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class="vector-toc-link" href="#Elections_as_estimation_procedures"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>Elections as estimation procedures</span> </div> </a> <ul id="toc-Elections_as_estimation_procedures-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Effect_of_irrelevant_candidates" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Effect_of_irrelevant_candidates"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2</span> <span>Effect of irrelevant candidates</span> </div> </a> <ul id="toc-Effect_of_irrelevant_candidates-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Other_properties" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Other_properties"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.3</span> <span>Other properties</span> </div> </a> <ul id="toc-Other_properties-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Equal_ranks" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Equal_ranks"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Equal ranks</span> </div> </a> <button aria-controls="toc-Equal_ranks-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 Equal ranks subsection</span> </button> <ul id="toc-Equal_ranks-sublist" class="vector-toc-list"> <li id="toc-Effects_on_strategy" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Effects_on_strategy"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1</span> <span>Effects on strategy</span> </div> </a> <ul id="toc-Effects_on_strategy-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Forced_truncation" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Forced_truncation"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2</span> <span>Forced truncation</span> </div> </a> <ul id="toc-Forced_truncation-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Multiple_winners" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Multiple_winners"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Multiple winners</span> </div> </a> <ul id="toc-Multiple_winners-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Related_systems" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Related_systems"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Related systems</span> </div> </a> <ul id="toc-Related_systems-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Potential_for_tactical_manipulation" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Potential_for_tactical_manipulation"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Potential for tactical manipulation</span> </div> </a> <button aria-controls="toc-Potential_for_tactical_manipulation-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 Potential for tactical manipulation subsection</span> </button> <ul id="toc-Potential_for_tactical_manipulation-sublist" class="vector-toc-list"> <li id="toc-Tactical_voting" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Tactical_voting"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.1</span> <span>Tactical voting</span> </div> </a> <ul id="toc-Tactical_voting-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Strategic_nomination" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Strategic_nomination"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.2</span> <span>Strategic nomination</span> </div> </a> <ul id="toc-Strategic_nomination-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Example" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Example"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Example</span> </div> </a> <button aria-controls="toc-Example-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 Example subsection</span> </button> <ul id="toc-Example-sublist" class="vector-toc-list"> <li id="toc-Dowdall" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Dowdall"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.1</span> <span>Dowdall</span> </div> </a> <ul id="toc-Dowdall-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Current_uses" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Current_uses"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>Current uses</span> </div> </a> <button aria-controls="toc-Current_uses-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 Current uses subsection</span> </button> <ul id="toc-Current_uses-sublist" class="vector-toc-list"> <li id="toc-Political_uses" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Political_uses"> <div class="vector-toc-text"> <span class="vector-toc-numb">8.1</span> <span>Political uses</span> </div> </a> <ul id="toc-Political_uses-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Other_uses" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Other_uses"> <div class="vector-toc-text"> <span class="vector-toc-numb">8.2</span> <span>Other uses</span> </div> </a> <ul id="toc-Other_uses-sublist" class="vector-toc-list"> <li id="toc-Sports_awards" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Sports_awards"> <div class="vector-toc-text"> <span class="vector-toc-numb">8.2.1</span> <span>Sports awards</span> </div> </a> <ul id="toc-Sports_awards-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-In_information_retrieval" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#In_information_retrieval"> <div class="vector-toc-text"> <span class="vector-toc-numb">8.3</span> <span>In information retrieval</span> </div> </a> <ul id="toc-In_information_retrieval-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Analogy_with_sporting_tournaments" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Analogy_with_sporting_tournaments"> <div class="vector-toc-text"> <span class="vector-toc-numb">8.4</span> <span>Analogy with sporting tournaments</span> </div> </a> <ul id="toc-Analogy_with_sporting_tournaments-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-History" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#History"> <div class="vector-toc-text"> <span class="vector-toc-numb">9</span> <span>History</span> </div> </a> <ul id="toc-History-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">10</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Notes" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Notes"> <div class="vector-toc-text"> <span class="vector-toc-numb">11</span> <span>Notes</span> </div> </a> <ul id="toc-Notes-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">12</span> <span>References</span> </div> </a> <button aria-controls="toc-References-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 References subsection</span> </button> <ul id="toc-References-sublist" class="vector-toc-list"> <li id="toc-Works_cited" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Works_cited"> <div class="vector-toc-text"> <span class="vector-toc-numb">12.1</span> <span>Works cited</span> </div> </a> <ul id="toc-Works_cited-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Further_reading" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Further_reading"> <div class="vector-toc-text"> <span class="vector-toc-numb">13</span> <span>Further reading</span> </div> </a> <ul id="toc-Further_reading-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> <span class="vector-toc-numb">14</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" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" title="Table of Contents" > <input type="checkbox" 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Available in 17 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-17" 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">17 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Bordovo_hlasov%C3%A1n%C3%AD" title="Bordovo hlasování – Czech" lang="cs" hreflang="cs" data-title="Bordovo hlasování" 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/Borda-Wahl" title="Borda-Wahl – German" lang="de" hreflang="de" data-title="Borda-Wahl" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Cuenta_de_Borda" title="Cuenta de Borda – Spanish" lang="es" hreflang="es" data-title="Cuenta de Borda" 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%B4%D9%85%D8%A7%D8%B1%D8%B4_%D8%A8%D9%88%D8%B1%D8%AF%D8%A7" title="شمارش بوردا – Persian" lang="fa" hreflang="fa" data-title="شمارش بوردا" 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_Borda" title="Méthode Borda – French" lang="fr" hreflang="fr" data-title="Méthode Borda" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Hitungan_borda" title="Hitungan borda – Indonesian" lang="id" hreflang="id" data-title="Hitungan borda" 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_Borda" title="Metodo Borda – Italian" lang="it" hreflang="it" data-title="Metodo Borda" 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%91%D7%95%D7%A8%D7%93%D7%94" title="שיטת בורדה – Hebrew" lang="he" hreflang="he" data-title="שיטת בורדה" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-ne mw-list-item"><a href="https://ne.wikipedia.org/wiki/%E0%A4%AA%E0%A5%8D%E0%A4%B0%E0%A4%BE%E0%A4%A5%E0%A4%AE%E0%A4%BF%E0%A4%95%E0%A4%A4%E0%A4%BE_%E0%A4%97%E0%A4%A3%E0%A4%A8%E0%A4%BE" title="प्राथमिकता गणना – Nepali" lang="ne" hreflang="ne" data-title="प्राथमिकता गणना" data-language-autonym="नेपाली" data-language-local-name="Nepali" class="interlanguage-link-target"><span>नेपाली</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E3%83%9C%E3%83%AB%E3%83%80%E5%BE%97%E7%82%B9" title="ボルダ得点 – Japanese" lang="ja" hreflang="ja" data-title="ボルダ得点" 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-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Bordavalg" title="Bordavalg – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Bordavalg" data-language-autonym="Norsk bokmål" data-language-local-name="Norwegian Bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Metoda_Bordy" title="Metoda Bordy – Polish" lang="pl" hreflang="pl" data-title="Metoda Bordy" 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/Contagem_de_Borda" title="Contagem de Borda – Portuguese" lang="pt" hreflang="pt" data-title="Contagem de Borda" 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%91%D0%BE%D1%80%D0%B4%D0%B0" title="Метод Борда – Russian" lang="ru" hreflang="ru" data-title="Метод Борда" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Bordar%C3%A4kning" title="Bordaräkning – Swedish" lang="sv" hreflang="sv" data-title="Bordaräkning" data-language-autonym="Svenska" data-language-local-name="Swedish" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Borda_kural%C4%B1" title="Borