ul></div></td></tr></tbody></table> <p>The <b>Schulze method</b> (<span class="rt-commentedText nowrap"><span class="IPA nopopups noexcerpt" lang="en-fonipa"><a href="/wiki/Help:IPA/English" title="Help:IPA/English">/<span style="border-bottom:1px dotted"><span title="/ˈ/: primary stress follows">ˈ</span><span title="/ʃ/: 'sh' in 'shy'">ʃ</span><span title="/ʊ/: 'u' in 'push'">ʊ</span><span title="'l' in 'lie'">l</span><span title="'t' in 'tie'">t</span><span title="'s' in 'sigh'">s</span><span title="/ə/: 'a' in 'about'">ə</span></span>/</a></span></span>), also known as the <b>beatpath method</b>, is a <a href="/wiki/Single_winner" class="mw-redirect" title="Single winner">single winner</a> <a href="/wiki/Ranked_voting" title="Ranked voting">ranked-choice voting rule</a> developed by Markus Schulze. The Schulze method is a <a href="/wiki/Condorcet_method" title="Condorcet method">Condorcet completion method</a>, which means it will elect a <a href="/wiki/Majority-preferred_candidate" class="mw-redirect" title="Majority-preferred candidate">majority-preferred candidate</a> if one exists. In other words, if most people rank <i>A</i> above <i>B</i>, <i>A</i> will defeat <i>B</i> (whenever this is possible). Schulze's method breaks <a href="/wiki/Cyclic_tie" class="mw-redirect" title="Cyclic tie">cyclic ties</a> by using indirect victories. The idea is that if <a href="/wiki/Alice_and_Bob" title="Alice and Bob">Alice</a> beats Bob, and Bob beats Charlie, then Alice (indirectly) beats Charlie; this kind of indirect win is called a <a href="/wiki/Beatpath" class="mw-redirect" title="Beatpath"><i>beatpath</i></a>. </p><p>For <a href="/wiki/Proportional_representation" title="Proportional representation">proportional representation</a>, a <a href="/wiki/Single_transferable_vote" title="Single transferable vote">single transferable vote</a> (STV) variant known as <a href="/wiki/Schulze_STV" title="Schulze STV">Schulze STV</a> also exists. The Schulze method is used by several organizations including <a href="/wiki/Debian" title="Debian">Debian</a>, <a href="/wiki/Ubuntu_(operating_system)" class="mw-redirect" title="Ubuntu (operating system)">Ubuntu</a>, <a href="/wiki/Gentoo_Linux" title="Gentoo Linux">Gentoo</a>, <a href="/wiki/Pirate_Party" title="Pirate Party">Pirate Party</a> political parties and <a class="mw-selflink-fragment" href="#Usage">many others</a>. It was also used by <a href="/wiki/Wikimedia" class="mw-redirect" title="Wikimedia">Wikimedia</a> prior to their adoption of <a href="/wiki/Score_voting" title="Score voting">score voting</a>. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Description_of_the_method">Description of the method</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Schulze_method&action=edit&section=1" title="Edit section: Description of the method"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Preferential_ballot.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/18/Preferential_ballot.svg/140px-Preferential_ballot.svg.png" decoding="async" width="140" height="181" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/18/Preferential_ballot.svg/210px-Preferential_ballot.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/18/Preferential_ballot.svg/280px-Preferential_ballot.svg.png 2x" data-file-width="765" data-file-height="990" /></a><figcaption>A sample ballot asking voters to order candidates by preference</figcaption></figure> <p>Schulze's method uses <a href="/wiki/Ranked_ballot" class="mw-redirect" title="Ranked ballot">ranked ballots</a> with equal ratings allowed. There are two common (equivalent) descriptions of Schulze's method. </p> <div class="mw-heading mw-heading3"><h3 id="Beatpath_explanation">Beatpath explanation</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Schulze_method&action=edit&section=2" title="Edit section: Beatpath explanation"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The idea behind Schulze's method is that if <a href="/wiki/Alice_and_Bob" title="Alice and Bob">Alice</a> defeats Bob, and Bob beats Charlie, then Alice "indirectly" defeats Charlie. These chained sequences of "beats" are called 'beatpaths'. </p><p>Every beatpath is assigned a particular <i>strength</i>. The strength of a single-step beatpath from Alice to Bob is just the number of voters who rank Alice over Bob. For a longer beatpath, consisting of multiple beats, a beatpath is as strong as its weakest link (i.e. the beat with the smallest number of winning votes). </p><p>We say Alice has a "beatpath-win" over Bob if her strongest beatpath to Bob is stronger than all of Bob's strongest beatpaths to Alice. The winner is the candidate who has a beatpath-win over every other candidate. </p><p>Markus Schulze proved that this definition of a beatpath-win is <a href="/wiki/Transitive_relation" title="Transitive relation">transitive</a>: in other words, if Alice has a beatpath-win over Bob, and Bob has a beatpath-win over Charlie, Alice has a beatpath-win over Charlie.<sup id="cite_ref-schulze201122_1-0" class="reference"><a href="#cite_note-schulze201122-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: §4.1">: §4.1 </span></sup> As a result, the Schulze method is a <a href="/wiki/Condorcet_method" title="Condorcet method">Condorcet method</a>, providing a full extension of the <a href="/wiki/Majority_rule" title="Majority rule">majority rule</a> to any set of ballots. </p> <div class="mw-heading mw-heading3"><h3 id="Iterative_description">Iterative description</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Schulze_method&action=edit&section=3" title="Edit section: Iterative description"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The Schulze winner can also be constructed iteratively, using a defeat-dropping method: </p> <ol><li>Draw a <a href="/wiki/Directed_graph" title="Directed graph">directed graph</a> with all the candidates as nodes; label the edges with the number of votes supporting the winner.</li> <li>If there is more than one candidate left: <ul><li>Check if any candidates are tied (and if so, break the ties by <a href="/wiki/Random_ballot" title="Random ballot">random ballot</a>).</li> <li>Eliminate all candidates outside the <a href="/wiki/Schwartz_set" class="mw-redirect" title="Schwartz set">majority-preferred set</a>.</li> <li>Delete the edge closest to being tied.</li></ul></li></ol> <p>The winner is the only candidate left at the end of the procedure. </p> <div class="mw-heading mw-heading2"><h2 id="Example">Example</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Schulze_method&action=edit&section=4" title="Edit section: Example"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In the following example 45 voters rank 5 candidates. </p> <table class="wikitable"> <tbody><tr> <th>Number of voters </th> <th>Order of preference </th></tr> <tr> <td>5 </td> <td>ACBED </td></tr> <tr> <td>5 </td> <td>ADECB </td></tr> <tr> <td>8 </td> <td>BEDAC </td></tr> <tr> <td>3 </td> <td>CABED </td></tr> <tr> <td>7 </td> <td>CAEBD </td></tr> <tr> <td>2 </td> <td>CBADE </td></tr> <tr> <td>7 </td> <td>DCEBA </td></tr> <tr> <td>8 </td> <td>EBADC </td></tr></tbody></table> <p>The pairwise preferences have to be computed first. For example, when comparing <i><span class="texhtml mvar" style="font-style:italic;">A</span></i> and <i><span class="texhtml mvar" style="font-style:italic;">B</span></i> pairwise, there are <span class="texhtml">5+5+3+7=20</span> voters who prefer <i><span class="texhtml mvar" style="font-style:italic;">A</span></i> to <i><span class="texhtml mvar" style="font-style:italic;">B</span></i>, and <span class="texhtml">8+2+7+8=25</span> voters who prefer <i><span class="texhtml mvar" style="font-style:italic;">B</span></i> to <i><span class="texhtml mvar" style="font-style:italic;">A</span></i>. So <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle d[A,B]=20}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <mo stretchy="false">[</mo> <mi>A</mi> <mo>,</mo> <mi>B</mi> <mo stretchy="false">]</mo> <mo>=</mo> <mn>20</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle d[A,B]=20}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/616fefcb8235a491fddf453df155781c9af635b9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:12.474ex; height:2.843ex;" alt="{\displaystyle d[A,B]=20}"></span> and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle d[B,A]=25}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <mo stretchy="false">[</mo> <mi>B</mi> <mo>,</mo> <mi>A</mi> <mo stretchy="false">]</mo> <mo>=</mo> <mn>25</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle d[B,A]=25}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/df14406da203e08b0a7de3d10fc3c4741ff5f2be" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:12.474ex; height:2.843ex;" alt="{\displaystyle d[B,A]=25}"></span>. The full set of pairwise preferences is: </p> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Schulze_method_example1.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e0/Schulze_method_example1.svg/300px-Schulze_method_example1.svg.png" decoding="async" width="300" height="288" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e0/Schulze_method_example1.svg/450px-Schulze_method_example1.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e0/Schulze_method_example1.svg/600px-Schulze_method_example1.svg.png 2x" data-file-width="363" data-file-height="349" /></a><figcaption><a href="/wiki/Directed_graph" title="Directed graph">Directed graph</a> labeled with pairwise preferences d[*, *] </figcaption></figure> <table class="wikitable" style="text-align:center"> <caption>Matrix of pairwise preferences </caption> <tbody><tr> <th></th> <th><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle d[*,A]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <mo stretchy="false">[</mo> <mo>∗</mo> <mo>,</mo> <mi>A</mi> <mo stretchy="false">]</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle d[*,A]}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d2433862a5da2042a5aa511a40d9ae3937fa80da" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.449ex; height:2.843ex;" alt="{\displaystyle d[*,A]}"></span></th> <th><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle d[*,B]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <mo stretchy="false">[</mo> <mo>∗</mo> <mo>,</mo> <mi>B</mi> <mo stretchy="false">]</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle d[*,B]}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d9a569a62e7e27ec155cdea7128dd9716bbbafad" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.47ex; height:2.843ex;" alt="{\displaystyle d[*,B]}"></span></th> <th><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle d[*,C]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <mo stretchy="false">[</mo> <mo>∗</mo> <mo>,</mo> <mi>C</mi> <mo stretchy="false">]</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle d[*,C]}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/051eb2e238d95060533be1d80a7dc129ffaae071" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.472ex; height:2.843ex;" alt="{\displaystyle d[*,C]}"></span></th> <th><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle d[*,D]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <mo stretchy="false">[</mo> <mo>∗</mo> <mo>,</mo> <mi>D</mi> <mo stretchy="false">]</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle d[*,D]}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6365f00dc82da401f2dacf3811636c0f04e74b76" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.63ex; height:2.843ex;" alt="{\displaystyle d[*,D]}"></span></th> <th><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle d[*,E]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <mo stretchy="false">[</mo> <mo>∗</mo> <mo>,</mo> <mi>E</mi> <mo stretchy="false">]</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle d[*,E]}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/510965cc123e859a1bd6c9f7b0b3a6fd9c7ef10f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.482ex; height:2.843ex;" alt="{\displaystyle d[*,E]}"></span> </th></tr> <tr> <th><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle d[A,*]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <mo stretchy="false">[</mo> <mi>A</mi> <mo>,</mo> <mo>∗</mo> <mo stretchy="false">]</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle d[A,*]}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e5e073ed6786afc665e2ae51f57b48780ab1b97e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.449ex; height:2.843ex;" alt="{\displaystyle d[A,*]}"></span> </th> <td></td> <td style="background:#fdd;">20</td> <td style="background:#dfd;">26</td> <td style="background:#dfd;">30</td> <td style="background:#fdd;">22 </td></tr> <tr> <th><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle d[B,*]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <mo stretchy="false">[</mo> <mi>B</mi> <mo>,</mo> <mo>∗</mo> <mo stretchy="false">]</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle d[B,*]}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dddd58b0010e6b9e833d9c16ea3a92a0f0e0b60e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.47ex; height:2.843ex;" alt="{\displaystyle d[B,*]}"></span> </th> <td style="background:#dfd;">25</td> <td></td> <td style="background:#fdd;">16</td> <td style="background:#dfd;">33</td> <td style="background:#fdd;">18 </td></tr> <tr> <th><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle d[C,*]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <mo stretchy="false">[</mo> <mi>C</mi> <mo>,</mo> <mo>∗</mo> <mo stretchy="false">]</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle d[C,*]}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1f3df13a469557e873323bdd8d90f51fd60975be" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.472ex; height:2.843ex;" alt="{\displaystyle d[C,*]}"></span> </th> <td style="background:#fdd;">19</td> <td style="background:#dfd;">29</td> <td></td> <td style="background:#fdd;">17</td> <td style="background:#dfd;">24 </td></tr> <tr> <th><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle d[D,*]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <mo stretchy="false">[</mo> <mi>D</mi> <mo>,</mo> <mo>∗</mo> <mo stretchy="false">]</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle d[D,*]}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3d181d2f3490676b9488069ae533aa12620ff560" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.63ex; height:2.843ex;" alt="{\displaystyle d[D,*]}"></span> </th> <td style="background:#fdd;">15</td> <td style="background:#fdd;">12</td> <td style="background:#dfd;">28</td> <td></td> <td style="background:#fdd;">14 </td></tr> <tr> <th><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle d[E,*]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <mo stretchy="false">[</mo> <mi>E</mi> <mo>,</mo> <mo>∗</mo> <mo stretchy="false">]</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle d[E,*]}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/404d8e35f83c4ea952ae013139f2cf0ed6724db9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.482ex; height:2.843ex;" alt="{\displaystyle d[E,*]}"></span> </th> <td style="background:#dfd;">23</td> <td style="background:#dfd;">27</td> <td style="background:#fdd;">21</td> <td style="background:#dfd;">31</td> <td> </td></tr></tbody></table> <p>The cells for d[X, Y] have a light green background if d[X, Y] > d[Y, X], otherwise the background is light red. There is no undisputed winner by only looking at the pairwise differences here. </p><p>Now the strongest paths have to be identified. To help visualize the strongest paths, the set of pairwise preferences is depicted in the diagram on the right in the form of a <a href="/wiki/Directed_graph" title="Directed graph">directed graph</a>. An arrow from the node representing a candidate X to the one representing a candidate Y is labelled with d[X, Y]. To avoid cluttering the diagram, an arrow has only been drawn from X to Y when d[X, Y] > d[Y, X] (i.e. the table cells with light green background), omitting the one in the opposite direction (the table cells with light red background). </p><p>One example of computing the strongest path strength is p[B, D] = 33: the strongest path from B to D is the direct path (B, D) which has strength 33. But when computing p[A, C], the strongest path from A to C is not the direct path (A, C) of strength 26, rather the strongest path is the indirect path (A, D, C) which has strength min(30, 28) = 28. The <i>strength</i> of a path is the strength of its weakest link. </p><p> For each pair of candidates X and Y, the following table shows the strongest path from candidate X to candidate Y in red, with the weakest link underlined.</p><div style="clear:both;" class=""></div> <table class="wikitable" style="text-align:center"> <caption>Strongest paths </caption> <tbody><tr> <th style="background:#EAECF0;background:linear-gradient(to top right,#EAECF0 49%,#AAA 49.5%,#AAA 50.5%,#EAECF0 51%);line-height:1.2;padding:0.1em 0.4em;"><div style="margin-left:2em;text-align:right">To</div><div style="margin-right:2em;text-align:left">From</div> </th> <th>A</th> <th>B</th> <th>C</th> <th>D</th> <th>E </th> <th> </th></tr> <tr> <th>A </th> <td data-sort-value="" style="background: var(--background-color-interactive, #ececec); color: var(--color-base, inherit); vertical-align: middle; text-align: center;" class="table-na">—</td> <td><figure class="mw-halign-none mw-image-border" typeof="mw:File"><a href="/wiki/File:Schulze_method_example1_AB.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f8/Schulze_method_example1_AB.svg/150px-Schulze_method_example1_AB.svg.png" decoding="async" width="150" height="144" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f8/Schulze_method_example1_AB.svg/225px-Schulze_method_example1_AB.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f8/Schulze_method_example1_AB.svg/300px-Schulze_method_example1_AB.svg.png 2x" data-file-width="363" data-file-height="349" /></a><figcaption></figcaption></figure> A-(30)-D-<u>(28)</u>-C-(29)-B</td> <td><figure class="mw-halign-none mw-image-border" typeof="mw:File"><a href="/wiki/File:Schulze_method_example1_AC.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/41/Schulze_method_example1_AC.svg/150px-Schulze_method_example1_AC.svg.png" decoding="async" width="150" height="144" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/41/Schulze_method_example1_AC.svg/225px-Schulze_method_example1_AC.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/41/Schulze_method_example1_AC.svg/300px-Schulze_method_example1_AC.svg.png 2x" data-file-width="363" data-file-height="349" /></a><figcaption></figcaption></figure> A-(30)-D-<u>(28)</u>-C</td> <td><figure class="mw-halign-none mw-image-border" typeof="mw:File"><a href="/wiki/File:Schulze_method_example1_AD.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/5e/Schulze_method_example1_AD.svg/150px-Schulze_method_example1_AD.svg.png" decoding="async" width="150" height="144" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/5e/Schulze_method_example1_AD.svg/225px-Schulze_method_example1_AD.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/5e/Schulze_method_example1_AD.svg/300px-Schulze_method_example1_AD.svg.png 2x" data-file-width="363" data-file-height="349" /></a><figcaption></figcaption></figure> A-<u>(30)</u>-D</td> <td><figure class="mw-halign-none mw-image-border" typeof="mw:File"><a href="/wiki/File:Schulze_method_example1_AE.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/00/Schulze_method_example1_AE.svg/150px-Schulze_method_example1_AE.svg.png" decoding="async" width="150" height="144" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/00/Schulze_method_example1_AE.svg/225px-Schulze_method_example1_AE.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/00/Schulze_method_example1_AE.svg/300px-Schulze_method_example1_AE.svg.png 2x" data-file-width="363" data-file-height="349" /></a><figcaption></figcaption></figure> A-(30)-D-(28)-C-<u>(24)</u>-E </td> <th>A </th></tr> <tr> <th>B </th> <td><figure class="mw-halign-none mw-image-border" typeof="mw:File"><a href="/wiki/File:Schulze_method_example1_BA.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/42/Schulze_method_example1_BA.svg/150px-Schulze_method_example1_BA.svg.png" decoding="async" width="150" height="144" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/42/Schulze_method_example1_BA.svg/225px-Schulze_method_example1_BA.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/42/Schulze_method_example1_BA.svg/300px-Schulze_method_example1_BA.svg.png 2x" data-file-width="363" data-file-height="349" /></a><figcaption></figcaption></figure> B-<u>(25)</u>-A</td> <td data-sort-value="" style="background: var(--background-color-interactive, #ececec); color: var(--color-base, inherit); vertical-align: middle; text-align: center;" class="table-na">—</td> <td><figure class="mw-halign-none mw-image-border" typeof="mw:File"><a href="/wiki/File:Schulze_method_example1_BC.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/93/Schulze_method_example1_BC.svg/150px-Schulze_method_example1_BC.svg.png" decoding="async" width="150" height="144" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/93/Schulze_method_example1_BC.svg/225px-Schulze_method_example1_BC.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/93/Schulze_method_example1_BC.svg/300px-Schulze_method_example1_BC.svg.png 2x" data-file-width="363" data-file-height="349" /></a><figcaption></figcaption></figure> B-(33)-D-<u>(28)</u>-C</td> <td><figure class="mw-halign-none mw-image-border" typeof="mw:File"><a href="/wiki/File:Schulze_method_example1_BD.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e2/Schulze_method_example1_BD.svg/150px-Schulze_method_example1_BD.svg.png" decoding="async" width="150" height="144" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e2/Schulze_method_example1_BD.svg/225px-Schulze_method_example1_BD.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e2/Schulze_method_example1_BD.svg/300px-Schulze_method_example1_BD.svg.png 2x" data-file-width="363" data-file-height="349" /></a><figcaption></figcaption></figure> B-<u>(33)</u>-D</td> <td><figure class="mw-halign-none mw-image-border" typeof="mw:File"><a href="/wiki/File:Schulze_method_example1_BE.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b5/Schulze_method_example1_BE.svg/150px-Schulze_method_example1_BE.svg.png" decoding="async" width="150" height="144" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b5/Schulze_method_example1_BE.svg/225px-Schulze_method_example1_BE.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b5/Schulze_method_example1_BE.svg/300px-Schulze_method_example1_BE.svg.png 2x" data-file-width="363" data-file-height="349" /></a><figcaption></figcaption></figure> B-(33)-D-(28)-C-<u>(24)</u>-E </td> <th>B </th></tr> <tr> <th>C </th> <td><figure class="mw-halign-none mw-image-border" typeof="mw:File"><a href="/wiki/File:Schulze_method_example1_CA.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/1d/Schulze_method_example1_CA.svg/150px-Schulze_method_example1_CA.svg.png" decoding="async" width="150" height="144" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/1d/Schulze_method_example1_CA.svg/225px-Schulze_method_example1_CA.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/1d/Schulze_method_example1_CA.svg/300px-Schulze_method_example1_CA.svg.png 2x" data-file-width="363" data-file-height="349" /></a><figcaption></figcaption></figure> C-(29)-B-<u>(25)</u>-A</td> <td><figure class="mw-halign-none mw-image-border" typeof="mw:File"><a href="/wiki/File:Schulze_method_example1_CB.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6d/Schulze_method_example1_CB.svg/150px-Schulze_method_example1_CB.svg.png" decoding="async" width="150" height="144" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6d/Schulze_method_example1_CB.svg/225px-Schulze_method_example1_CB.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/6d/Schulze_method_example1_CB.svg/300px-Schulze_method_example1_CB.svg.png 2x" data-file-width="363" data-file-height="349" /></a><figcaption></figcaption></figure> C-<u>(29)</u>-B</td> <td data-sort-value="" style="background: var(--background-color-interactive, #ececec); color: var(--color-base, inherit); vertical-align: middle; text-align: center;" class="table-na">—</td> <td><figure class="mw-halign-none mw-image-border" typeof="mw:File"><a href="/wiki/File:Schulze_method_example1_CD.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a6/Schulze_method_example1_CD.svg/150px-Schulze_method_example1_CD.svg.png" decoding="async" width="150" height="144" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a6/Schulze_method_example1_CD.svg/225px-Schulze_method_example1_CD.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a6/Schulze_method_example1_CD.svg/300px-Schulze_method_example1_CD.svg.png 2x" data-file-width="363" data-file-height="349" /></a><figcaption></figcaption></figure> C-<u>(29)</u>-B-(33)-D</td> <td><figure class="mw-halign-none mw-image-border" typeof="mw:File"><a href="/wiki/File:Schulze_method_example1_CE.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b3/Schulze_method_example1_CE.svg/150px-Schulze_method_example1_CE.svg.png" decoding="async" width="150" height="144" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b3/Schulze_method_example1_CE.svg/225px-Schulze_method_example1_CE.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b3/Schulze_method_example1_CE.svg/300px-Schulze_method_example1_CE.svg.png 2x" data-file-width="363" data-file-height="349" /></a><figcaption></figcaption></figure> C-<u>(24)</u>-E </td> <th>C </th></tr> <tr> <th>D </th> <td><figure class="mw-halign-none mw-image-border" typeof="mw:File"><a href="/wiki/File:Schulze_method_example1_DA.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/ed/Schulze_method_example1_DA.svg/150px-Schulze_method_example1_DA.svg.png" decoding="async" width="150" height="144" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/ed/Schulze_method_example1_DA.svg/225px-Schulze_method_example1_DA.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/ed/Schulze_method_example1_DA.svg/300px-Schulze_method_example1_DA.svg.png 2x" data-file-width="363" data-file-height="349" /></a><figcaption></figcaption></figure> D-(28)-C-(29)-B-<u>(25)</u>-A</td> <td><figure class="mw-halign-none mw-image-border" typeof="mw:File"><a href="/wiki/File:Schulze_method_example1_DB.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/2b/Schulze_method_example1_DB.svg/150px-Schulze_method_example1_DB.svg.png" decoding="async" width="150" height="144" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/2b/Schulze_method_example1_DB.svg/225px-Schulze_method_example1_DB.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/2b/Schulze_method_example1_DB.svg/300px-Schulze_method_example1_DB.svg.png 2x" data-file-width="363" data-file-height="349" /></a><figcaption></figcaption></figure> D-<u>(28)</u>-C-(29)-B</td> <td><figure class="mw-halign-none mw-image-border" typeof="mw:File"><a href="/wiki/File:Schulze_method_example1_DC.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/52/Schulze_method_example1_DC.svg/150px-Schulze_method_example1_DC.svg.png" decoding="async" width="150" height="144" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/52/Schulze_method_example1_DC.svg/225px-Schulze_method_example1_DC.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/52/Schulze_method_example1_DC.svg/300px-Schulze_method_example1_DC.svg.png 2x" data-file-width="363" data-file-height="349" /></a><figcaption></figcaption></figure> D-<u>(28)</u>-C</td> <td data-sort-value="" style="background: var(--background-color-interactive, #ececec); color: var(--color-base, inherit); vertical-align: middle; text-align: center;" class="table-na">—</td> <td><figure class="mw-halign-none mw-image-border" typeof="mw:File"><a href="/wiki/File:Schulze_method_example1_DE.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/14/Schulze_method_example1_DE.svg/150px-Schulze_method_example1_DE.svg.png" decoding="async" width="150" height="144" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/14/Schulze_method_example1_DE.svg/225px-Schulze_method_example1_DE.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/14/Schulze_method_example1_DE.svg/300px-Schulze_method_example1_DE.svg.png 2x" data-file-width="363" data-file-height="349" /></a><figcaption></figcaption></figure> D-(28)-C-<u>(24)</u>-E </td> <th>D </th></tr> <tr> <th>E </th> <td><figure class="mw-halign-none mw-image-border" typeof="mw:File"><a href="/wiki/File:Schulze_method_example1_EA.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/2d/Schulze_method_example1_EA.svg/150px-Schulze_method_example1_EA.svg.png" decoding="async" width="150" height="144" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/2d/Schulze_method_example1_EA.svg/225px-Schulze_method_example1_EA.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/2d/Schulze_method_example1_EA.svg/300px-Schulze_method_example1_EA.svg.png 2x" data-file-width="363" data-file-height="349" /></a><figcaption></figcaption></figure> E-(31)-D-(28)-C-(29)-B-<u>(25)</u>-A</td> <td><figure class="mw-halign-none mw-image-border" typeof="mw:File"><a href="/wiki/File:Schulze_method_example1_EB.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/ff/Schulze_method_example1_EB.svg/150px-Schulze_method_example1_EB.svg.png" decoding="async" width="150" height="144" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/ff/Schulze_method_example1_EB.svg/225px-Schulze_method_example1_EB.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/ff/Schulze_method_example1_EB.svg/300px-Schulze_method_example1_EB.svg.png 2x" data-file-width="363" data-file-height="349" /></a><figcaption></figcaption></figure> E-(31)-D-<u>(28)</u>-C-(29)-B</td> <td><figure class="mw-halign-none mw-image-border" typeof="mw:File"><a href="/wiki/File:Schulze_method_example1_EC.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/97/Schulze_method_example1_EC.svg/150px-Schulze_method_example1_EC.svg.png" decoding="async" width="150" height="144" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/97/Schulze_method_example1_EC.svg/225px-Schulze_method_example1_EC.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/97/Schulze_method_example1_EC.svg/300px-Schulze_method_example1_EC.svg.png 2x" data-file-width="363" data-file-height="349" /></a><figcaption></figcaption></figure> E-(31)-D-<u>(28)</u>-C</td> <td><figure class="mw-halign-none mw-image-border" typeof="mw:File"><a href="/wiki/File:Schulze_method_example1_ED.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/47/Schulze_method_example1_ED.svg/150px-Schulze_method_example1_ED.svg.png" decoding="async" width="150" height="144" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/47/Schulze_method_example1_ED.svg/225px-Schulze_method_example1_ED.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/47/Schulze_method_example1_ED.svg/300px-Schulze_method_example1_ED.svg.png 2x" data-file-width="363" data-file-height="349" /></a><figcaption></figcaption></figure> E-<u>(31)</u>-D</td> <td data-sort-value="" style="background: var(--background-color-interactive, #ececec); color: var(--color-base, inherit); vertical-align: middle; text-align: center;" class="table-na">— </td> <th>E </th></tr> <tr> <th> </th> <th>A</th> <th>B</th> <th>C</th> <th>D</th> <th>E </th> <th style="background:#EAECF0;background:linear-gradient(to top right,#EAECF0 49%,#AAA 49.5%,#AAA 50.5%,#EAECF0 51%);line-height:1.2;padding:0.1em 0.4em;"><div style="margin-left:2em;text-align:right">From</div><div style="margin-right:2em;text-align:left">To</div> </th></tr></tbody></table> <table class="wikitable" style="text-align:center"> <caption>Strengths of the strongest paths </caption> <tbody><tr> <th></th> <th><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle p[*,A]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>p</mi> <mo stretchy="false">[</mo> <mo>∗</mo> <mo>,</mo> <mi>A</mi> <mo stretchy="false">]</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p[*,A]}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e7ed62bbfc48846cad8299f1ae2cbd73539776e7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; margin-left: -0.089ex; width:6.492ex; height:2.843ex;" alt="{\displaystyle p[*,A]}"></span></th> <th><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle p[*,B]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>p</mi> <mo stretchy="false">[</mo> <mo>∗</mo> <mo>,</mo> <mi>B</mi> <mo stretchy="false">]</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p[*,B]}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/333750cdd31bc0ef53aae51b21a4a940adf6ae82" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; margin-left: -0.089ex; width:6.513ex; height:2.843ex;" alt="{\displaystyle p[*,B]}"></span></th> <th><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle p[*,C]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>p</mi> <mo stretchy="false">[</mo> <mo>∗</mo> <mo>,</mo> <mi>C</mi> <mo stretchy="false">]</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p[*,C]}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2bc85a3d9d6ba41f0bc19b56087c96f375226f93" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; margin-left: -0.089ex; width:6.515ex; height:2.843ex;" alt="{\displaystyle p[*,C]}"></span></th> <th><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle p[*,D]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>p</mi> <mo stretchy="false">[</mo> <mo>∗</mo> <mo>,</mo> <mi>D</mi> <mo stretchy="false">]</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p[*,D]}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cec9a2f8ae04fc767a071a03bd0ea9caa6644fe2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; margin-left: -0.089ex; width:6.673ex; height:2.843ex;" alt="{\displaystyle p[*,D]}"></span></th> <th><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle p[*,E]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>p</mi> <mo stretchy="false">[</mo> <mo>∗</mo> <mo>,</mo> <mi>E</mi> <mo stretchy="false">]</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p[*,E]}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cadbd7f5d672332d9f9cf60a84f33e6655191c6c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; margin-left: -0.089ex; width:6.525ex; height:2.843ex;" alt="{\displaystyle p[*,E]}"></span> </th></tr> <tr> <th><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle p[A,*]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>p</mi> <mo stretchy="false">[</mo> <mi>A</mi> <mo>,</mo> <mo>∗</mo> <mo stretchy="false">]</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p[A,*]}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6d4c21f5b64afaf82d43e8721055de525787e983" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; margin-left: -0.089ex; width:6.492ex; height:2.843ex;" alt="{\displaystyle p[A,*]}"></span> </th> <td></td> <td style="background:#dfd;">28</td> <td style="background:#dfd;">28</td> <td style="background:#dfd;">30</td> <td style="background:#fdd;">24 </td></tr> <tr> <th><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle p[B,*]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>p</mi> <mo stretchy="false">[</mo> <mi>B</mi> <mo>,</mo> <mo>∗</mo> <mo stretchy="false">]</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p[B,*]}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7022a11349de2d0fc5af2f3f820b1beca2d191f8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; margin-left: -0.089ex; width:6.513ex; height:2.843ex;" alt="{\displaystyle p[B,*]}"></span> </th> <td style="background:#fdd;">25</td> <td></td> <td style="background:#fdd;">28</td> <td style="background:#dfd;">33</td> <td style="background:#fdd;">24 </td></tr> <tr> <th><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle p[C,*]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>p</mi> <mo stretchy="false">[</mo> <mi>C</mi> <mo>,</mo> <mo>∗</mo> <mo stretchy="false">]</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p[C,*]}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/96902cfcb1a6c52549e109378f3975ac1e67b24f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; margin-left: -0.089ex; width:6.515ex; height:2.843ex;" alt="{\displaystyle p[C,*]}"></span> </th> <td style="background:#fdd;">25</td> <td style="background:#dfd;">29</td> <td></td> <td style="background:#dfd;">29</td> <td style="background:#fdd;">24 </td></tr> <tr> <th><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle p[D,*]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>p</mi> <mo stretchy="false">[</mo> <mi>D</mi> <mo>,</mo> <mo>∗</mo> <mo stretchy="false">]</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p[D,*]}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f99b88bf3741f0817bb81d0955904c5a6bde9d1e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; margin-left: -0.089ex; width:6.673ex; height:2.843ex;" alt="{\displaystyle p[D,*]}"></span> </th> <td style="background:#fdd;">25</td> <td style="background:#fdd;">28</td> <td style="background:#fdd;">28</td> <td></td> <td style="background:#fdd;">24 </td></tr> <tr> <th><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle p[E,*]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>p</mi> <mo stretchy="false">[</mo> <mi>E</mi> <mo>,</mo> <mo>∗</mo> <mo stretchy="false">]</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p[E,*]}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7b3f4b64482d398508522ebbddad2ebbe18cdf0e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; margin-left: -0.089ex; width:6.525ex; height:2.843ex;" alt="{\displaystyle p[E,*]}"></span> </th> <td style="background:#dfd;">25</td> <td style="background:#dfd;">28</td> <td style="background:#dfd;">28</td> <td style="background:#dfd;">31</td> <td> </td></tr></tbody></table> <p>Now the output of the Schulze method can be determined. For example, when comparing <i><span class="texhtml mvar" style="font-style:italic;">A</span></i> and <i><span class="texhtml mvar" style="font-style:italic;">B</span></i>, since <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (28=)p[A,B]>p[B,A](=25)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mn>28</mn> <mo>=</mo> <mo stretchy="false">)</mo> <mi>p</mi> <mo stretchy="false">[</mo> <mi>A</mi> <mo>,</mo> <mi>B</mi> <mo stretchy="false">]</mo> <mo>></mo> <mi>p</mi> <mo stretchy="false">[</mo> <mi>B</mi> <mo>,</mo> <mi>A</mi> <mo stretchy="false">]</mo> <mo stretchy="false">(</mo> <mo>=</mo> <mn>25</mn> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (28=)p[A,B]>p[B,A](=25)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5102460dac92bbf79a731ebea0174b87e2dbc302" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:30.282ex; height:2.843ex;" alt="{\displaystyle (28=)p[A,B]>p[B,A](=25)}"></span>, for the Schulze method candidate <i><span class="texhtml mvar" style="font-style:italic;">A</span></i> is <i>better</i> than candidate <i><span class="texhtml mvar" style="font-style:italic;">B</span></i>. Another example is that <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (31=)p[E,D]>p[D,E](=24)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mn>31</mn> <mo>=</mo> <mo stretchy="false">)</mo> <mi>p</mi> <mo stretchy="false">[</mo> <mi>E</mi> <mo>,</mo> <mi>D</mi> <mo stretchy="false">]</mo> <mo>></mo> <mi>p</mi> <mo stretchy="false">[</mo> <mi>D</mi> <mo>,</mo> <mi>E</mi> <mo stretchy="false">]</mo> <mo stretchy="false">(</mo> <mo>=</mo> <mn>24</mn> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (31=)p[E,D]>p[D,E](=24)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/db687fa2ae0ee4b059387c4eb8665b88c88e0237" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:30.667ex; height:2.843ex;" alt="{\displaystyle (31=)p[E,D]>p[D,E](=24)}"></span>, so candidate E is <i>better</i> than candidate D. Continuing in this way, the result is that the Schulze ranking is <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E>A>C>B>D}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>E</mi> <mo>></mo> <mi>A</mi> <mo>></mo> <mi>C</mi> <mo>></mo> <mi>B</mi> <mo>></mo> <mi>D</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E>A>C>B>D}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9d9993c0f931bc4720f09a14584e42559d0a0d1b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:21.367ex; height:2.176ex;" alt="{\displaystyle E>A>C>B>D}"></span>, and <i><span class="texhtml mvar" style="font-style:italic;">E</span></i> wins. In other words, <i><span class="texhtml mvar" style="font-style:italic;">E</span></i> wins since <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle p[E,X]\geq p[X,E]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>p</mi> <mo stretchy="false">[</mo> <mi>E</mi> <mo>,</mo> <mi>X</mi> <mo stretchy="false">]</mo> <mo>≥</mo> <mi>p</mi> <mo stretchy="false">[</mo> <mi>X</mi> <mo>,</mo> <mi>E</mi> <mo stretchy="false">]</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p[E,X]\geq p[X,E]}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a93b3547fa268c146f1723b3c2327d148e926562" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; margin-left: -0.089ex; width:17.693ex; height:2.843ex;" alt="{\displaystyle p[E,X]\geq p[X,E]}"></span> for every other candidate X. </p> <div class="mw-heading mw-heading2"><h2 id="Implementation">Implementation</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Schulze_method&action=edit&section=5" title="Edit section: Implementation"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div><p> The only difficult step in implementing the Schulze method is computing the strongest path strengths. However, this is a well-known problem in graph theory sometimes called the <a href="/wiki/Widest_path_problem" title="Widest path problem">widest path problem</a>. One simple way to compute the strengths, therefore, is a variant of the <a href="/wiki/Floyd%E2%80%93Warshall_algorithm" title="Floyd–Warshall algorithm">Floyd–Warshall algorithm</a>. The following <a href="/wiki/Pseudocode" title="Pseudocode">pseudocode</a> illustrates the algorithm.</p><div class="mw-highlight mw-highlight-lang-text mw-content-ltr mw-highlight-lines" dir="ltr"><pre><span></span><span class="linenos" data-line="1"></span># Input: d[i,j], the number of voters who prefer candidate i to candidate j. <span class="linenos" data-line="2"></span># Output: p[i,j], the strength of the strongest path from candidate i to candidate j. <span class="linenos" data-line="3"></span> <span class="linenos" data-line="4"></span>for i from 1 to C <span class="linenos" data-line="5"></span> for j from 1 to C <span class="linenos" data-line="6"></span> if i ≠ j then <span class="linenos" data-line="7"></span> if d[i,j] > d[j,i] then <span class="linenos" data-line="8"></span> p[i,j] := d[i,j] <span class="linenos" data-line="9"></span> else <span class="linenos" data-line="10"></span> p[i,j] := 0 <span class="linenos" data-line="11"></span> <span class="linenos" data-line="12"></span>for i from 1 to C <span class="linenos" data-line="13"></span> for j from 1 to C <span class="linenos" data-line="14"></span> if i ≠ j then <span class="linenos" data-line="15"></span> for k from 1 to C <span class="linenos" data-line="16"></span> if i ≠ k and j ≠ k then <span class="linenos" data-line="17"></span> p[j,k] := max (p[j,k], min (p[j,i], p[i,k])) </pre></div><p>This algorithm is <a href="/wiki/P_(complexity)" title="P (complexity)">efficient</a> and has <a href="/wiki/Time_complexity" title="Time complexity">running time</a> <a href="/wiki/Big_O_notation" title="Big O notation">O(<i>C</i><sup>3</sup>)</a> where <i>C</i> is the number of candidates. </p><div class="mw-heading mw-heading2"><h2 id="Ties_and_alternative_implementations">Ties and alternative implementations</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Schulze_method&action=edit&section=6" title="Edit section: Ties and alternative implementations"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>When allowing users to have ties in their preferences, the outcome of the Schulze method naturally depends on how these ties are interpreted in defining d[*,*]. Two natural choices are that d[A, B] represents either the number of voters who strictly prefer A to B (A>B), or the <i>margin</i> of (voters with A>B) minus (voters with B>A). But no matter how the <i>d</i>s are defined, the Schulze ranking has no cycles, and assuming the <i>d</i>s are unique it has no ties.<sup id="cite_ref-schulze20113_2-0" class="reference"><a href="#cite_note-schulze20113-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p><p>Although ties in the Schulze ranking are unlikely, they are possible. Schulze's original paper recommended breaking ties by <a href="/wiki/Random_ballot" title="Random ballot">random ballot</a>.<sup id="cite_ref-schulze20113_2-1" class="reference"><a href="#cite_note-schulze20113-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p><p>There is another alternative way to <i>demonstrate</i> the winner of the Schulze method. This method is equivalent to the others described here, but the presentation is optimized for the significance of steps being <i>visually apparent</i> as a human goes through it, not for computation. </p> <ol><li>Make the results table, called the "matrix of pairwise preferences", such as used above in the example. Then, every positive number is a pairwise win for the candidate on that row (and marked green), ties are zeroes, and losses are negative (marked red). Order the candidates by how long they last in elimination.</li> <li>If there is a candidate with no red on their line, they win.</li> <li>Otherwise, draw a square box around the Schwartz set in the upper left corner. It can be described as the minimal "winner's circle" of candidates who do not lose to anyone outside the circle. Note that to the right of the box there is no red, which means it is a winner's circle, and note that within the box there is no reordering possible that would produce a smaller winner's circle.</li> <li>Cut away every part of the table outside the box.</li> <li>If there is still no candidate with no red on their line, something needs to be compromised on; every candidate lost some race, and the loss we tolerate the best is the one where the loser obtained the most votes. So, take the red cell with the highest number (if going by margins, the least negative), make it green—or any color other than red—and go back step 2.</li></ol> <p>Here is a margins table made from the above example. Note the change of order used for demonstration purposes. </p> <table class="wikitable" style="text-align:center"> <caption>Initial results table </caption> <tbody><tr> <th></th> <th>E</th> <th>A</th> <th>C</th> <th>B</th> <th>D </th></tr> <tr> <th>E </th> <td></td> <td style="background:#dfd;">1</td> <td style="background:#fdd;">−3</td> <td style="background:#dfd;">9</td> <td style="background:#dfd;">17 </td></tr> <tr> <th>A </th> <td style="background:#fdd;">−1</td> <td></td> <td style="background:#dfd;">7</td> <td style="background:#fdd;">−5</td> <td style="background:#dfd;">15 </td></tr> <tr> <th>C </th> <td style="background:#dfd;">3</td> <td style="background:#fdd;">−7</td> <td></td> <td style="background:#dfd;">13</td> <td style="background:#fdd;">−11 </td></tr> <tr> <th>B </th> <td style="background:#fdd;">−9</td> <td style="background:#dfd;">5</td> <td style="background:#fdd;">−13</td> <td></td> <td style="background:#dfd;">21 </td></tr> <tr> <th>D </th> <td style="background:#fdd;">−17</td> <td style="background:#fdd;">−15</td> <td style="background:#dfd;">11</td> <td style="background:#fdd;">−21</td> <td> </td></tr></tbody></table> <p>The first drop (A's loss to E by 1 vote) does not help shrink the Schwartz set. </p> <table class="wikitable" style="text-align:center"> <caption>First drop </caption> <tbody><tr> <th></th> <th>E</th> <th>A</th> <th>C</th> <th>B</th> <th>D </th></tr> <tr> <th>E </th> <td></td> <td style="background:#dfd;">1</td> <td style="background:#fdd;">−3</td> <td style="background:#dfd;">9</td> <td style="background:#dfd;">17 </td></tr> <tr> <th>A </th> <td style="background:#ddd;">−1</td> <td></td> <td style="background:#dfd;">7</td> <td style="background:#fdd;">−5</td> <td style="background:#dfd;">15 </td></tr> <tr> <th>C </th> <td style="background:#dfd;">3</td> <td style="background:#fdd;">−7</td> <td></td> <td style="background:#dfd;">13</td> <td style="background:#fdd;">−11 </td></tr> <tr> <th>B </th> <td style="background:#fdd;">−9</td> <td style="background:#dfd;">5</td> <td style="background:#fdd;">−13</td> <td></td> <td style="background:#dfd;">21 </td></tr> <tr> <th>D </th> <td style="background:#fdd;">−17</td> <td style="background:#fdd;">−15</td> <td style="background:#dfd;">11</td> <td style="background:#fdd;">−21</td> <td> </td></tr></tbody></table> <p>So we get straight to the second drop (E's loss to C by 3 votes), and that shows us the winner, E, with its clear row. </p> <table class="wikitable" style="text-align:center"> <caption>Second drop, final </caption> <tbody><tr> <th></th> <th>E</th> <th>A</th> <th>C</th> <th>B</th> <th>D </th></tr> <tr> <th>E </th> <td></td> <td style="background:#efe;">1</td> <td style="background:#eee;">−3</td> <td style="background:#efe;">9</td> <td style="background:#efe;">17 </td></tr> <tr> <th>A </th> <td style="background:#ddd;">−1</td> <td></td> <td style="background:#dfd;">7</td> <td style="background:#fdd;">−5</td> <td style="background:#dfd;">15 </td></tr> <tr> <th>C </th> <td style="background:#dfd;">3</td> <td style="background:#fdd;">−7</td> <td></td> <td style="background:#dfd;">13</td> <td style="background:#fdd;">−11 </td></tr> <tr> <th>B </th> <td style="background:#fdd;">−9</td> <td style="background:#dfd;">5</td> <td style="background:#fdd;">−13</td> <td></td> <td style="background:#dfd;">21 </td></tr> <tr> <th>D </th> <td style="background:#fdd;">−17</td> <td style="background:#fdd;">−15</td> <td style="background:#dfd;">11</td> <td style="background:#fdd;">−21</td> <td> </td></tr></tbody></table> <p>This method can also be used to calculate a result, if the table is remade in such a way that one can conveniently and reliably rearrange the order of the candidates on both the row and the column, with the same order used on both at all times. </p> <div class="mw-heading mw-heading2"><h2 id="Satisfied_and_failed_criteria">Satisfied and failed criteria</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Schulze_method&action=edit&section=7" title="Edit section: Satisfied and failed criteria"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Satisfied_criteria">Satisfied criteria</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Schulze_method&action=edit&section=8" title="Edit section: Satisfied criteria"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The Schulze method satisfies the following criteria: </p> <style data-mw-deduplicate="TemplateStyles:r1184024115">.mw-parser-output .div-col{margin-top:0.3em;column-width:30em}.mw-parser-output .div-col-small{font-size:90%}.mw-parser-output .div-col-rules{column-rule:1px solid #aaa}.mw-parser-output .div-col dl,.mw-parser-output .div-col ol,.mw-parser-output .div-col ul{margin-top:0}.mw-parser-output .div-col li,.mw-parser-output .div-col dd{page-break-inside:avoid;break-inside:avoid-column}</style><div class="div-col" style="column-width: 30em;"> <ul><li><a href="/wiki/Monotonicity_criterion" class="mw-redirect" title="Monotonicity criterion">Monotonicity criterion</a><sup id="cite_ref-schulze2011_3-0" class="reference"><a href="#cite_note-schulze2011-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: §4.5">: §4.5 </span></sup></li> <li><a href="/wiki/Majority_favorite_criterion" class="mw-redirect" title="Majority favorite criterion">Majority criterion</a></li> <li><a href="/wiki/Majority_loser_criterion" title="Majority loser criterion">Majority loser criterion</a></li> <li><a href="/wiki/Condorcet_criterion" class="mw-redirect" title="Condorcet criterion">Condorcet criterion</a></li> <li><a href="/wiki/Condorcet_loser_criterion" title="Condorcet loser criterion">Condorcet loser criterion</a></li> <li><a href="/wiki/Smith_criterion" class="mw-redirect" title="Smith criterion">Smith criterion</a><sup id="cite_ref-schulze2011_3-1" class="reference"><a href="#cite_note-schulze2011-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: §4.7">: §4.7 </span></sup></li> <li><a href="/wiki/Independence_of_Smith-dominated_alternatives" title="Independence of Smith-dominated alternatives">Independence of Smith-dominated alternatives</a><sup id="cite_ref-schulze2011_3-2" class="reference"><a href="#cite_note-schulze2011-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: §4.7">: §4.7 </span></sup></li> <li><a href="/wiki/Mutual_majority_criterion" title="Mutual majority criterion">Mutual majority criterion</a></li> <li><a href="/wiki/Independence_of_clones_criterion" title="Independence of clones criterion">Independence of clones</a><sup id="cite_ref-schulze2011_3-3" class="reference"><a href="#cite_note-schulze2011-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: §4.6">: §4.6 </span></sup></li> <li><a href="/wiki/Reversal_symmetry" class="mw-redirect" title="Reversal symmetry">Reversal symmetry</a><sup id="cite_ref-schulze2011_3-4" class="reference"><a href="#cite_note-schulze2011-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: §4.4">: §4.4 </span></sup></li> <li>Mono-append<sup id="cite_ref-woodall1994_4-0" class="reference"><a href="#cite_note-woodall1994-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup></li> <li>Mono-add-plump<sup id="cite_ref-woodall1994_4-1" class="reference"><a href="#cite_note-woodall1994-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup></li> <li><a href="/wiki/Resolvability_criterion" title="Resolvability criterion">Resolvability criterion</a><sup id="cite_ref-schulze2011_3-5" class="reference"><a href="#cite_note-schulze2011-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: §4.2">: §4.2 </span></sup></li> <li><a href="/wiki/Polynomial_time" class="mw-redirect" title="Polynomial time">Polynomial runtime</a><sup id="cite_ref-schulze2011_3-6" class="reference"><a href="#cite_note-schulze2011-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: §2.3"">: §2.3" </span></sup></li> <li>prudence<sup id="cite_ref-schulze2011_3-7" class="reference"><a href="#cite_note-schulze2011-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: §4.9"">: §4.9" </span></sup></li> <li>MinMax sets<sup id="cite_ref-schulze2011_3-8" class="reference"><a href="#cite_note-schulze2011-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: §4.8"">: §4.8" </span></sup></li> <li><a href="/wiki/Plurality_criterion" title="Plurality criterion">Woodall's plurality criterion</a> if <a href="/wiki/Condorcet_method#Defeat_strength" title="Condorcet method">winning votes</a> are used for d[X,Y]</li> <li>Symmetric-completion<sup id="cite_ref-woodall1994_4-2" class="reference"><a href="#cite_note-woodall1994-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> if <a href="/wiki/Condorcet_method#Defeat_strength" title="Condorcet method">margins</a> are used for d[X,Y]</li></ul> </div> <div class="mw-heading mw-heading3"><h3 id="Failed_criteria">Failed criteria</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Schulze_method&action=edit&section=9" title="Edit section: Failed criteria"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Since the Schulze method satisfies the Condorcet criterion, it automatically fails the following criteria: </p> <ul><li><a href="/wiki/Participation_criterion" class="mw-redirect" title="Participation criterion">Participation</a><sup id="cite_ref-schulze20113_2-2" class="reference"><a href="#cite_note-schulze20113-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: §3.4">: §3.4 </span></sup></li> <li><a href="/wiki/Consistency_criterion" class="mw-redirect" title="Consistency criterion">Consistency</a></li> <li><a href="/wiki/Tactical_voting#Burying" class="mw-redirect" title="Tactical voting">Invulnerability to burying</a></li> <li><a href="/wiki/Later-no-harm_criterion" title="Later-no-harm criterion">Later-no-harm</a></li></ul> <p>Likewise, since the Schulze method is not a <a href="/wiki/Dictatorship_mechanism" title="Dictatorship mechanism">dictatorship</a> and is a <a href="/wiki/Ranked_voting" title="Ranked voting">ranked voting</a> system (not <a href="/wiki/Rated_voting" title="Rated voting">rated</a>), <a href="/wiki/Arrow%27s_Theorem" class="mw-redirect" title="Arrow's Theorem">Arrow's Theorem</a> implies it fails <a href="/wiki/Independence_of_irrelevant_alternatives" title="Independence of irrelevant alternatives">independence of irrelevant alternatives</a>, meaning it can be vulnerable to the <a href="/wiki/Spoiler_effect" title="Spoiler effect">spoiler effect</a> in some rare circumstances. The Schulze method also fails <a href="/wiki/Peyton_Young" title="Peyton Young">Peyton Young</a>'s criterion of <a href="/wiki/Local_independence_of_irrelevant_alternatives" class="mw-redirect" title="Local independence of irrelevant alternatives">Local Independence of Irrelevant Alternatives</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Comparison_table">Comparison table</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Schulze_method&action=edit&section=10" title="Edit section: Comparison table"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The following table compares the Schulze method with other single-winner election methods: <style data-mw-deduplicate="TemplateStyles:r1245584064">@media screen{html.client-js .mw-parser-output .sort-under.sortable.wikitable th.headerSort,html.client-js .mw-parser-output .sort-under-right.sortable.wikitable th.headerSort,html.client-js 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.sort-under-right.sortable.wikitable th.headerSort,html.client-js .mw-parser-output .sort-under-right.sortable.wikitable th.unsortable,html.client-js .mw-parser-output .sort-under-center.sortable.wikitable th.headerSort,html.client-js .mw-parser-output .sort-under-center.sortable.wikitable th.unsortable{padding-bottom:1.6em}html.client-js body.skin-timeless .mw-parser-output .sort-under.sortable.wikitable th.headerSort,html.client-js body.skin-timeless .mw-parser-output .sort-under.sortable.wikitable th.unsortable,html.client-js body.skin-timeless .mw-parser-output .sort-under-right.sortable.wikitable th.headerSort,html.client-js body.skin-timeless .mw-parser-output .sort-under-right.sortable.wikitable th.unsortable,html.client-js body.skin-timeless .mw-parser-output .sort-under-center.sortable.wikitable th.headerSort,html.client-js body.skin-timeless .mw-parser-output .sort-under-center.sortable.wikitable th.unsortable{padding-bottom:1.8em}html.client-js .mw-parser-output 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.sticky-table-collapsible:not(.mw-collapsed) table,body.skin-vector-2022 .mw-parser-output .sticky-table-collapsible:not(.mw-collapsed) table{display:table}body.skin-minerva .mw-parser-output .sticky-table-collapsible:not(.mw-collapsed) table>caption{display:table-caption}}.mw-parser-output .sticky-table-collapsible:not(.mw-collapsed) .jquery-tablesorter>thead,.mw-parser-output .sticky-table-collapsible:not(.mw-collapsed) .mw-sticky-header>thead{top:0!important}.mw-parser-output .sticky-table-collapsible:not(.mw-collapsed) .jquery-tablesorter>tfoot,.mw-parser-output .sticky-table-collapsible:not(.mw-collapsed) .mw-sticky-header>tfoot{position:static;bottom:auto}}@media all{.mw-parser-output .sticky-table-collapsible.mw-collapsed .sticky-table-scroll{max-height:none!important;max-width:none!important}}</style><div class="sticky-table-collapsible mw-collapsible" data-expandtext="enable" data-collapsetext="disable"><div class="sticky-table-scroll"> <table class="wikitable sortable sort-under mw-collapsible sticky-table-row1 sticky-table-col1" style="text-align:center;"> <caption>Comparison of single-winner voting systems </caption> <tbody><tr> <th style="border-bottom:2px solid #a0a0a0;"><div style="margin-left:2em;text-align:right">Criterion</div><div style="margin-right:2em;text-align:left"><br /><br />Method</div> </th> <th style="border-bottom:2px solid #a0a0a0;"><a href="/wiki/Majority_winner_criterion" title="Majority winner criterion">Majority winner</a> </th> <th style="border-bottom:2px solid #a0a0a0;"><a href="/wiki/Majority_loser_criterion" title="Majority loser criterion">Majority loser</a> </th> <th style="border-bottom:2px solid #a0a0a0;"><a href="/wiki/Mutual_majority_criterion" title="Mutual majority criterion">Mutual majority</a> </th> <th style="border-bottom:2px solid #a0a0a0;"><a href="/wiki/Condorcet_winner" class="mw-redirect" title="Condorcet winner">Condorcet winner</a><wbr /><sup id="cite_ref-condorcet-iia-incompatibility_5-0" class="reference"><a href="#cite_note-condorcet-iia-incompatibility-5"><span class="cite-bracket">[</span>Tn 1<span class="cite-bracket">]</span></a></sup> </th> <th style="border-bottom:2px solid #a0a0a0;"><a href="/wiki/Condorcet_loser" class="mw-redirect" title="Condorcet loser">Condorcet loser</a> </th> <th style="border-bottom:2px solid #a0a0a0;"><a href="/wiki/Smith_criterion" class="mw-redirect" title="Smith criterion">Smith</a><wbr /><sup id="cite_ref-condorcet-iia-incompatibility_5-1" class="reference"><a href="#cite_note-condorcet-iia-incompatibility-5"><span class="cite-bracket">[</span>Tn 1<span class="cite-bracket">]</span></a></sup> </th> <th style="border-bottom:2px solid #a0a0a0;"><a href="/wiki/Independence_of_Smith-dominated_alternatives" title="Independence of Smith-dominated alternatives">Smith-IIA</a><wbr /><sup id="cite_ref-condorcet-iia-incompatibility_5-2" class="reference"><a href="#cite_note-condorcet-iia-incompatibility-5"><span class="cite-bracket">[</span>Tn 1<span class="cite-bracket">]</span></a></sup> </th> <th style="border-bottom:2px solid #a0a0a0;"><a href="/wiki/Independence_of_irrelevant_alternatives" title="Independence of irrelevant alternatives">IIA</a>/<a href="/wiki/Independence_of_irrelevant_alternatives#Local_independence" title="Independence of irrelevant alternatives">LIIA</a><wbr /><sup id="cite_ref-condorcet-iia-incompatibility_5-3" class="reference"><a href="#cite_note-condorcet-iia-incompatibility-5"><span class="cite-bracket">[</span>Tn 1<span class="cite-bracket">]</span></a></sup> </th> <th style="border-bottom:2px solid #a0a0a0;"><a href="/wiki/Independence_of_clones" class="mw-redirect" title="Independence of clones">Cloneproof</a> </th> <th style="border-bottom:2px solid #a0a0a0;"><a href="/wiki/Monotonicity_criterion" class="mw-redirect" title="Monotonicity criterion">Monotone</a> </th> <th style="border-bottom:2px solid #a0a0a0;"><a href="/wiki/Participation_criterion" class="mw-redirect" title="Participation criterion">Participation</a> </th> <th style="border-bottom:2px solid #a0a0a0;"><a href="/wiki/Later-no-harm" class="mw-redirect" title="Later-no-harm">Later-no-harm</a><wbr /><sup id="cite_ref-condorcet-iia-incompatibility_5-4" class="reference"><a href="#cite_note-condorcet-iia-incompatibility-5"><span class="cite-bracket">[</span>Tn 1<span class="cite-bracket">]</span></a></sup> </th> <th style="border-bottom:2px solid #a0a0a0;"><a href="/wiki/Later-no-help" class="mw-redirect" title="Later-no-help">Later-no-help</a><wbr /><sup id="cite_ref-condorcet-iia-incompatibility_5-5" class="reference"><a href="#cite_note-condorcet-iia-incompatibility-5"><span class="cite-bracket">[</span>Tn 1<span class="cite-bracket">]</span></a></sup> </th> <th style="border-bottom:2px solid #a0a0a0;"><a href="/wiki/No_favorite_betrayal" class="mw-redirect" title="No favorite betrayal">No favorite betrayal</a><wbr /><sup id="cite_ref-condorcet-iia-incompatibility_5-6" class="reference"><a href="#cite_note-condorcet-iia-incompatibility-5"><span class="cite-bracket">[</span>Tn 1<span class="cite-bracket">]</span></a></sup> </th> <th style="border-bottom:2px solid #a0a0a0; border-left:2px solid #a0a0a0;">Ballot <p>type </p> </th></tr> <tr> <th style="font-weight:bold"><a href="/wiki/First-past-the-post_voting" title="First-past-the-post voting">First-past-the-post voting</a> </th> <td style="vertical-align:middle; background-color:#9EFF9E;">Yes </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#9EFF9E;">Yes </td> <td style="vertical-align:middle; background-color:#9EFF9E;">Yes </td> <td style="vertical-align:middle; background-color:#9EFF9E;">Yes </td> <td style="vertical-align:middle; background-color:#9EFF9E;">Yes </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td data-sort-value="6" style="border-left:2px solid #a0a0a0;">Single mark </td></tr> <tr> <th style="font-weight:bold"><a href="/wiki/Anti-plurality_voting" title="Anti-plurality voting">Anti-plurality</a> </th> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#9EFF9E;">Yes </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#9EFF9E;">Yes </td> <td style="vertical-align:middle; background-color:#9EFF9E;">Yes </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#9EFF9E;">Yes </td> <td data-sort-value="6" style="border-left:2px solid #a0a0a0;">Single mark </td></tr> <tr> <th><a href="/wiki/Two-round_system" title="Two-round system">Two round system</a> </th> <td style="vertical-align:middle; background-color:#9EFF9E;">Yes </td> <td style="vertical-align:middle; background-color:#9EFF9E;">Yes </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#9EFF9E;">Yes </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#9EFF9E;">Yes </td> <td style="vertical-align:middle; background-color:#9EFF9E;">Yes </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td data-sort-value="6" style="border-left:2px solid #a0a0a0;">Single mark </td></tr> <tr> <th style="font-weight:bold"><a href="/wiki/Instant-runoff_voting" title="Instant-runoff voting">Instant-runoff</a> </th> <td style="vertical-align:middle; background-color:#9EFF9E;">Yes </td> <td style="vertical-align:middle; background-color:#9EFF9E;">Yes </td> <td style="vertical-align:middle; background-color:#9EFF9E;">Yes </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#9EFF9E;">Yes </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#9EFF9E;">Yes </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#9EFF9E;">Yes </td> <td style="vertical-align:middle; background-color:#9EFF9E;">Yes </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td data-sort-value="2" style="border-left:2px solid #a0a0a0;">Ranking </td></tr> <tr> <th style="font-weight:bold"><a href="/wiki/Coombs%27_method" title="Coombs' method">Coombs</a> </th> <td style="vertical-align:middle; background-color:#9EFF9E;">Yes </td> <td style="vertical-align:middle; background-color:#9EFF9E;">Yes </td> <td style="vertical-align:middle; background-color:#9EFF9E;">Yes </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#9EFF9E;">Yes </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#9EFF9E;">Yes </td> <td data-sort-value="2" style="border-left:2px solid #a0a0a0;">Ranking </td></tr> <tr> <th style="font-weight:bold"><a href="/wiki/Nanson%27s_method" title="Nanson's method">Nanson</a> </th> <td style="vertical-align:middle; background-color:#9EFF9E;">Yes </td> <td style="vertical-align:middle; background-color:#9EFF9E;">Yes </td> <td style="vertical-align:middle; background-color:#9EFF9E;">Yes </td> <td style="vertical-align:middle; background-color:#9EFF9E;">Yes </td> <td style="vertical-align:middle; background-color:#9EFF9E;">Yes </td> <td style="vertical-align:middle; background-color:#9EFF9E;">Yes </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td data-sort-value="2" style="border-left:2px solid #a0a0a0;">Ranking </td></tr> <tr> <th style="font-weight:bold"><a href="/wiki/Baldwin%27s_method" class="mw-redirect" title="Baldwin's method">Baldwin</a> </th> <td style="vertical-align:middle; background-color:#9EFF9E;">Yes </td> <td style="vertical-align:middle; background-color:#9EFF9E;">Yes </td> <td style="vertical-align:middle; background-color:#9EFF9E;">Yes </td> <td style="vertical-align:middle; background-color:#9EFF9E;">Yes </td> <td style="vertical-align:middle; background-color:#9EFF9E;">Yes </td> <td style="vertical-align:middle; background-color:#9EFF9E;">Yes </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td data-sort-value="2" style="border-left:2px solid #a0a0a0;">Ranking </td></tr> <tr> <th style="font-weight:bold"><a href="/wiki/Tideman_alternative_method" title="Tideman alternative method">Tideman alternative</a> </th> <td style="vertical-align:middle; background-color:#9EFF9E;">Yes </td> <td style="vertical-align:middle; background-color:#9EFF9E;">Yes </td> <td style="vertical-align:middle; background-color:#9EFF9E;">Yes </td> <td style="vertical-align:middle; background-color:#9EFF9E;">Yes </td> <td style="vertical-align:middle; background-color:#9EFF9E;">Yes </td> <td style="vertical-align:middle; background-color:#9EFF9E;">Yes </td> <td style="vertical-align:middle; background-color:#9EFF9E;">Yes </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#9EFF9E;">Yes </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td data-sort-value="2" style="border-left:2px solid #a0a0a0;">Ranking </td></tr> <tr> <th style="font-weight:bold"><a href="/wiki/Minimax_Condorcet" class="mw-redirect" title="Minimax Condorcet">Minimax</a> </th> <td style="vertical-align:middle; background-color:#9EFF9E;">Yes </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#9EFF9E;">Yes<wbr /><sup id="cite_ref-MinimaxVarient_6-0" class="reference"><a href="#cite_note-MinimaxVarient-6"><span class="cite-bracket">[</span>Tn 2<span class="cite-bracket">]</span></a></sup> </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#9EFF9E;">Yes </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No<wbr /><sup id="cite_ref-MinimaxVarient_6-1" class="reference"><a href="#cite_note-MinimaxVarient-6"><span class="cite-bracket">[</span>Tn 2<span class="cite-bracket">]</span></a></sup> </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td data-sort-value="2" style="border-left:2px solid #a0a0a0;">Ranking </td></tr> <tr> <th style="font-weight:bold"><a href="/wiki/Copeland%27s_method" title="Copeland's method">Copeland</a> </th> <td style="vertical-align:middle; background-color:#9EFF9E;">Yes </td> <td style="vertical-align:middle; background-color:#9EFF9E;">Yes </td> <td style="vertical-align:middle; background-color:#9EFF9E;">Yes </td> <td style="vertical-align:middle; background-color:#9EFF9E;">Yes </td> <td style="vertical-align:middle; background-color:#9EFF9E;">Yes </td> <td style="vertical-align:middle; background-color:#9EFF9E;">Yes </td> <td style="vertical-align:middle; background-color:#9EFF9E;">Yes </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#9EFF9E;">Yes </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td data-sort-value="2" style="border-left:2px solid #a0a0a0;">Ranking </td></tr> <tr> <th style="font-weight:bold"><a href="/wiki/Black%27s_method" title="Black's method">Black</a> </th> <td style="vertical-align:middle; background-color:#9EFF9E;">Yes </td> <td style="vertical-align:middle; background-color:#9EFF9E;">Yes </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#9EFF9E;">Yes </td> <td style="vertical-align:middle; background-color:#9EFF9E;">Yes </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#9EFF9E;">Yes </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td data-sort-value="2" style="border-left:2px solid #a0a0a0;">Ranking </td></tr> <tr> <th style="font-weight:bold"><a href="/wiki/Kemeny-Young_method" class="mw-redirect" title="Kemeny-Young method">Kemeny–Young</a> </th> <td style="vertical-align:middle; background-color:#9EFF9E;">Yes </td> <td style="vertical-align:middle; background-color:#9EFF9E;">Yes </td> <td style="vertical-align:middle; background-color:#9EFF9E;">Yes </td> <td style="vertical-align:middle; background-color:#9EFF9E;">Yes </td> <td style="vertical-align:middle; background-color:#9EFF9E;">Yes </td> <td style="vertical-align:middle; background-color:#9EFF9E;">Yes </td> <td style="vertical-align:middle; background-color:#9EFF9E;">Yes </td> <td style="vertical-align:middle; background-color:#FFC7C7;">LIIA Only </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#9EFF9E;">Yes </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td data-sort-value="2" style="border-left:2px solid #a0a0a0;">Ranking </td></tr> <tr> <th style="font-weight:bold"><a href="/wiki/Ranked_pairs" title="Ranked pairs">Ranked pairs</a> </th> <td style="vertical-align:middle; background-color:#9EFF9E;">Yes </td> <td style="vertical-align:middle; background-color:#9EFF9E;">Yes </td> <td style="vertical-align:middle; background-color:#9EFF9E;">Yes </td> <td style="vertical-align:middle; background-color:#9EFF9E;">Yes </td> <td style="vertical-align:middle; background-color:#9EFF9E;">Yes </td> <td style="vertical-align:middle; background-color:#9EFF9E;">Yes </td> <td style="vertical-align:middle; background-color:#9EFF9E;">Yes </td> <td style="vertical-align:middle; background-color:#FFC7C7;">LIIA Only </td> <td style="vertical-align:middle; background-color:#9EFF9E;">Yes </td> <td style="vertical-align:middle; background-color:#9EFF9E;">Yes </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No<wbr /><sup id="cite_ref-semipc_7-0" class="reference"><a href="#cite_note-semipc-7"><span class="cite-bracket">[</span>Tn 3<span class="cite-bracket">]</span></a></sup> </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td data-sort-value="2" style="border-left:2px solid #a0a0a0;">Ranking </td></tr> <tr> <th style="font-weight:bold"><a class="mw-selflink selflink">Schulze</a> </th> <td style="vertical-align:middle; background-color:#9EFF9E;">Yes </td> <td style="vertical-align:middle; background-color:#9EFF9E;">Yes </td> <td style="vertical-align:middle; background-color:#9EFF9E;">Yes </td> <td style="vertical-align:middle; background-color:#9EFF9E;">Yes </td> <td style="vertical-align:middle; background-color:#9EFF9E;">Yes </td> <td style="vertical-align:middle; background-color:#9EFF9E;">Yes </td> <td style="vertical-align:middle; background-color:#9EFF9E;">Yes </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#9EFF9E;">Yes </td> <td style="vertical-align:middle; background-color:#9EFF9E;">Yes </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No<wbr /><sup id="cite_ref-semipc_7-1" class="reference"><a href="#cite_note-semipc-7"><span class="cite-bracket">[</span>Tn 3<span class="cite-bracket">]</span></a></sup> </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td data-sort-value="2" style="border-left:2px solid #a0a0a0;">Ranking </td></tr> <tr> <th style="font-weight:bold"><a href="/wiki/Borda_count" title="Borda count">Borda</a> </th> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#9EFF9E;">Yes </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#9EFF9E;">Yes </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#9EFF9E;">Yes </td> <td style="vertical-align:middle; background-color:#9EFF9E;">Yes </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#9EFF9E;">Yes </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td data-sort-value="2" style="border-left:2px solid #a0a0a0;">Ranking </td></tr> <tr> <th style="font-weight:bold"><a href="/wiki/Bucklin_voting" title="Bucklin voting">Bucklin</a> </th> <td style="vertical-align:middle; background-color:#9EFF9E;">Yes </td> <td style="vertical-align:middle; background-color:#9EFF9E;">Yes </td> <td style="vertical-align:middle; background-color:#9EFF9E;">Yes </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#9EFF9E;">Yes </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#9EFF9E;">Yes </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td data-sort-value="2" style="border-left:2px solid #a0a0a0;">Ranking </td></tr> <tr> <th style="font-weight:bold"><a href="/wiki/Approval_voting" title="Approval voting">Approval</a> </th> <td style="vertical-align:middle; background-color:#9EFF9E;">Yes </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#9EFF9E;">Yes<wbr /><sup id="cite_ref-IIA_rating_methods_8-0" class="reference"><a href="#cite_note-IIA_rating_methods-8"><span class="cite-bracket">[</span>Tn 4<span class="cite-bracket">]</span></a></sup> </td> <td style="vertical-align:middle; background-color:#9EFF9E;">Yes </td> <td style="vertical-align:middle; background-color:#9EFF9E;">Yes </td> <td style="vertical-align:middle; background-color:#9EFF9E;">Yes </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#9EFF9E;">Yes </td> <td style="vertical-align:middle; background-color:#9EFF9E;">Yes </td> <td data-sort-value="2" style="border-left:2px solid #a0a0a0;">Approvals </td></tr> <tr> <th style="font-weight:bold"><a href="/wiki/Majority_judgment" title="Majority judgment">Majority Judgement</a> </th> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No<wbr /><sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>Tn 5<span class="cite-bracket">]</span></a></sup> </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No<wbr /><sup id="cite_ref-mjmmc_10-0" class="reference"><a href="#cite_note-mjmmc-10"><span class="cite-bracket">[</span>Tn 6<span class="cite-bracket">]</span></a></sup> </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#9EFF9E;">Yes<wbr /><sup id="cite_ref-IIA_rating_methods_8-1" class="reference"><a href="#cite_note-IIA_rating_methods-8"><span class="cite-bracket">[</span>Tn 4<span class="cite-bracket">]</span></a></sup> </td> <td style="vertical-align:middle; background-color:#9EFF9E;">Yes </td> <td style="vertical-align:middle; background-color:#9EFF9E;">Yes </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No<wbr /><sup id="cite_ref-semipc_7-2" class="reference"><a href="#cite_note-semipc-7"><span class="cite-bracket">[</span>Tn 3<span class="cite-bracket">]</span></a></sup> </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#9EFF9E;">Yes </td> <td style="vertical-align:middle; background-color:#9EFF9E;">Yes </td> <td data-sort-value="1" style="border-left:2px solid #a0a0a0;">Scores </td></tr> <tr> <th style="font-weight:bold"><a href="/wiki/Score_voting" title="Score voting">Score</a> </th> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#9EFF9E;">Yes<wbr /><sup id="cite_ref-IIA_rating_methods_8-2" class="reference"><a href="#cite_note-IIA_rating_methods-8"><span class="cite-bracket">[</span>Tn 4<span class="cite-bracket">]</span></a></sup> </td> <td style="vertical-align:middle; background-color:#9EFF9E;">Yes </td> <td style="vertical-align:middle; background-color:#9EFF9E;">Yes </td> <td style="vertical-align:middle; background-color:#9EFF9E;">Yes </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#9EFF9E;">Yes </td> <td style="vertical-align:middle; background-color:#9EFF9E;">Yes </td> <td data-sort-value="1" style="border-left:2px solid #a0a0a0;">Scores </td></tr> <tr> <th style="font-weight:bold"><a href="/wiki/STAR_voting" title="STAR voting">STAR</a> </th> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#9EFF9E;">Yes </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#9EFF9E;">Yes </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#9EFF9E;">Yes </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td data-sort-value="1" style="border-left:2px solid #a0a0a0;">Scores </td></tr> <tr> <th style="font-weight:bold"><a href="/wiki/Random_ballot" title="Random ballot">Random ballot</a><wbr /><sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>Tn 7<span class="cite-bracket">]</span></a></sup> </th> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#9EFF9E;">Yes </td> <td style="vertical-align:middle; background-color:#9EFF9E;">Yes </td> <td style="vertical-align:middle; background-color:#9EFF9E;">Yes </td> <td style="vertical-align:middle; background-color:#9EFF9E;">Yes </td> <td style="vertical-align:middle; background-color:#9EFF9E;">Yes </td> <td style="vertical-align:middle; background-color:#9EFF9E;">Yes </td> <td style="vertical-align:middle; background-color:#9EFF9E;">Yes </td> <td data-sort-value="6" style="border-left:2px solid #a0a0a0;">Single mark </td></tr> <tr> <th style="font-weight:bold"><a href="/wiki/Sortition" title="Sortition">Sortition</a><wbr /><sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>Tn 8<span class="cite-bracket">]</span></a></sup> </th> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#9EFF9E;">Yes </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td style="vertical-align:middle; background-color:#9EFF9E;">Yes </td> <td style="vertical-align:middle; background-color:#9EFF9E;">Yes </td> <td style="vertical-align:middle; background-color:#9EFF9E;">Yes </td> <td style="vertical-align:middle; background-color:#9EFF9E;">Yes </td> <td style="vertical-align:middle; background-color:#9EFF9E;">Yes </td> <td data-sort-value="6" style="border-left:2px solid #a0a0a0;">None </td></tr> <tr class="sortbottom"> <th>Table Notes </th> <td colspan="16" style="text-align: left;"> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-condorcet-iia-incompatibility-5"><span class="mw-cite-backlink">^ <a href="#cite_ref-condorcet-iia-incompatibility_5-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-condorcet-iia-incompatibility_5-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-condorcet-iia-incompatibility_5-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-condorcet-iia-incompatibility_5-3"><sup><i><b>d</b></i></sup></a> <a href="#cite_ref-condorcet-iia-incompatibility_5-4"><sup><i><b>e</b></i></sup></a> <a href="#cite_ref-condorcet-iia-incompatibility_5-5"><sup><i><b>f</b></i></sup></a> <a href="#cite_ref-condorcet-iia-incompatibility_5-6"><sup><i><b>g</b></i></sup></a></span> <span class="reference-text"><a href="/wiki/Condorcet_criterion" class="mw-redirect" title="Condorcet criterion">Condorcet's criterion</a> is incompatible with the <a href="/wiki/Consistency_criterion" class="mw-redirect" title="Consistency criterion">consistency</a>, <a href="/wiki/Participation_criterion" class="mw-redirect" title="Participation criterion">participation</a>, <a href="/wiki/Later-no-harm" class="mw-redirect" title="Later-no-harm">later-no-harm</a>, <a href="/wiki/Later-no-help_criterion" title="Later-no-help criterion">later-no-help</a>, and <a href="/wiki/Sincere_favorite_criterion" title="Sincere favorite criterion">sincere favorite</a> criteria.</span> </li> <li id="cite_note-MinimaxVarient-6"><span class="mw-cite-backlink">^ <a href="#cite_ref-MinimaxVarient_6-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-MinimaxVarient_6-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text">A variant of Minimax that counts only pairwise opposition, not opposition minus support, fails the Condorcet criterion and meets later-no-harm.</span> </li> <li id="cite_note-semipc-7"><span class="mw-cite-backlink">^ <a href="#cite_ref-semipc_7-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-semipc_7-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-semipc_7-2"><sup><i><b>c</b></i></sup></a></span> <span class="reference-text">In Highest median, Ranked Pairs, and Schulze voting, there is always a regret-free, semi-honest ballot for any voter, holding all other ballots constant and assuming they know enough about how others will vote. Under such circumstances, there is always at least one way for a voter to participate without grading any less-preferred candidate above any more-preferred one.</span> </li> <li id="cite_note-IIA_rating_methods-8"><span class="mw-cite-backlink">^ <a href="#cite_ref-IIA_rating_methods_8-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-IIA_rating_methods_8-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-IIA_rating_methods_8-2"><sup><i><b>c</b></i></sup></a></span> <span class="reference-text">Approval voting, score voting, and majority judgment satisfy IIA if it is assumed that voters rate candidates independently using their own <a href="/wiki/Approval_voting#Dichotomous_cutoff" title="Approval voting">absolute scale</a>. For this to hold, in some elections, some voters must use less than their full voting power despite having meaningful preferences among viable candidates.</span> </li> <li id="cite_note-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-9">^</a></b></span> <span class="reference-text">Majority Judgment may elect a candidate uniquely least-preferred by over half of voters, but it never elects the candidate uniquely bottom-rated by over half of voters.</span> </li> <li id="cite_note-mjmmc-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-mjmmc_10-0">^</a></b></span> <span class="reference-text">Majority Judgment fails the mutual majority criterion, but satisfies the criterion if the majority ranks the mutually favored set above a given absolute grade and all others below that grade.</span> </li> <li id="cite_note-11"><span class="mw-cite-backlink"><b><a href="#cite_ref-11">^</a></b></span> <span class="reference-text">A randomly chosen ballot determines winner. This and closely related methods are of mathematical interest and included here to demonstrate that even unreasonable methods can pass voting method criteria.</span> </li> <li id="cite_note-12"><span class="mw-cite-backlink"><b><a href="#cite_ref-12">^</a></b></span> <span class="reference-text">Where a winner is randomly chosen from the candidates, sortition is included to demonstrate that even non-voting methods can pass some criteria.</span> </li> </ol></div> </td></tr></tbody></table> </div></div> <p><br /> </p><p><br /> </p> <div class="mw-heading mw-heading3"><h3 id="Difference_from_ranked_pairs">Difference from ranked pairs</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Schulze_method&action=edit&section=11" title="Edit section: Difference from ranked pairs"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/Ranked_pairs" title="Ranked pairs">Ranked pairs</a> is another <a href="/wiki/Condorcet_method" title="Condorcet method">Condorcet method</a> which is very similar to Schulze's rule, and typically produces the same outcome. There are slight differences, however. The main difference between the beatpath method and <a href="/wiki/Ranked_pairs" title="Ranked pairs">ranked pairs</a> is that Schulze retains behavior closer to <a href="/wiki/Minimax_Condorcet_method" title="Minimax Condorcet method">minimax</a>. Say that the <a href="/wiki/Minimax_Condorcet_method" title="Minimax Condorcet method">minimax</a> score of a set <b>X</b> of candidates is the strength of the strongest pairwise win of a candidate A ∉ <b>X</b> against a candidate B ∈ <b>X</b>. Then the Schulze method, but not ranked pairs, guarantees the winner is always a candidate of the set with minimum minimax score.<sup id="cite_ref-schulze20113_2-3" class="reference"><a href="#cite_note-schulze20113-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: §4.8">: §4.8 </span></sup> This is the sense in which the Schulze method minimizes the largest majority that has to be reversed when determining the winner. </p><p>On the other hand, Ranked Pairs minimizes the largest majority that has to be reversed to determine the order of finish.<sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> In other words, when Ranked Pairs and the Schulze method produce different orders of finish, for the majorities on which the two orders of finish disagree, the Schulze order reverses a larger majority than the Ranked Pairs order. </p> <div class="mw-heading mw-heading2"><h2 id="History">History</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Schulze_method&action=edit&section=12" title="Edit section: History"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The Schulze method was developed by Markus Schulze in 1997. It was first discussed in public mailing lists in 1997–1998<sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> and in 2000.<sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> In 2011, Schulze published the method in the academic journal <i><a href="/wiki/Social_Choice_and_Welfare" title="Social Choice and Welfare">Social Choice and Welfare</a></i>.<sup id="cite_ref-schulze20113_2-4" class="reference"><a href="#cite_note-schulze20113-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Usage">Usage</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Schulze_method&action=edit&section=13" title="Edit section: Usage"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Voting2.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/b/b6/Voting2.png" decoding="async" width="179" height="272" class="mw-file-element" data-file-width="179" data-file-height="272" /></a><figcaption>Sample ballot for <a href="/wiki/Wikimedia_Foundation" title="Wikimedia Foundation">Wikimedia's Board of Trustees</a> elections</figcaption></figure> <div class="mw-heading mw-heading3"><h3 id="Government">Government</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Schulze_method&action=edit&section=14" title="Edit section: Government"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The Schulze method is used by the city of <a href="/wiki/Silla,_Valencia" class="mw-redirect" title="Silla, Valencia">Silla</a> for all referendums.<sup id="cite_ref-16" class="reference"><a href="#cite_note-16"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-17" class="reference"><a href="#cite_note-17"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> It is also used by the cities of <a href="/wiki/Turin" title="Turin">Turin</a> and <a href="/wiki/San_Don%C3%A0_di_Piave" title="San Donà di Piave">San Donà di Piave</a> and by the <a href="/wiki/London_Borough_of_Southwark" title="London Borough of Southwark">London Borough of Southwark</a> through their use of the WeGovNow platform, which in turn uses the <a href="/wiki/LiquidFeedback" title="LiquidFeedback">LiquidFeedback</a> decision tool.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (September 2023)">citation needed</span></a></i>]</sup> </p> <div class="mw-heading mw-heading3"><h3 id="Political_parties">Political parties</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Schulze_method&action=edit&section=15" title="Edit section: Political parties"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Schulze was adopted by the <a href="/wiki/Pirate_Party_of_Sweden" class="mw-redirect" title="Pirate Party of Sweden">Pirate Party of Sweden</a> (2009),<sup id="cite_ref-PiratePartySweden2_18-0" class="reference"><a href="#cite_note-PiratePartySweden2-18"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> and the <a href="/wiki/Pirate_Party_Germany" title="Pirate Party Germany">Pirate Party of Germany</a> (2010).<sup id="cite_ref-PiratePartyGermany2_19-0" class="reference"><a href="#cite_note-PiratePartyGermany2-19"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> The <a href="/wiki/Boise,_Idaho" title="Boise, Idaho">Boise, Idaho</a> chapter of the <a href="/wiki/Democratic_Socialists_of_America" title="Democratic Socialists of America">Democratic Socialists of America</a> in February chose this method for their first special election held in March 2018.<sup id="cite_ref-Boise_DSA2_20-0" class="reference"><a href="#cite_note-Boise_DSA2-20"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> </p> <ul><li><a href="/wiki/Five_Star_Movement" title="Five Star Movement">Five Star Movement</a> of <a href="/wiki/Campobasso" title="Campobasso">Campobasso</a>,<sup id="cite_ref-21" class="reference"><a href="#cite_note-21"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Fondi" title="Fondi">Fondi</a>,<sup id="cite_ref-22" class="reference"><a href="#cite_note-22"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Monte_Compatri" title="Monte Compatri">Monte Compatri</a>,<sup id="cite_ref-23" class="reference"><a href="#cite_note-23"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Montemurlo" title="Montemurlo">Montemurlo</a>,<sup id="cite_ref-24" class="reference"><a href="#cite_note-24"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Pescara" title="Pescara">Pescara</a>,<sup id="cite_ref-25" class="reference"><a href="#cite_note-25"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup> and <a href="/wiki/San_Cesareo" title="San Cesareo">San Cesareo</a><sup id="cite_ref-26" class="reference"><a href="#cite_note-26"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup></li> <li><a href="/wiki/Pirate_Party" title="Pirate Party">Pirate Parties</a> of <a href="/wiki/Pirate_Party_Australia" title="Pirate Party Australia">Australia</a>,<sup id="cite_ref-27" class="reference"><a href="#cite_note-27"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Pirate_Party_of_Austria" title="Pirate Party of Austria">Austria</a>,<sup id="cite_ref-28" class="reference"><a href="#cite_note-28"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Pirate_Party_(Belgium)" title="Pirate Party (Belgium)">Belgium</a>,<sup id="cite_ref-29" class="reference"><a href="#cite_note-29"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Pirate_Party_of_Brazil" title="Pirate Party of Brazil">Brazil</a>, <a href="/wiki/Pirate_Party_Germany" title="Pirate Party Germany">Germany</a>,<sup id="cite_ref-PiratePartyGermany2_19-1" class="reference"><a href="#cite_note-PiratePartyGermany2-19"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Pirate_Party_(Iceland)" title="Pirate Party (Iceland)">Iceland</a>,<sup id="cite_ref-30" class="reference"><a href="#cite_note-30"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Pirate_Party_(Italy)" class="mw-redirect" title="Pirate Party (Italy)">Italy</a>,<sup id="cite_ref-31" class="reference"><a href="#cite_note-31"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Pirate_Party_of_the_Netherlands" class="mw-redirect" title="Pirate Party of the Netherlands">the Netherlands</a>,<sup id="cite_ref-32" class="reference"><a href="#cite_note-32"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Pirate_Party_of_Sweden" class="mw-redirect" title="Pirate Party of Sweden">Sweden</a>,<sup id="cite_ref-PiratePartySweden2_18-1" class="reference"><a href="#cite_note-PiratePartySweden2-18"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Pirate_Party_Switzerland" title="Pirate Party Switzerland">Switzerland</a>,<sup id="cite_ref-33" class="reference"><a href="#cite_note-33"><span class="cite-bracket">[</span>25<span class="cite-bracket">]</span></a></sup> and <a href="/wiki/United_States_Pirate_Party" title="United States Pirate Party">the United States</a><sup id="cite_ref-34" class="reference"><a href="#cite_note-34"><span class="cite-bracket">[</span>26<span class="cite-bracket">]</span></a></sup></li> <li>SustainableUnion<sup id="cite_ref-35" class="reference"><a href="#cite_note-35"><span class="cite-bracket">[</span>27<span class="cite-bracket">]</span></a></sup></li> <li><a href="/wiki/Volt_Europe" class="mw-redirect" title="Volt Europe">Volt Europe</a><sup id="cite_ref-36" class="reference"><a href="#cite_note-36"><span class="cite-bracket">[</span>28<span class="cite-bracket">]</span></a></sup></li></ul> <div class="mw-heading mw-heading3"><h3 id="Student_government_and_associations">Student government and associations</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Schulze_method&action=edit&section=16" title="Edit section: Student government and associations"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Association_des_%C3%89tats_G%C3%A9n%C3%A9raux_des_%C3%89tudiants_de_l%27Europe" title="Association des États Généraux des Étudiants de l'Europe">AEGEE – European Students' Forum</a><sup id="cite_ref-37" class="reference"><a href="#cite_note-37"><span class="cite-bracket">[</span>29<span class="cite-bracket">]</span></a></sup></li> <li>Club der Ehemaligen der Deutschen SchülerAkademien e. V.<sup id="cite_ref-38" class="reference"><a href="#cite_note-38"><span class="cite-bracket">[</span>30<span class="cite-bracket">]</span></a></sup></li> <li>Associated Student Government at <a href="/wiki/%C3%89cole_normale_sup%C3%A9rieure_(Paris)" title="École normale supérieure (Paris)">École normale supérieure de Paris</a><sup id="cite_ref-39" class="reference"><a href="#cite_note-39"><span class="cite-bracket">[</span>31<span class="cite-bracket">]</span></a></sup></li> <li>Flemish Society of Engineering Students Leuven<sup id="cite_ref-40" class="reference"><a href="#cite_note-40"><span class="cite-bracket">[</span>32<span class="cite-bracket">]</span></a></sup></li> <li>Graduate Student Organization at the State University of New York: Computer Science (GSOCS)<sup id="cite_ref-41" class="reference"><a href="#cite_note-41"><span class="cite-bracket">[</span>33<span class="cite-bracket">]</span></a></sup></li> <li><a href="/wiki/Hillegass_Parker_House" class="mw-redirect" title="Hillegass Parker House">Hillegass Parker House</a><sup id="cite_ref-42" class="reference"><a href="#cite_note-42"><span class="cite-bracket">[</span>34<span class="cite-bracket">]</span></a></sup></li> <li><a href="/wiki/Kingman_Hall" title="Kingman Hall">Kingman Hall</a><sup id="cite_ref-43" class="reference"><a href="#cite_note-43"><span class="cite-bracket">[</span>35<span class="cite-bracket">]</span></a></sup></li> <li>Associated Students of <a href="/wiki/Minerva_University" title="Minerva University">Minerva Schools at KGI</a><sup id="cite_ref-44" class="reference"><a href="#cite_note-44"><span class="cite-bracket">[</span>36<span class="cite-bracket">]</span></a></sup></li> <li>Associated Student Government at <a href="/wiki/Northwestern_University" title="Northwestern University">Northwestern University</a><sup id="cite_ref-45" class="reference"><a href="#cite_note-45"><span class="cite-bracket">[</span>37<span class="cite-bracket">]</span></a></sup></li> <li>Associated Student Government at <a href="/wiki/University_of_Freiburg" title="University of Freiburg">University of Freiburg</a><sup id="cite_ref-46" class="reference"><a href="#cite_note-46"><span class="cite-bracket">[</span>38<span class="cite-bracket">]</span></a></sup></li> <li>Associated Student Government at the Computer Sciences Department of the <a href="/wiki/University_of_Kaiserslautern" class="mw-redirect" title="University of Kaiserslautern">University of Kaiserslautern</a><sup id="cite_ref-47" class="reference"><a href="#cite_note-47"><span class="cite-bracket">[</span>39<span class="cite-bracket">]</span></a></sup></li></ul> <div class="mw-heading mw-heading3"><h3 id="Organizations">Organizations</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Schulze_method&action=edit&section=17" title="Edit section: Organizations"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>It is used by the <a href="/wiki/Institute_of_Electrical_and_Electronics_Engineers" title="Institute of Electrical and Electronics Engineers">Institute of Electrical and Electronics Engineers</a>, by the <a href="/wiki/Association_for_Computing_Machinery" title="Association for Computing Machinery">Association for Computing Machinery</a>, and by <a href="/wiki/USENIX" title="USENIX">USENIX</a><sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (October 2024)">citation needed</span></a></i>]</sup> through their use of the HotCRP decision tool.<sup class="noprint Inline-Template" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Manual_of_Style#Technical_language" title="Wikipedia:Manual of Style"><span title="The material near this tag may be using jargon that limits the article's accessibility. (October 2024)">jargon</span></a></i>]</sup> </p><p>Organizations which currently use the Schulze method include: </p> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1184024115"><div class="div-col" style="column-width: 30em;"> <ul><li><a href="/wiki/Annodex" title="Annodex">Annodex Association</a><sup id="cite_ref-48" class="reference"><a href="#cite_note-48"><span class="cite-bracket">[</span>40<span class="cite-bracket">]</span></a></sup></li> <li><a href="/w/index.php?title=Berufsverband_der_Kinder-_und_Jugend%C3%A4rzte&action=edit&redlink=1" class="new" title="Berufsverband der Kinder- und Jugendärzte (page does not exist)">Berufsverband der Kinder- und Jugendärzte</a><span class="noprint" style="font-size:85%; font-style: normal;"> [<a href="https://de.wikipedia.org/wiki/Berufsverband_der_Kinder-_und_Jugend%C3%A4rzte" class="extiw" title="de:Berufsverband der Kinder- und Jugendärzte">de</a>]</span> (BVKJ)<sup id="cite_ref-49" class="reference"><a href="#cite_note-49"><span class="cite-bracket">[</span>41<span class="cite-bracket">]</span></a></sup></li> <li><a href="/wiki/BoardGameGeek" title="BoardGameGeek">BoardGameGeek</a><sup id="cite_ref-50" class="reference"><a href="#cite_note-50"><span class="cite-bracket">[</span>42<span class="cite-bracket">]</span></a></sup></li> <li><a href="/wiki/Cloud_Foundry" title="Cloud Foundry">Cloud Foundry Foundation</a><sup id="cite_ref-51" class="reference"><a href="#cite_note-51"><span class="cite-bracket">[</span>43<span class="cite-bracket">]</span></a></sup></li> <li>County Highpointers<sup id="cite_ref-52" class="reference"><a href="#cite_note-52"><span class="cite-bracket">[</span>44<span class="cite-bracket">]</span></a></sup></li> <li><a href="/wiki/Dapr" title="Dapr">Dapr</a><sup id="cite_ref-53" class="reference"><a href="#cite_note-53"><span class="cite-bracket">[</span>45<span class="cite-bracket">]</span></a></sup></li> <li><a href="/wiki/Debian" title="Debian">Debian</a><sup id="cite_ref-Debian_54-0" class="reference"><a href="#cite_note-Debian-54"><span class="cite-bracket">[</span>46<span class="cite-bracket">]</span></a></sup></li> <li><a href="/wiki/EuroBillTracker" title="EuroBillTracker">EuroBillTracker</a></li> <li><a href="/wiki/European_Democratic_Education_Community" title="European Democratic Education Community">European Democratic Education Community</a> (EUDEC)<sup id="cite_ref-55" class="reference"><a href="#cite_note-55"><span class="cite-bracket">[</span>47<span class="cite-bracket">]</span></a></sup></li> <li><a href="/wiki/FFmpeg" title="FFmpeg">FFmpeg</a><sup id="cite_ref-56" class="reference"><a href="#cite_note-56"><span class="cite-bracket">[</span>48<span class="cite-bracket">]</span></a></sup></li> <li><a href="/wiki/Free_Geek" title="Free Geek">Free Geek</a><sup id="cite_ref-57" class="reference"><a href="#cite_note-57"><span class="cite-bracket">[</span>49<span class="cite-bracket">]</span></a></sup></li> <li>Free Hardware Foundation of Italy</li> <li><a href="/wiki/Gentoo_Linux" title="Gentoo Linux">Gentoo Foundation</a><sup id="cite_ref-Gentoo_58-0" class="reference"><a href="#cite_note-Gentoo-58"><span class="cite-bracket">[</span>50<span class="cite-bracket">]</span></a></sup></li> <li><a href="/wiki/GNU_Privacy_Guard" title="GNU Privacy Guard">GNU Privacy Guard</a> (GnuPG)<sup id="cite_ref-59" class="reference"><a href="#cite_note-59"><span class="cite-bracket">[</span>51<span class="cite-bracket">]</span></a></sup></li> <li><a href="/wiki/Haskell_(programming_language)" class="mw-redirect" title="Haskell (programming language)">Haskell</a><sup id="cite_ref-60" class="reference"><a href="#cite_note-60"><span class="cite-bracket">[</span>52<span class="cite-bracket">]</span></a></sup></li> <li><a href="/wiki/Homebrew_(package_manager)" title="Homebrew (package manager)">Homebrew</a><sup id="cite_ref-61" class="reference"><a href="#cite_note-61"><span class="cite-bracket">[</span>53<span class="cite-bracket">]</span></a></sup></li> <li><a href="/wiki/ICANN" title="ICANN">Internet Corporation for Assigned Names and Numbers</a> (ICANN) (until 2023)<sup id="cite_ref-62" class="reference"><a href="#cite_note-62"><span class="cite-bracket">[</span>54<span class="cite-bracket">]</span></a></sup></li> <li>Kanawha Valley Scrabble Club<sup id="cite_ref-63" class="reference"><a href="#cite_note-63"><span class="cite-bracket">[</span>55<span class="cite-bracket">]</span></a></sup></li> <li><a href="/wiki/KDE" title="KDE">KDE e.V.</a><sup id="cite_ref-KDE_64-0" class="reference"><a href="#cite_note-KDE-64"><span class="cite-bracket">[</span>56<span class="cite-bracket">]</span></a></sup></li> <li><a href="/wiki/John_S._and_James_L._Knight_Foundation" class="mw-redirect" title="John S. and James L. Knight Foundation">Knight Foundation</a><sup id="cite_ref-65" class="reference"><a href="#cite_note-65"><span class="cite-bracket">[</span>57<span class="cite-bracket">]</span></a></sup></li> <li><a href="/wiki/Kubernetes" title="Kubernetes">Kubernetes</a><sup id="cite_ref-66" class="reference"><a href="#cite_note-66"><span class="cite-bracket">[</span>58<span class="cite-bracket">]</span></a></sup></li> <li><a href="/wiki/Kumoricon" title="Kumoricon">Kumoricon</a><sup id="cite_ref-67" class="reference"><a href="#cite_note-67"><span class="cite-bracket">[</span>59<span class="cite-bracket">]</span></a></sup></li> <li><a href="/wiki/League_of_Professional_System_Administrators" title="League of Professional System Administrators">League of Professional System Administrators</a> (LOPSA)<sup id="cite_ref-68" class="reference"><a href="#cite_note-68"><span class="cite-bracket">[</span>60<span class="cite-bracket">]</span></a></sup></li> <li><a href="/wiki/LiquidFeedback" title="LiquidFeedback">LiquidFeedback</a><sup id="cite_ref-PrinciplesOfLiquidFeedback_69-0" class="reference"><a href="#cite_note-PrinciplesOfLiquidFeedback-69"><span class="cite-bracket">[</span>61<span class="cite-bracket">]</span></a></sup></li> <li>Madisonium<sup id="cite_ref-70" class="reference"><a href="#cite_note-70"><span class="cite-bracket">[</span>62<span class="cite-bracket">]</span></a></sup></li> <li><a href="/wiki/Metalab" title="Metalab">Metalab</a><sup id="cite_ref-71" class="reference"><a href="#cite_note-71"><span class="cite-bracket">[</span>63<span class="cite-bracket">]</span></a></sup></li> <li><a href="/wiki/MTV" title="MTV">MTV</a><sup id="cite_ref-72" class="reference"><a href="#cite_note-72"><span class="cite-bracket">[</span>64<span class="cite-bracket">]</span></a></sup></li> <li><a href="/wiki/Neo_(keyboard_layout)" title="Neo (keyboard layout)">Neo</a><sup id="cite_ref-73" class="reference"><a href="#cite_note-73"><span class="cite-bracket">[</span>65<span class="cite-bracket">]</span></a></sup></li> <li><a href="/wiki/Noisebridge" title="Noisebridge">Noisebridge</a><sup id="cite_ref-74" class="reference"><a href="#cite_note-74"><span class="cite-bracket">[</span>66<span class="cite-bracket">]</span></a></sup></li> <li><a href="/wiki/OpenEmbedded" title="OpenEmbedded">OpenEmbedded</a><sup id="cite_ref-75" class="reference"><a href="#cite_note-75"><span class="cite-bracket">[</span>67<span class="cite-bracket">]</span></a></sup></li> <li><a href="/wiki/Open_Neural_Network_Exchange" title="Open Neural Network Exchange">Open Neural Network Exchange</a><sup id="cite_ref-76" class="reference"><a href="#cite_note-76"><span class="cite-bracket">[</span>68<span class="cite-bracket">]</span></a></sup></li> <li><a href="/wiki/OpenStack" title="OpenStack">OpenStack</a><sup id="cite_ref-77" class="reference"><a href="#cite_note-77"><span class="cite-bracket">[</span>69<span class="cite-bracket">]</span></a></sup></li> <li>OpenSwitch<sup id="cite_ref-78" class="reference"><a href="#cite_note-78"><span class="cite-bracket">[</span>70<span class="cite-bracket">]</span></a></sup></li> <li><a href="/wiki/RLLMUK" title="RLLMUK">RLLMUK</a><sup id="cite_ref-79" class="reference"><a href="#cite_note-79"><span class="cite-bracket">[</span>71<span class="cite-bracket">]</span></a></sup></li> <li><a href="/wiki/Squeak" title="Squeak">Squeak</a><sup id="cite_ref-80" class="reference"><a href="#cite_note-80"><span class="cite-bracket">[</span>72<span class="cite-bracket">]</span></a></sup></li> <li><a href="/wiki/Students_for_Free_Culture" title="Students for Free Culture">Students for Free Culture</a><sup id="cite_ref-81" class="reference"><a href="#cite_note-81"><span class="cite-bracket">[</span>73<span class="cite-bracket">]</span></a></sup></li> <li><a href="/wiki/Sugar_Labs" title="Sugar Labs">Sugar Labs</a><sup id="cite_ref-82" class="reference"><a href="#cite_note-82"><span class="cite-bracket">[</span>74<span class="cite-bracket">]</span></a></sup></li> <li><a href="/wiki/Sverok" title="Sverok">Sverok</a><sup id="cite_ref-83" class="reference"><a href="#cite_note-83"><span class="cite-bracket">[</span>75<span class="cite-bracket">]</span></a></sup></li> <li><a href="/wiki/TopCoder" class="mw-redirect" title="TopCoder">TopCoder</a><sup id="cite_ref-TopCoder_84-0" class="reference"><a href="#cite_note-TopCoder-84"><span class="cite-bracket">[</span>76<span class="cite-bracket">]</span></a></sup></li> <li><a href="/wiki/Ubuntu_(operating_system)" class="mw-redirect" title="Ubuntu (operating system)">Ubuntu</a><sup id="cite_ref-85" class="reference"><a href="#cite_note-85"><span class="cite-bracket">[</span>77<span class="cite-bracket">]</span></a></sup></li> <li><a href="/w/index.php?title=Vidya_Gaem_Awards&action=edit&redlink=1" class="new" title="Vidya Gaem Awards (page does not exist)">Vidya Gaem Awards</a><sup id="cite_ref-86" class="reference"><a href="#cite_note-86"><span class="cite-bracket">[</span>78<span class="cite-bracket">]</span></a></sup></li> <li><a href="/wiki/Wikimedia_Foundation" title="Wikimedia Foundation">Wikimedia</a> (2008)<sup id="cite_ref-Wikimedia_87-0" class="reference"><a href="#cite_note-Wikimedia-87"><span class="cite-bracket">[</span>79<span class="cite-bracket">]</span></a></sup></li> <li><a href="/wiki/Wikipedia" title="Wikipedia">Wikipedia</a> in <a href="/wiki/French_Wikipedia" title="French Wikipedia">French</a>,<sup id="cite_ref-FrenchWikipedia_88-0" class="reference"><a href="#cite_note-FrenchWikipedia-88"><span class="cite-bracket">[</span>80<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Hebrew_Wikipedia" title="Hebrew Wikipedia">Hebrew</a>,<sup id="cite_ref-89" class="reference"><a href="#cite_note-89"><span class="cite-bracket">[</span>81<span class="cite-bracket">]</span></a></sup><sup class="noprint Inline-Template noprint Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Verifiability#Wikipedia_and_sources_that_mirror_or_use_it" title="Wikipedia:Verifiability"><span title="This claim cites another Wikipedia article. Articles need references to reliable third-party sources. (August 2024)">circular reference</span></a></i>]</sup><sup id="cite_ref-90" class="reference"><a href="#cite_note-90"><span class="cite-bracket">[</span>82<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Hungarian_Wikipedia" title="Hungarian Wikipedia">Hungarian</a>,<sup id="cite_ref-91" class="reference"><a href="#cite_note-91"><span class="cite-bracket">[</span>83<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Russian_Wikipedia" title="Russian Wikipedia">Russian</a>,<sup id="cite_ref-92" class="reference"><a href="#cite_note-92"><span class="cite-bracket">[</span>84<span class="cite-bracket">]</span></a></sup> and <a href="/wiki/Persian_Wikipedia" title="Persian Wikipedia">Persian</a>.<sup id="cite_ref-93" class="reference"><a href="#cite_note-93"><span class="cite-bracket">[</span>85<span class="cite-bracket">]</span></a></sup></li></ul> </div> <div class="mw-heading mw-heading2"><h2 id="Notes">Notes</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Schulze_method&action=edit&section=18" title="Edit section: Notes"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-references-wrap mw-references-columns"><ol class="references"> <li id="cite_note-schulze201122-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-schulze201122_1-0">^</a></b></span> <span class="reference-text">Markus Schulze, "<a href="//doi.org/10.1007/s00355-010-0475-4" class="extiw" title="doi:10.1007/s00355-010-0475-4">A new monotonic, clone-independent, reversal symmetric, and Condorcet-consistent single-winner election method</a>", Social Choice and Welfare, volume 36, number 2, page 267–303, 2011. Preliminary version in <i>Voting Matters</i>, 17:9-19, 2003.</span> </li> <li id="cite_note-schulze20113-2"><span class="mw-cite-backlink">^ <a href="#cite_ref-schulze20113_2-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-schulze20113_2-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-schulze20113_2-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-schulze20113_2-3"><sup><i><b>d</b></i></sup></a> <a href="#cite_ref-schulze20113_2-4"><sup><i><b>e</b></i></sup></a></span> <span class="reference-text">Markus Schulze, "<a href="//doi.org/10.1007/s00355-010-0475-4" class="extiw" title="doi:10.1007/s00355-010-0475-4">A new monotonic, clone-independent, reversal symmetric, and condorcet-consistent single-winner election method</a>", Social Choice and Welfare, volume 36, number 2, page 267–303, 2011. Preliminary version in <i>Voting Matters</i>, 17:9-19, 2003.</span> </li> <li id="cite_note-schulze2011-3"><span class="mw-cite-backlink">^ <a href="#cite_ref-schulze2011_3-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-schulze2011_3-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-schulze2011_3-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-schulze2011_3-3"><sup><i><b>d</b></i></sup></a> <a href="#cite_ref-schulze2011_3-4"><sup><i><b>e</b></i></sup></a> <a href="#cite_ref-schulze2011_3-5"><sup><i><b>f</b></i></sup></a> <a href="#cite_ref-schulze2011_3-6"><sup><i><b>g</b></i></sup></a> <a href="#cite_ref-schulze2011_3-7"><sup><i><b>h</b></i></sup></a> <a href="#cite_ref-schulze2011_3-8"><sup><i><b>i</b></i></sup></a></span> <span class="reference-text">Markus Schulze, "<a rel="nofollow" class="external text" href="https://doi.org/10.1007/s00355-010-0475-4">A new monotonic, clone-independent, reversal symmetric, and condorcet-consistent single-winner election method</a>", Social Choice and Welfare, volume 36, number 2, page 267–303, 2011. Preliminary version in <i>Voting Matters</i>, 17:9-19, 2003.</span> </li> <li id="cite_note-woodall1994-4"><span class="mw-cite-backlink">^ <a href="#cite_ref-woodall1994_4-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-woodall1994_4-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-woodall1994_4-2"><sup><i><b>c</b></i></sup></a></span> <span class="reference-text">Douglas R. Woodall, <a rel="nofollow" class="external text" href="http://www.votingmatters.org.uk/ISSUE3/P5.HTM">Properties of Preferential Election Rules</a>, <i>Voting Matters</i>, issue 3, pages 8–15, December 1994</span> </li> <li id="cite_note-13"><span class="mw-cite-backlink"><b><a href="#cite_ref-13">^</a></b></span> <span class="reference-text">Tideman, T. Nicolaus, "Independence of clones as a criterion for voting rules", Social Choice and Welfare vol 4 #3 (1987), pp. 185–206.</span> </li> <li id="cite_note-14"><span class="mw-cite-backlink"><b><a href="#cite_ref-14">^</a></b></span> <span class="reference-text">See: <ul><li>Markus Schulze, <a rel="nofollow" class="external text" href="http://lists.electorama.com/pipermail/election-methods-electorama.com/1997-October/001570.html">Condorect sub-cycle rule</a>, October 1997</li> <li>Mike Ossipoff, <a rel="nofollow" class="external text" href="http://lists.electorama.com/pipermail/election-methods-electorama.com/1998-July/099943.html">Party List P.S.</a>, July 1998</li> <li>Markus Schulze, <a rel="nofollow" class="external text" href="http://lists.electorama.com/pipermail/election-methods-electorama.com/1998-August/100045.html">Tiebreakers, Subcycle Rules</a>, August 1998</li> <li>Markus Schulze, <a rel="nofollow" class="external text" href="http://lists.electorama.com/pipermail/election-methods-electorama.com/1998-August/100131.html">Maybe Schulze is decisive</a>, August 1998</li> <li>Norman Petry, <a rel="nofollow" class="external text" href="http://lists.electorama.com/pipermail/election-methods-electorama.com/1998-September/067383.html">Schulze Method - Simpler Definition</a>, September 1998</li> <li>Markus Schulze, <a rel="nofollow" class="external text" href="http://lists.electorama.com/pipermail/election-methods-electorama.com/1998-November/068099.html">Schulze Method</a>, November 1998</li></ul> </span></li> <li id="cite_note-15"><span class="mw-cite-backlink"><b><a href="#cite_ref-15">^</a></b></span> <span class="reference-text">See: <ul><li>Anthony Towns, <a rel="nofollow" class="external text" href="https://lists.debian.org/debian-vote/2000/11/msg00121.html">Disambiguation of 4.1.5</a>, November 2000</li> <li>Norman Petry, <a rel="nofollow" class="external text" href="https://lists.debian.org/debian-vote/2000/12/msg00045.html">Constitutional voting, definition of cumulative preference</a>, December 2000</li></ul> </span></li> <li id="cite_note-16"><span class="mw-cite-backlink"><b><a href="#cite_ref-16">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFHortanoticias2016" class="citation web cs1 cs1-prop-foreign-lang-source">Hortanoticias, Redacción (2016-02-23). <a rel="nofollow" class="external text" href="https://www.hortanoticias.com/al-voltant-de-2-000-participants-en-dos-dies-en-la-primera-enquesta-popular-de-silla-que-decidira-sobre-espectacles-taurins/">"Al voltant de 2.000 participants en dos dies en la primera enquesta popular de Silla que decidirà sobre espectacles taurins"</a>. <i>Hortanoticias.com</i> (in Spanish)<span class="reference-accessdate">. Retrieved <span class="nowrap">2022-09-24</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Hortanoticias.com&rft.atitle=Al+voltant+de+2.000+participants+en+dos+dies+en+la+primera+enquesta+popular+de+Silla+que+decidir%C3%A0+sobre+espectacles+taurins&rft.date=2016-02-23&rft.aulast=Hortanoticias&rft.aufirst=Redacci%C3%B3n&rft_id=https%3A%2F%2Fwww.hortanoticias.com%2Fal-voltant-de-2-000-participants-en-dos-dies-en-la-primera-enquesta-popular-de-silla-que-decidira-sobre-espectacles-taurins%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASchulze+method" class="Z3988"></span></span> </li> <li id="cite_note-17"><span class="mw-cite-backlink"><b><a href="#cite_ref-17">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSilla2016" class="citation web cs1 cs1-prop-foreign-lang-source">Silla, ~ El Cresol de (2016-05-26). <a rel="nofollow" class="external text" href="https://elcresoldesilla.wordpress.com/2016/05/26/un-any-daprofundiment-democratic-a-silla/">"Un any d'aprofundiment democràtic a Silla"</a>. <i>El Cresol de Silla</i> (in Catalan)<span class="reference-accessdate">. Retrieved <span class="nowrap">2022-09-24</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=El+Cresol+de+Silla&rft.atitle=Un+any+d%27aprofundiment+democr%C3%A0tic+a+Silla&rft.date=2016-05-26&rft.aulast=Silla&rft.aufirst=~+El+Cresol+de&rft_id=https%3A%2F%2Felcresoldesilla.wordpress.com%2F2016%2F05%2F26%2Fun-any-daprofundiment-democratic-a-silla%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASchulze+method" class="Z3988"></span></span> </li> <li id="cite_note-PiratePartySweden2-18"><span class="mw-cite-backlink">^ <a href="#cite_ref-PiratePartySweden2_18-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-PiratePartySweden2_18-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text">See: <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1 cs1-prop-foreign-lang-source"><a rel="nofollow" class="external text" href="https://archive.today/20121224194036/https://forum.piratpartiet.se/showthread.php?p=172218">"Inför primärvalen"</a> [Before the primary elections] (in Swedish). 8 October 2009. Archived from <a rel="nofollow" class="external text" href="https://forum.piratpartiet.se/showthread.php?p=172218">the original</a> on 24 December 2012.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Inf%C3%B6r+prim%C3%A4rvalen&rft.date=2009-10-08&rft_id=https%3A%2F%2Fforum.piratpartiet.se%2Fshowthread.php%3Fp%3D172218&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASchulze+method" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1 cs1-prop-foreign-lang-source"><a rel="nofollow" class="external text" href="https://archive.today/20140723081035/https://forum.piratpartiet.se/showthread.php?p=173792">"Dags att kandidera till riksdagen"</a> [Time to run for the Riksdag] (in Swedish). 17 October 2009. Archived from <a rel="nofollow" class="external text" href="https://forum.piratpartiet.se/showthread.php?p=173792">the original</a> on 23 July 2014.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Dags+att+kandidera+till+riksdagen&rft.date=2009-10-17&rft_id=https%3A%2F%2Fforum.piratpartiet.se%2Fshowthread.php%3Fp%3D173792&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASchulze+method" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1 cs1-prop-foreign-lang-source"><a rel="nofollow" class="external text" href="https://archive.today/20121224195649/https://forum.piratpartiet.se/showthread.php?p=190840">"Råresultat primärvalet"</a> [The raw result of the primary election] (in Swedish). 19 January 2010. Archived from <a rel="nofollow" class="external text" href="https://forum.piratpartiet.se/showthread.php?p=190840">the original</a> on 24 December 2012.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=R%C3%A5resultat+prim%C3%A4rvalet&rft.date=2010-01-19&rft_id=https%3A%2F%2Fforum.piratpartiet.se%2Fshowthread.php%3Fp%3D190840&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASchulze+method" class="Z3988"></span></li></ul> </span></li> <li id="cite_note-PiratePartyGermany2-19"><span class="mw-cite-backlink">^ <a href="#cite_ref-PiratePartyGermany2_19-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-PiratePartyGermany2_19-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text">11 of the 16 regional sections and the federal section of the <a href="/wiki/Pirate_Party_Germany" title="Pirate Party Germany">Pirate Party of Germany</a> are using <a rel="nofollow" class="external text" href="https://liquidfeedback.org/">LiquidFeedback</a> for unbinding internal opinion polls. In 2010/2011, the Pirate Parties of <a href="/wiki/Neuk%C3%B6lln" title="Neukölln">Neukölln</a> (<a rel="nofollow" class="external text" href="http://wiki.piratenpartei.de/BE:Neuk%C3%B6lln/Gebietsversammlungen/2010.3/Protokoll">link</a>), <a href="/wiki/Mitte" title="Mitte">Mitte</a> (<a rel="nofollow" class="external text" href="https://berlin.piratenpartei.de/innerparteiliches/kandidaten-der-piraten-in-mitte-aufgestellt/">link</a>), <a href="/wiki/Steglitz-Zehlendorf" title="Steglitz-Zehlendorf">Steglitz-Zehlendorf</a> (<a rel="nofollow" class="external text" href="http://wiki.piratenpartei.de/wiki/images/d/da/BE_Gebietsversammlung_Steglitz_Zehlendorf_2011_01_20_Protokoll.pdf">link</a>), <a href="/wiki/Lichtenberg" title="Lichtenberg">Lichtenberg</a> (<a rel="nofollow" class="external text" href="http://piraten-lichtenberg.de/2011/02/02/groser-schritt-in-richtung-wahl/">link</a>), and <a href="/wiki/Tempelhof-Sch%C3%B6neberg" title="Tempelhof-Schöneberg">Tempelhof-Schöneberg</a> (<a rel="nofollow" class="external text" href="http://wiki.piratenpartei.de/BE:Gebietsversammlungen/Tempelhof-Schoeneberg/Protokoll_2011.1">link</a>) adopted the Schulze method for its primaries. Furthermore, the Pirate Party of <a href="/wiki/Berlin" title="Berlin">Berlin</a> (in 2011) (<a rel="nofollow" class="external text" href="http://wiki.piratenpartei.de/BE:Parteitag/2011.1/Protokoll">link</a>) and the Pirate Party of <a href="/wiki/Regensburg" title="Regensburg">Regensburg</a> (in 2012) (<a rel="nofollow" class="external text" href="http://wiki.piratenpartei.de/BY:Regensburg/Gr%C3%BCndung/Gesch%C3%A4ftsordnung#Anlage_A">link</a>) adopted this method for their primaries.</span> </li> <li id="cite_note-Boise_DSA2-20"><span class="mw-cite-backlink"><b><a href="#cite_ref-Boise_DSA2_20-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFChumich" class="citation web cs1">Chumich, Andrew. <a rel="nofollow" class="external text" href="https://www.boisedsa.org/statements/yjmtibx8okazm7i7042c10tuld0gm5">"DSA Special Election"</a><span class="reference-accessdate">. Retrieved <span class="nowrap">2018-02-25</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=DSA+Special+Election&rft.aulast=Chumich&rft.aufirst=Andrew&rft_id=https%3A%2F%2Fwww.boisedsa.org%2Fstatements%2Fyjmtibx8okazm7i7042c10tuld0gm5&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASchulze+method" class="Z3988"></span></span> </li> <li id="cite_note-21"><span class="mw-cite-backlink"><b><a href="#cite_ref-21">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="http://www.quotidianomolise.com/campobasso-comunali-scattano-le-primarie-a-5-stelle/">Campobasso. Comunali, scattano le primarie a 5 Stelle</a>, February 2014</span> </li> <li id="cite_note-22"><span class="mw-cite-backlink"><b><a href="#cite_ref-22">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMacaro2015" class="citation web cs1 cs1-prop-foreign-lang-source">Macaro, Mirko (2015-03-03). <a rel="nofollow" class="external text" href="https://www.h24notizie.com/2015/03/03/fondi-punto-sui-candidati-sindaco-certezze-novita-colpi-scena/">"Fondi, il punto sui candidati a sindaco. Certezze, novità e colpi di scena"</a>. <i>h24 notizie - portale indipendente di news dalla provincia</i> (in Italian)<span class="reference-accessdate">. Retrieved <span class="nowrap">2022-09-24</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=h24+notizie+-+portale+indipendente+di+news+dalla+provincia&rft.atitle=Fondi%2C+il+punto+sui+candidati+a+sindaco.+Certezze%2C+novit%C3%A0+e+colpi+di+scena&rft.date=2015-03-03&rft.aulast=Macaro&rft.aufirst=Mirko&rft_id=https%3A%2F%2Fwww.h24notizie.com%2F2015%2F03%2F03%2Ffondi-punto-sui-candidati-sindaco-certezze-novita-colpi-scena%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASchulze+method" class="Z3988"></span></span> </li> <li id="cite_note-23"><span class="mw-cite-backlink"><b><a href="#cite_ref-23">^</a></b></span> <span class="reference-text">article 25(5) of the <a rel="nofollow" class="external text" href="http://www.5stellemontecompatri.it/wp-content/uploads/2013/11/REGOLAMENTO-M5S-Montecompatri1.doc">bylaws</a>, October 2013</span> </li> <li id="cite_note-24"><span class="mw-cite-backlink"><b><a href="#cite_ref-24">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20150402230827/http://www.montemurlo5stelle.net/2013/11/2-step-comunarie-di-montemurlo.html">"MoVimento 5 Stelle - Montemurlo: 2° Step Comunarie di Montemurlo"</a>. November 2013. Archived from <a rel="nofollow" class="external text" href="http://www.montemurlo5stelle.net/2013/11/2-step-comunarie-di-montemurlo.html">the original</a> on 2015-04-02<span class="reference-accessdate">. Retrieved <span class="nowrap">2022-09-24</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=MoVimento+5+Stelle+-+Montemurlo%3A+2%C2%B0+Step+Comunarie+di+Montemurlo&rft.date=2013-11&rft_id=http%3A%2F%2Fwww.montemurlo5stelle.net%2F2013%2F11%2F2-step-comunarie-di-montemurlo.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASchulze+method" class="Z3988"></span></span> </li> <li id="cite_note-25"><span class="mw-cite-backlink"><b><a href="#cite_ref-25">^</a></b></span> <span class="reference-text">article 12 of the <a rel="nofollow" class="external text" href="http://movimento5stellepescara.it/wp-content/uploads/2015/02/Regolamento-m5S-pescara_rev.03_del_30_01_-2015.pdf">bylaws</a>, January 2015</span> </li> <li id="cite_note-26"><span class="mw-cite-backlink"><b><a href="#cite_ref-26">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="https://www.meetup.com/MoVimento-5-Stelle-San-Cesareo/events/166108572/">Ridefinizione della lista di San Cesareo con Metodo Schulze</a>, February 2014</span> </li> <li id="cite_note-27"><span class="mw-cite-backlink"><b><a href="#cite_ref-27">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://pirateparty.org.au/2011/11/18/national-congress-2011-results/">"National Congress 2011 Results – Pirate Party Australia"</a>. <i>pirateparty.org.au</i>. 18 November 2011<span class="reference-accessdate">. Retrieved <span class="nowrap">2022-09-24</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=pirateparty.org.au&rft.atitle=National+Congress+2011+Results+%E2%80%93+Pirate+Party+Australia&rft.date=2011-11-18&rft_id=https%3A%2F%2Fpirateparty.org.au%2F2011%2F11%2F18%2Fnational-congress-2011-results%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASchulze+method" class="Z3988"></span></span> </li> <li id="cite_note-28"><span class="mw-cite-backlink"><b><a href="#cite_ref-28">^</a></b></span> <span class="reference-text">§6(10) of the <a rel="nofollow" class="external text" href="http://wiki.piratenpartei.at/wiki/Satzung">bylaws</a></span> </li> <li id="cite_note-29"><span class="mw-cite-backlink"><b><a href="#cite_ref-29">^</a></b></span> <span class="reference-text">Article III.3.4 of the Statutory Rules (<a rel="nofollow" class="external text" href="https://wiki.pirateparty.be/images/9/9f/Ppbe-statutes-fr_be.pdf">french</a>, <a rel="nofollow" class="external text" href="https://wiki.pirateparty.be/images/e/e7/Ppbe-statutes-nl_be.pdf">dutch</a>)</span> </li> <li id="cite_note-30"><span class="mw-cite-backlink"><b><a href="#cite_ref-30">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPíratar2013" class="citation web cs1 cs1-prop-foreign-lang-source">Píratar (2013-10-23). <a rel="nofollow" class="external text" href="https://piratar.is/frettir/piratafraedarinn/schulze-adferdin/">"Schulze aðferðin"</a>. <i>Píratar</i> (in Icelandic)<span class="reference-accessdate">. Retrieved <span class="nowrap">2022-09-24</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=P%C3%ADratar&rft.atitle=Schulze+a%C3%B0fer%C3%B0in&rft.date=2013-10-23&rft.au=P%C3%ADratar&rft_id=https%3A%2F%2Fpiratar.is%2Ffrettir%2Fpiratafraedarinn%2Fschulze-adferdin%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASchulze+method" class="Z3988"></span></span> </li> <li id="cite_note-31"><span class="mw-cite-backlink"><b><a href="#cite_ref-31">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="https://www.partito-pirata.it/statute/">Rules adopted on 18 December 2011</a></span> </li> <li id="cite_note-32"><span class="mw-cite-backlink"><b><a href="#cite_ref-32">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPontier2015" class="citation web cs1 cs1-prop-foreign-lang-source">Pontier, Matthijs (2015-01-11). <a rel="nofollow" class="external text" href="https://noord-holland.piratenpartij.nl/711/">"Verslag ledenraadpleging 4 januari"</a>. <i>Piratenpartij Noord Holland</i> (in Dutch)<span class="reference-accessdate">. Retrieved <span class="nowrap">2022-09-24</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Piratenpartij+Noord+Holland&rft.atitle=Verslag+ledenraadpleging+4+januari&rft.date=2015-01-11&rft.aulast=Pontier&rft.aufirst=Matthijs&rft_id=https%3A%2F%2Fnoord-holland.piratenpartij.nl%2F711%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASchulze+method" class="Z3988"></span></span> </li> <li id="cite_note-33"><span class="mw-cite-backlink"><b><a href="#cite_ref-33">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPankerl2010" class="citation web cs1 cs1-prop-foreign-lang-source">Pankerl, Florian (2010-09-18). <a rel="nofollow" class="external text" href="https://blog.florian-pankerl.de/2010/piratenversammlung-der-piratenpartei-schweiz-2010-samstag/">"Piratenversammlung der Piratenpartei Schweiz 2010 – Samstag"</a> (in German)<span class="reference-accessdate">. Retrieved <span class="nowrap">2022-09-24</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Piratenversammlung+der+Piratenpartei+Schweiz+2010+%E2%80%93+Samstag&rft.date=2010-09-18&rft.aulast=Pankerl&rft.aufirst=Florian&rft_id=https%3A%2F%2Fblog.florian-pankerl.de%2F2010%2Fpiratenversammlung-der-piratenpartei-schweiz-2010-samstag%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASchulze+method" class="Z3988"></span></span> </li> <li id="cite_note-34"><span class="mw-cite-backlink"><b><a href="#cite_ref-34">^</a></b></span> <span class="reference-text">article IV section 3 of the <a rel="nofollow" class="external text" href="https://wiki.uspirates.org/w/index.php?title=Pirate_National_Committee_(PNC)/Bylaws">bylaws</a>, July 2012</span> </li> <li id="cite_note-35"><span class="mw-cite-backlink"><b><a href="#cite_ref-35">^</a></b></span> <span class="reference-text">§10 III of its <a rel="nofollow" class="external text" href="http://sustainableunion.yolasite.com/resources/130614_Satzung_sud_fBayern.pdf">bylaws</a>, June 2013</span> </li> <li id="cite_note-36"><span class="mw-cite-backlink"><b><a href="#cite_ref-36">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFThe_Board_of_Directors_of_Volt_Europe_in_Spain" class="citation web cs1 cs1-prop-foreign-lang-source">The Board of Directors of Volt Europe in Spain. <a rel="nofollow" class="external text" href="https://archive.today/20240820145337/https://web.archive.org/web/20211113112113/https://medium.com/volt-espa%C3%B1a/algunas-consideraciones-sobre-en-qu%C3%A9-grupo-estar%C3%A1-volt-europa-en-el-parlamento-europeo-b10b7431d947">"Algunas consideraciones sobre en qué grupo estará Volt Europa en el Parlamento Europeo"</a> [Some considerations on which group Volt Europe will join in the European Parliament]. <i><a href="/wiki/Medium_(website)" title="Medium (website)">Medium</a></i> (in Spanish). Archived from <a rel="nofollow" class="external text" href="https://medium.com/volt-espa%C3%B1a/algunas-consideraciones-sobre-en-qu%C3%A9-grupo-estar%C3%A1-volt-europa-en-el-parlamento-europeo-b10b7431d947">the original</a> on 20 August 2024.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Medium&rft.atitle=Algunas+consideraciones+sobre+en+qu%C3%A9+grupo+estar%C3%A1+Volt+Europa+en+el+Parlamento+Europeo&rft.au=The+Board+of+Directors+of+Volt+Europe+in+Spain&rft_id=https%3A%2F%2Fmedium.com%2Fvolt-espa%25C3%25B1a%2Falgunas-consideraciones-sobre-en-qu%25C3%25A9-grupo-estar%25C3%25A1-volt-europa-en-el-parlamento-europeo-b10b7431d947&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASchulze+method" class="Z3988"></span></span> </li> <li id="cite_note-37"><span class="mw-cite-backlink"><b><a href="#cite_ref-37">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHajdu2017" class="citation web cs1">Hajdu, Tekla (2017-09-24). <a rel="nofollow" class="external text" href="https://www.zeus.aegee.org/magazine/2017/09/24/the-schulze-method-agora-101/">"The Schulze Method – Agora 101"</a>. <i>The AEGEEan - AEGEE's online magazine - AEGEE-Europe</i><span class="reference-accessdate">. Retrieved <span class="nowrap">2022-09-24</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=The+AEGEEan+-+AEGEE%27s+online+magazine+-+AEGEE-Europe&rft.atitle=The+Schulze+Method+%E2%80%93+Agora+101&rft.date=2017-09-24&rft.aulast=Hajdu&rft.aufirst=Tekla&rft_id=https%3A%2F%2Fwww.zeus.aegee.org%2Fmagazine%2F2017%2F09%2F24%2Fthe-schulze-method-agora-101%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASchulze+method" class="Z3988"></span></span> </li> <li id="cite_note-38"><span class="mw-cite-backlink"><b><a href="#cite_ref-38">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="https://db.cde-ev.de/doc/Realm_Assembly_Voting-Details.html">Voting Details</a>, January 2021</span> </li> <li id="cite_note-39"><span class="mw-cite-backlink"><b><a href="#cite_ref-39">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="https://www.dg.ens.fr/documents/148/note_explicative.pdf">Référendum sur la réforme du thurnage</a>, June 2021</span> </li> <li id="cite_note-40"><span class="mw-cite-backlink"><b><a href="#cite_ref-40">^</a></b></span> <span class="reference-text">article 57 of the <a rel="nofollow" class="external text" href="https://www.vtk.be/page/file/ef87370c1d5798758d1730a14f7410d96783301e/">statutory rules</a></span> </li> <li id="cite_note-41"><span class="mw-cite-backlink"><b><a href="#cite_ref-41">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20130909055056/http://gso.cs.binghamton.edu/index.php/Voting">"User Voting Instructions"</a>. Gso.cs.binghamton.edu. Archived from <a rel="nofollow" class="external text" href="http://gso.cs.binghamton.edu/index.php/Voting">the original</a> on 2013-09-09<span class="reference-accessdate">. Retrieved <span class="nowrap">2010-05-08</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=User+Voting+Instructions&rft.pub=Gso.cs.binghamton.edu&rft_id=http%3A%2F%2Fgso.cs.binghamton.edu%2Findex.php%2FVoting&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASchulze+method" class="Z3988"></span></span> </li> <li id="cite_note-42"><span class="mw-cite-backlink"><b><a href="#cite_ref-42">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://sites.google.com/a/bsc.coop/hip-house/bylaws-and-policies/bylaws-bylaw-appendix">"Hillegass-Parker House Bylaws § 5. Elections"</a>. <i>Hillegass-Parker House website</i><span class="reference-accessdate">. Retrieved <span class="nowrap">4 October</span> 2015</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Hillegass-Parker+House+website&rft.atitle=Hillegass-Parker+House+Bylaws+%C2%A7+5.+Elections&rft_id=https%3A%2F%2Fsites.google.com%2Fa%2Fbsc.coop%2Fhip-house%2Fbylaws-and-policies%2Fbylaws-bylaw-appendix&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASchulze+method" class="Z3988"></span></span> </li> <li id="cite_note-43"><span class="mw-cite-backlink"><b><a href="#cite_ref-43">^</a></b></span> <span class="reference-text">See: <ul><li>Konglig Datasektionen KTH</li></ul> <ul><li>Ka-Ping Yee, <a rel="nofollow" class="external text" href="https://zestyping.livejournal.com/102718.html">Condorcet elections</a>, March 2005</li> <li>Ka-Ping Yee, <a rel="nofollow" class="external text" href="https://zestyping.livejournal.com/111588.html">Kingman adopts Condorcet voting</a>, April 2005</li></ul> </span></li> <li id="cite_note-44"><span class="mw-cite-backlink"><b><a href="#cite_ref-44">^</a></b></span> <span class="reference-text">article 9.4.5.h of the <a rel="nofollow" class="external text" href="https://associatedstudents.minerva.community/wp-content/uploads/2017/11/ASM-Charter-November-2017.pdf">charter</a>, November 2017</span> </li> <li id="cite_note-45"><span class="mw-cite-backlink"><b><a href="#cite_ref-45">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="http://www.northbynorthwestern.com/story/ajith-van-atta-win-asg-election/">Ajith, Van Atta win ASG election</a>, April 2013</span> </li> <li id="cite_note-46"><span class="mw-cite-backlink"><b><a href="#cite_ref-46">^</a></b></span> <span class="reference-text">§6 and §7 of its <a rel="nofollow" class="external text" href="http://www.u-asta.uni-freiburg.de/vs/stura/stura-go-entgultig-beschlossene-form-13.05.2014.pdf">bylaws</a>, May 2014</span> </li> <li id="cite_note-47"><span class="mw-cite-backlink"><b><a href="#cite_ref-47">^</a></b></span> <span class="reference-text">§6(6) of the <a rel="nofollow" class="external text" href="https://www.fachschaft.informatik.uni-kl.de/wp-content/uploads/2020/06/go.pdf">bylaws</a></span> </li> <li id="cite_note-48"><span class="mw-cite-backlink"><b><a href="#cite_ref-48">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="https://civs.cs.cornell.edu/cgi-bin/results.pl?id=E_50cfc592ae8f13d9">Election of the Annodex Association committee for 2007</a>, February 2007</span> </li> <li id="cite_note-49"><span class="mw-cite-backlink"><b><a href="#cite_ref-49">^</a></b></span> <span class="reference-text">§9a of the <a rel="nofollow" class="external text" href="https://www.bvkj.de/mitgliedschaft/satzung">bylaws</a>, October 2013</span> </li> <li id="cite_note-50"><span class="mw-cite-backlink"><b><a href="#cite_ref-50">^</a></b></span> <span class="reference-text">See: <ul><li>2013 Golden Geek Awards - Nominations Open, January 2014</li> <li>2014 Golden Geek Awards - Nominations Open, January 2015</li> <li>2015 Golden Geek Awards - Nominations Open, March 2016</li> <li>2016 Golden Geek Awards - Nominations Open, January 2017</li> <li>2017 Golden Geek Awards - Nominations Open, February 2018</li> <li>2018 Golden Geek Awards - Nominations Open, March 2019</li></ul> </span></li> <li id="cite_note-51"><span class="mw-cite-backlink"><b><a href="#cite_ref-51">^</a></b></span> <span class="reference-text">article 7(e)(iii)(2) of the <a rel="nofollow" class="external text" href="https://www.cloudfoundry.org/wp-content/uploads/cff-charter-changes-with-TOC.-2021.pdf">charter</a>, May 2021</span> </li> <li id="cite_note-52"><span class="mw-cite-backlink"><b><a href="#cite_ref-52">^</a></b></span> <span class="reference-text">Adam Helman, <a rel="nofollow" class="external text" href="http://www.cohp.org/records/votes/family_affair_voting_scheme.html">Family Affair Voting Scheme - Schulze Method</a></span> </li> <li id="cite_note-53"><span class="mw-cite-backlink"><b><a href="#cite_ref-53">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="https://github.com/dapr/community/blob/master/steering-and-technical-committee-charter.md">Steering and Technical committee</a>, November 2021</span> </li> <li id="cite_note-Debian-54"><span class="mw-cite-backlink"><b><a href="#cite_ref-Debian_54-0">^</a></b></span> <span class="reference-text">See: <ul><li><a rel="nofollow" class="external text" href="https://www.debian.org/vote/2003/vote_0002">Constitutional Amendment: Condorcet/Clone Proof SSD Voting Method</a>, June 2003</li> <li><a rel="nofollow" class="external text" href="https://www.debian.org/devel/constitution">Constitution for the Debian Project</a>, appendix A6</li> <li><a rel="nofollow" class="external text" href="https://www.debian.org/vote/">Debian Voting Information</a></li></ul> </span></li> <li id="cite_note-55"><span class="mw-cite-backlink"><b><a href="#cite_ref-55">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://eudec.org/about-us/guidance-document/">"Guidance Document"</a>. 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Retrieved <span class="nowrap">2022-09-24</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Kumoricon&rft.atitle=Kumoricon+%E2%80%93+Mascot+Contest&rft_id=https%3A%2F%2Fwww.kumoricon.org%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASchulze+method" class="Z3988"></span></span> </li> <li id="cite_note-68"><span class="mw-cite-backlink"><b><a href="#cite_ref-68">^</a></b></span> <span class="reference-text">article 8.3 of the <a rel="nofollow" class="external text" href="http://governance.lopsa.org/LOPSA_Bylaws">bylaws</a></span> </li> <li id="cite_note-PrinciplesOfLiquidFeedback-69"><span class="mw-cite-backlink"><b><a href="#cite_ref-PrinciplesOfLiquidFeedback_69-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation book cs1"><a rel="nofollow" class="external text" href="http://principles.liquidfeedback.org/"><i>The Principles of LiquidFeedback</i></a>. 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Retrieved <span class="nowrap">2022-09-24</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=governance.openstack.org&rft.atitle=OpenStack+Election+%E2%80%94+OpenStack+Governance&rft_id=https%3A%2F%2Fgovernance.openstack.org%2Felection%2F%23election-system&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASchulze+method" class="Z3988"></span></span> </li> <li id="cite_note-78"><span class="mw-cite-backlink"><b><a href="#cite_ref-78">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMark2016" class="citation web cs1">Mark, Atwood (May 25, 2016). <a rel="nofollow" class="external text" href="https://lists.linuxfoundation.org/pipermail/ops-partners/2016-May/000030.html">"[Partners] text of OpenSwitch Project Charter 2016-05-03"</a><span class="reference-accessdate">. Retrieved <span class="nowrap">2022-09-24</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=%5BPartners%5D+text+of+OpenSwitch+Project+Charter+2016-05-03&rft.date=2016-05-25&rft.aulast=Mark&rft.aufirst=Atwood&rft_id=https%3A%2F%2Flists.linuxfoundation.org%2Fpipermail%2Fops-partners%2F2016-May%2F000030.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASchulze+method" class="Z3988"></span></span> </li> <li id="cite_note-79"><span class="mw-cite-backlink"><b><a href="#cite_ref-79">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.rllmukforum.com/index.php?/topic/260622-committee-elections-2012/">"Committee Elections 2012"</a>. <i>rllmuk</i>. 10 April 2012<span class="reference-accessdate">. Retrieved <span class="nowrap">2022-09-24</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=rllmuk&rft.atitle=Committee+Elections+2012&rft.date=2012-04-10&rft_id=https%3A%2F%2Fwww.rllmukforum.com%2Findex.php%3F%2Ftopic%2F260622-committee-elections-2012%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASchulze+method" class="Z3988"></span></span> </li> <li id="cite_note-80"><span class="mw-cite-backlink"><b><a href="#cite_ref-80">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="https://civs.cs.cornell.edu/cgi-bin/results.pl?num_winners=7&id=E_716d8c257e6cf36b&algorithm=beatpath">Squeak Oversight Board Election 2010</a>, March 2010</span> </li> <li id="cite_note-81"><span class="mw-cite-backlink"><b><a href="#cite_ref-81">^</a></b></span> <span class="reference-text">See: <ul><li><a rel="nofollow" class="external text" href="http://wiki.freeculture.org/Bylaws">Bylaws of the Students for Free Culture</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20130318164643/http://wiki.freeculture.org/Bylaws">Archived</a> 2013-03-18 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a>, article V, section 1.1.1</li> <li><a rel="nofollow" class="external text" href="https://blog.selectricity.org/2008/02/15/free-culture-student-board-elected-using-selectricity/">Free Culture Student Board Elected Using Selectricity</a>, February 2008</li></ul> </span></li> <li id="cite_note-82"><span class="mw-cite-backlink"><b><a href="#cite_ref-82">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://lists.sugarlabs.org/archive/iaep/2009-September/008620.html">"[IAEP] Election status update"</a>. <i>lists.sugarlabs.org</i><span class="reference-accessdate">. Retrieved <span class="nowrap">2022-09-24</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=lists.sugarlabs.org&rft.atitle=%5BIAEP%5D+Election+status+update&rft_id=http%3A%2F%2Flists.sugarlabs.org%2Farchive%2Fiaep%2F2009-September%2F008620.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASchulze+method" class="Z3988"></span></span> </li> <li id="cite_note-83"><span class="mw-cite-backlink"><b><a href="#cite_ref-83">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="https://medlem.sverok.se/2019/01/18/vad-hande-pa-riksmotet-2018/">Minutes of the 2018 Annual Sverok Meeting</a>, November 2018</span> </li> <li id="cite_note-TopCoder-84"><span class="mw-cite-backlink"><b><a href="#cite_ref-TopCoder_84-0">^</a></b></span> <span class="reference-text"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://community.topcoder.com/tc?module=Static&d1=tournaments&d2=tccc07&d3=blog&d4=description">"2007 TopCoder Collegiate Challenge"</a>. <i>community.topcoder.com</i><span class="reference-accessdate">. Retrieved <span class="nowrap">2022-09-24</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=community.topcoder.com&rft.atitle=2007+TopCoder+Collegiate+Challenge&rft_id=https%3A%2F%2Fcommunity.topcoder.com%2Ftc%3Fmodule%3DStatic%26d1%3Dtournaments%26d2%3Dtccc07%26d3%3Dblog%26d4%3Ddescription&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASchulze+method" class="Z3988"></span></span> </li> <li id="cite_note-85"><span class="mw-cite-backlink"><b><a href="#cite_ref-85">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBell2012" class="citation web cs1">Bell, Alan (May 17, 2012). <a rel="nofollow" class="external text" href="https://lists.ubuntu.com/archives/ubuntu-irc/2012-May/001538.html">"Ubuntu IRC Council Position"</a><span class="reference-accessdate">. Retrieved <span class="nowrap">2022-09-24</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Ubuntu+IRC+Council+Position&rft.date=2012-05-17&rft.aulast=Bell&rft.aufirst=Alan&rft_id=https%3A%2F%2Flists.ubuntu.com%2Farchives%2Fubuntu-irc%2F2012-May%2F001538.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASchulze+method" class="Z3988"></span></span> </li> <li id="cite_note-86"><span class="mw-cite-backlink"><b><a href="#cite_ref-86">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://2012.vidyagaemawards.com/voting/results/pairwise">"/v/GAs - Pairwise voting results"</a>. <i>vidyagaemawards.com</i>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=vidyagaemawards.com&rft.atitle=%2Fv%2FGAs+-+Pairwise+voting+results&rft_id=https%3A%2F%2F2012.vidyagaemawards.com%2Fvoting%2Fresults%2Fpairwise&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASchulze+method" class="Z3988"></span></span> </li> <li id="cite_note-Wikimedia-87"><span class="mw-cite-backlink"><b><a href="#cite_ref-Wikimedia_87-0">^</a></b></span> <span class="reference-text">See: <ul><li><a href="https://meta.wikimedia.org/wiki/Board_elections/2008/Results/en" class="extiw" title="metawiki:Board elections/2008/Results/en">2008 Board Elections</a>, June 2008</li> <li><a href="https://meta.wikimedia.org/wiki/Board_elections/2009/Results/en" class="extiw" title="metawiki:Board elections/2009/Results/en">2009 Board Elections</a>, August 2009</li> <li><a href="https://meta.wikimedia.org/wiki/Board_elections/2011/Results/en" class="extiw" title="metawiki:Board elections/2011/Results/en">2011 Board Elections</a>, June 2011</li></ul> </span></li> <li id="cite_note-FrenchWikipedia-88"><span class="mw-cite-backlink"><b><a href="#cite_ref-FrenchWikipedia_88-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation cs2 cs1-prop-foreign-lang-source"><a class="external text" href="https://fr.wikipedia.org/w/index.php?title=Wikip%C3%A9dia:Prise_de_d%C3%A9cision/Choix_dans_les_votes&oldid=162034454">"Wikipédia:Prise de décision/Choix dans les votes"</a>, <i>Wikipédia</i> (in French), 2019-08-22<span class="reference-accessdate">, retrieved <span class="nowrap">2022-09-24</span></span></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Wikip%C3%A9dia&rft.atitle=Wikip%C3%A9dia%3APrise+de+d%C3%A9cision%2FChoix+dans+les+votes&rft.date=2019-08-22&rft_id=https%3A%2F%2Ffr.wikipedia.org%2Fw%2Findex.php%3Ftitle%3DWikip%25C3%25A9dia%3APrise_de_d%25C3%25A9cision%2FChoix_dans_les_votes%26oldid%3D162034454&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASchulze+method" class="Z3988"></span></span> </li> <li id="cite_note-89"><span class="mw-cite-backlink"><b><a href="#cite_ref-89">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1 cs1-prop-foreign-lang-source"><a class="external text" href="https://he.wikipedia.org/wiki/ויקיפדיה:פרלמנט/הכרעה">"ויקיפדיה:פרלמנט/הכרעה"</a> [Wikipedia:Parliament/Decisionmaking]. <i>he.wikipedia.org</i> (in Hebrew).</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=he.wikipedia.org&rft.atitle=%D7%95%D7%99%D7%A7%D7%99%D7%A4%D7%93%D7%99%D7%94%3A%D7%A4%D7%A8%D7%9C%D7%9E%D7%A0%D7%98%2F%D7%94%D7%9B%D7%A8%D7%A2%D7%94&rft_id=https%3A%2F%2Fhe.wikipedia.org%2Fwiki%2F%D7%95%D7%99%D7%A7%D7%99%D7%A4%D7%93%D7%99%D7%94%3A%D7%A4%D7%A8%D7%9C%D7%9E%D7%A0%D7%98%2F%D7%94%D7%9B%D7%A8%D7%A2%D7%94&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASchulze+method" class="Z3988"></span></span> </li> <li id="cite_note-90"><span class="mw-cite-backlink"><b><a href="#cite_ref-90">^</a></b></span> <span class="reference-text">See e.g. here <a class="external autonumber" href="https://he.wikipedia.org/w/index.php?title=ויקיפדיה:פרלמנט&oldid=7014412">[1]</a> (May 2009), here <a class="external autonumber" href="https://he.wikipedia.org/w/index.php?title=ויקיפדיה:סדנה_לגרפיקה/סמליל&oldid=7388447">[2]</a> (August 2009), and here <a class="external autonumber" href="https://he.wikipedia.org/w/index.php?title=ויקיפדיה:סדנה_לגרפיקה/100,000/הצבעה&oldid=8057743">[3]</a> (December 2009).</span> </li> <li id="cite_note-91"><span class="mw-cite-backlink"><b><a href="#cite_ref-91">^</a></b></span> <span class="reference-text">See <a href="https://hu.wikipedia.org/wiki/Wikip%C3%A9dia:Szavaz%C3%A1s/Az_%E2%80%9EArbitr%C3%A1ci%C3%B3s_Bizotts%C3%A1g%E2%80%9D_magyar_neve" class="extiw" title="hu:Wikipédia:Szavazás/Az „Arbitrációs Bizottság” magyar neve">here</a> and <a href="https://hu.wikipedia.org/wiki/Sablonvita:B%C5%91vebben/Szavaz%C3%A1s#A_szavazás_módja" class="extiw" title="hu:Sablonvita:Bővebben/Szavazás">here</a>.</span> </li> <li id="cite_note-92"><span class="mw-cite-backlink"><b><a href="#cite_ref-92">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1 cs1-prop-script cs1-prop-foreign-lang-source"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20150222225428/http://y.kalan.cc/schulze"><bdi lang="ru">Девятнадцатые выборы арбитров, второй тур</bdi></a> [Result of Arbitration Committee Elections]. <i>kalan.cc</i> (in Russian). Archived from <a rel="nofollow" class="external text" href="http://y.kalan.cc/schulze">the original</a> on 2015-02-22.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=kalan.cc&rft.atitle=%D0%94%D0%B5%D0%B2%D1%8F%D1%82%D0%BD%D0%B0%D0%B4%D1%86%D0%B0%D1%82%D1%8B%D0%B5+%D0%B2%D1%8B%D0%B1%D0%BE%D1%80%D1%8B+%D0%B0%D1%80%D0%B1%D0%B8%D1%82%D1%80%D0%BE%D0%B2%2C+%D0%B2%D1%82%D0%BE%D1%80%D0%BE%D0%B9+%D1%82%D1%83%D1%80&rft_id=http%3A%2F%2Fy.kalan.cc%2Fschulze&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASchulze+method" class="Z3988"></span></span> </li> <li id="cite_note-93"><span class="mw-cite-backlink"><b><a href="#cite_ref-93">^</a></b></span> <span class="reference-text">See <a class="external text" href="https://fa.wikipedia.org/w/index.php?oldid=18462330">here</a></span> </li> </ol></div> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Schulze_method&action=edit&section=19" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1235681985">.mw-parser-output .side-box{margin:4px 0;box-sizing:border-box;border:1px solid #aaa;font-size:88%;line-height:1.25em;background-color:var(--background-color-interactive-subtle,#f8f9fa);display:flow-root}.mw-parser-output .side-box-abovebelow,.mw-parser-output .side-box-text{padding:0.25em 0.9em}.mw-parser-output .side-box-image{padding:2px 0 2px 0.9em;text-align:center}.mw-parser-output .side-box-imageright{padding:2px 0.9em 2px 0;text-align:center}@media(min-width:500px){.mw-parser-output .side-box-flex{display:flex;align-items:center}.mw-parser-output .side-box-text{flex:1;min-width:0}}@media(min-width:720px){.mw-parser-output .side-box{width:238px}.mw-parser-output .side-box-right{clear:right;float:right;margin-left:1em}.mw-parser-output .side-box-left{margin-right:1em}}</style><style data-mw-deduplicate="TemplateStyles:r1237033735">@media print{body.ns-0 .mw-parser-output .sistersitebox{display:none!important}}@media screen{html.skin-theme-clientpref-night .mw-parser-output .sistersitebox img[src*="Wiktionary-logo-en-v2.svg"]{background-color:white}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .sistersitebox img[src*="Wiktionary-logo-en-v2.svg"]{background-color:white}}</style><div class="side-box side-box-right plainlinks sistersitebox"><style data-mw-deduplicate="TemplateStyles:r1126788409">.mw-parser-output .plainlist ol,.mw-parser-output .plainlist ul{line-height:inherit;list-style:none;margin:0;padding:0}.mw-parser-output .plainlist ol li,.mw-parser-output .plainlist ul li{margin-bottom:0}</style> <div class="side-box-flex"> <div class="side-box-image"><span class="noviewer" typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/30px-Commons-logo.svg.png" decoding="async" width="30" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/45px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/59px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></span></span></div> <div class="side-box-text plainlist">Wikimedia Commons has media related to <a href="https://commons.wikimedia.org/wiki/Schulze_method" class="extiw" title="commons:Schulze method"><span style="font-style:italic; font-weight:bold;">Schulze method</span></a>.</div></div> </div> <ul><li><a href="https://arxiv.org/abs/1804.02973" class="extiw" title="arxiv:1804.02973">The Schulze Method of Voting</a> by Markus Schulze</li> <li><a rel="nofollow" class="external text" href="https://www.youtube.com/watch?v=_HVeN0GnnuA">The Schulze Method</a> by <a href="/wiki/Hubert_Bray" title="Hubert Bray">Hubert Bray</a></li> <li><a rel="nofollow" class="external text" href="http://www.informatik.uni-freiburg.de/~ki/teaching/ss09/gametheory/spieltheorie.pdf">Spieltheorie</a> <span class="languageicon">(in German)</span> by <a href="/wiki/Bernhard_Nebel" title="Bernhard Nebel">Bernhard Nebel</a></li> <li><a rel="nofollow" class="external text" href="http://accuratedemocracy.com/voting_rules.htm">Accurate Democracy</a> by Rob Loring</li> <li>Christoph Börgers (2009), <i><a rel="nofollow" class="external text" href="https://books.google.com/books?id=dccBaphP1G4C&pg=PA37">Mathematics of Social Choice: Voting, Compensation, and Division</a></i>, SIAM, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-89871-695-0" title="Special:BookSources/0-89871-695-0">0-89871-695-0</a></li> <li><a href="/wiki/Nicolaus_Tideman" title="Nicolaus Tideman">Nicolaus Tideman</a> (2006), <i><a rel="nofollow" class="external text" href="https://books.google.com/books?id=RN5q_LuByUoC&pg=PA228">Collective Decisions and Voting: The Potential for Public Choice</a></i>, Burlington: Ashgate, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-7546-4717-X" title="Special:BookSources/0-7546-4717-X">0-7546-4717-X</a></li> <li><a rel="nofollow" class="external text" href="http://www.public-software-group.org/preftools">preftools</a> by the Public Software Group</li> <li><a rel="nofollow" class="external text" href="http://apps.azsos.gov/election/2008/general/ballotmeasuretext/I-21-2008.pdf">Arizonans for Condorcet Ranked Voting</a></li> <li><a rel="nofollow" class="external text" href="https://github.com/julien-boudry/Condorcet">Condorcet PHP</a> Command line application and <a href="/wiki/PHP" title="PHP">PHP</a> <a href="/wiki/Library_(computing)" title="Library (computing)">library</a>, supporting multiple Condorcet methods, including Schulze.</li> <li><a rel="nofollow" class="external text" href="https://github.com/zephyr/schulze-voting">Implementation in Java</a></li> <li><a rel="nofollow" class="external text" href="https://github.com/coorasse/schulze-vote">Implementation in Ruby</a></li> <li><a rel="nofollow" class="external text" href="https://github.com/bradbeattie/python-vote-core">Implementation in Python 2</a></li> <li><a rel="nofollow" class="external text" href="https://github.com/woctezuma/schulze-method">Implementation in Python 3</a></li></ul> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><style 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.navbox-image img{max-width:none!important}@media print{body.ns-0 .mw-parser-output .navbox{display:none!important}}</style></div><div role="navigation" class="navbox" aria-labelledby="Electoral_systems" style="padding:3px"><table class="nowraplinks mw-collapsible mw-collapsed navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Electoral_systems_footer" title="Template:Electoral systems footer"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Electoral_systems_footer" title="Template talk:Electoral systems footer"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Electoral_systems_footer" title="Special:EditPage/Template:Electoral systems footer"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Electoral_systems" style="font-size:114%;margin:0 4em"><a href="/wiki/Electoral_system" title="Electoral system">Electoral systems</a></div></th></tr><tr><td class="navbox-abovebelow" colspan="2"><div><i>Part of the <a href="/wiki/Portal:Politics" title="Portal:Politics">politics</a> and <a href="/wiki/Portal:Economics" title="Portal:Economics">Economics</a> series</i></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Single-winner_voting_system" class="mw-redirect" title="Single-winner voting system">Single-winner</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Approval_voting" title="Approval voting">Approval voting</a> <ul><li><a href="/wiki/Combined_approval_voting" title="Combined approval voting">Combined approval voting</a></li> <li><a href="/wiki/Unified_primary" title="Unified primary">Unified primary</a></li></ul></li> <li><a href="/wiki/Borda_count" title="Borda count">Borda count</a></li> <li><a href="/wiki/Bucklin_voting" title="Bucklin voting">Bucklin voting</a></li> <li><a href="/wiki/Condorcet_methods" class="mw-redirect" title="Condorcet methods">Condorcet methods</a> <ul><li><a href="/wiki/Copeland%27s_method" title="Copeland's method">Copeland's method</a></li> <li><a href="/wiki/Dodgson%27s_method" title="Dodgson's method">Dodgson's method</a></li> <li><a href="/wiki/Kemeny%E2%80%93Young_method" title="Kemeny–Young method">Kemeny–Young method</a></li> <li><a href="/wiki/Minimax_Condorcet_method" title="Minimax Condorcet method">Minimax Condorcet method</a></li> <li><a href="/wiki/Nanson%27s_method" title="Nanson's method">Nanson's method</a></li> <li><a href="/wiki/Ranked_pairs" title="Ranked pairs">Ranked pairs</a></li> <li><a class="mw-selflink selflink">Schulze method</a></li></ul></li> <li><a href="/wiki/Exhaustive_ballot" title="Exhaustive ballot">Exhaustive ballot</a></li> <li><a href="/wiki/First-past-the-post_voting" title="First-past-the-post voting">First-past-the-post voting</a></li> <li><a href="/wiki/Instant-runoff_voting" title="Instant-runoff voting">Instant-runoff voting</a> <ul><li><a href="/wiki/Coombs%27_method" title="Coombs' method">Coombs' method</a></li> <li><a href="/wiki/Contingent_vote" title="Contingent vote">Contingent vote</a></li> <li><a href="/wiki/Supplementary_vote" class="mw-redirect" title="Supplementary vote">Supplementary vote</a></li></ul></li> <li><a href="/wiki/Majority_rule" title="Majority rule">Simple majoritarianism</a></li> <li><a href="/wiki/Plurality_voting_system" class="mw-redirect" title="Plurality voting system">Plurality</a></li> <li><a href="/wiki/Positional_voting_system" class="mw-redirect" title="Positional voting system">Positional voting system</a></li> <li><a href="/wiki/Score_voting" title="Score voting">Score voting</a></li> <li><a href="/wiki/STAR_voting" title="STAR voting">STAR voting</a></li> <li><a href="/wiki/Two-round_system" title="Two-round system">Two-round system</a></li> <li><a href="/wiki/Graduated_majority_judgment" title="Graduated majority judgment">Graduated majority judgment</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Proportional_representation" title="Proportional representation">Proportional</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%">Systems</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Mixed-member_proportional_representation" title="Mixed-member proportional representation">Mixed-member</a></li> <li><a href="/wiki/Mixed_single_vote#Proportional_systems" title="Mixed single vote">Mixed single vote</a></li> <li><a href="/wiki/Party-list_proportional_representation" title="Party-list proportional representation">Party-list</a></li> <li><a href="/wiki/Proportional_approval_voting" title="Proportional approval voting">Proportional approval voting</a></li> <li><a href="/wiki/Rural%E2%80%93urban_proportional_representation" title="Rural–urban proportional representation">Rural–urban</a></li> <li><a href="/wiki/Sequential_proportional_approval_voting" title="Sequential proportional approval voting">Sequential proportional approval voting</a></li> <li><a href="/wiki/Single_transferable_vote" title="Single transferable vote">Single transferable vote</a> <ul><li><a href="/wiki/CPO-STV" title="CPO-STV">CPO-STV</a></li> <li><a href="/wiki/Hare%E2%80%93Clark_electoral_system" title="Hare–Clark electoral system">Hare-Clark</a></li> <li><a href="/wiki/Schulze_STV" title="Schulze STV">Schulze STV</a></li></ul></li> <li><a href="/wiki/Spare_vote" title="Spare vote">Spare vote</a></li> <li><a href="/wiki/Indirect_single_transferable_voting" title="Indirect single transferable voting">Indirect single transferable voting</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Allocation</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Highest_averages_method" title="Highest averages method">Highest averages method</a> <ul><li><a href="/wiki/Sainte-Lagu%C3%AB_method" title="Sainte-Laguë method">Webster/Sainte-Laguë</a></li> <li><a href="/wiki/D%27Hondt_method" title="D'Hondt method">D'Hondt</a></li></ul></li> <li><a href="/wiki/Largest_remainders_method" class="mw-redirect" title="Largest remainders method">Largest remainders method</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Quotas</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Droop_quota" title="Droop quota">Droop quota</a></li> <li><a href="/wiki/Hagenbach-Bischoff_quota" class="mw-redirect" title="Hagenbach-Bischoff quota">Hagenbach-Bischoff quota</a></li> <li><a href="/wiki/Hare_quota" title="Hare quota">Hare quota</a></li> <li><a href="/wiki/Imperiali_quota" title="Imperiali quota">Imperiali quota</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Mixed_electoral_system" title="Mixed electoral system">Mixed</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Parallel_voting" title="Parallel voting">Parallel voting</a></li> <li><a href="/wiki/Mixed-member_proportional_representation" title="Mixed-member proportional representation">MMP</a></li> <li><a href="/wiki/Additional_member_system" class="mw-redirect" title="Additional member system">Additional member system</a></li> <li><a href="/wiki/Alternative_vote_plus" title="Alternative vote plus">Alternative vote plus</a></li> <li><a href="/wiki/Mixed_single_vote" title="Mixed single vote">Mixed single vote</a></li> <li><a href="/wiki/Mixed_ballot_transferable_vote" title="Mixed ballot transferable vote">Mixed ballot transferable vote</a></li> <li><a href="/wiki/Scorporo" title="Scorporo">Scorporo</a></li> <li><a href="/wiki/Vote_linkage_mixed_system" class="mw-redirect" title="Vote linkage mixed system">Vote linkage mixed system</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Semi-proportional_representation" title="Semi-proportional representation">Semi-proportional</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Single_non-transferable_vote" title="Single non-transferable vote">Single non-transferable vote</a></li> <li><a href="/wiki/Limited_voting" title="Limited voting">Limited voting</a></li> <li><a href="/wiki/Cumulative_voting" title="Cumulative voting">Cumulative voting</a></li> <li><a href="/wiki/Satisfaction_approval_voting" title="Satisfaction approval voting">Satisfaction approval voting</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Criteria</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Condorcet_winner_criterion" title="Condorcet winner criterion">Condorcet winner criterion</a></li> <li><a href="/wiki/Condorcet_loser_criterion" title="Condorcet loser criterion">Condorcet loser criterion</a></li> <li><a href="/wiki/Consistency_criterion" class="mw-redirect" title="Consistency criterion">Consistency criterion</a></li> <li><a href="/wiki/Independence_of_clones_criterion" title="Independence of clones criterion">Independence of clones</a></li> <li><a href="/wiki/Independence_of_irrelevant_alternatives" title="Independence of irrelevant alternatives">Independence of irrelevant alternatives</a></li> <li><a href="/wiki/Independence_of_Smith-dominated_alternatives" title="Independence of Smith-dominated alternatives">Independence of Smith-dominated alternatives</a></li> <li><a href="/wiki/Later-no-harm_criterion" title="Later-no-harm criterion">Later-no-harm criterion</a></li> <li><a href="/wiki/Majority_favorite_criterion" class="mw-redirect" title="Majority favorite criterion">Majority criterion</a></li> <li><a href="/wiki/Majority_loser_criterion" title="Majority loser criterion">Majority loser criterion</a></li> <li><a href="/wiki/Monotonicity_criterion" class="mw-redirect" title="Monotonicity criterion">Monotonicity criterion</a></li> <li><a href="/wiki/Mutual_majority_criterion" title="Mutual majority criterion">Mutual majority criterion</a></li> <li><a href="/wiki/Participation_criterion" class="mw-redirect" title="Participation criterion">Participation criterion</a></li> <li><a href="/wiki/Plurality_criterion" title="Plurality criterion">Plurality criterion</a></li> <li><a href="/wiki/Resolvability_criterion" title="Resolvability criterion">Resolvability criterion</a></li> <li><a href="/wiki/Reversal_symmetry" class="mw-redirect" title="Reversal symmetry">Reversal symmetry</a></li> <li><a href="/wiki/Smith_criterion" class="mw-redirect" title="Smith criterion">Smith criterion</a></li> <li><a href="/wiki/Seats-to-votes_ratio" title="Seats-to-votes ratio">Seats-to-votes ratio</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Other</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Ballot" title="Ballot">Ballot</a></li> <li><a href="/wiki/Election_threshold" class="mw-redirect" title="Election threshold">Election threshold</a></li> <li><a href="/wiki/First-preference_votes" title="First-preference votes">First-preference votes</a></li> <li><a href="/wiki/Liquid_democracy" title="Liquid democracy">Liquid democracy</a></li> <li><a href="/wiki/Spoilt_vote" title="Spoilt vote">Spoilt vote</a></li> <li><a href="/wiki/Sortition" title="Sortition">Sortition</a></li> <li><a href="/wiki/Unseating" title="Unseating">Unseating</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Comparison</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Comparison_of_electoral_systems" class="mw-redirect" title="Comparison of electoral systems">Comparison of voting systems</a></li> <li><a href="/wiki/List_of_electoral_systems_by_country" title="List of electoral systems by country">Voting systems by country</a></li></ul> </div></td></tr><tr><td class="navbox-abovebelow" colspan="2"><div><b><a href="/wiki/Portal:Politics" title="Portal:Politics">Portal</a></b> — <b><a href="/wiki/Wikipedia:WikiProject_Politics" title="Wikipedia:WikiProject Politics">Project</a></b></div></td></tr></tbody></table></div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Retrieved from "<a dir="ltr" href="https://en.wikipedia.org/w/index.php?title=Schulze_method&oldid=1256500949">https://en.wikipedia.org/w/index.php?title=Schulze_method&oldid=1256500949</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div 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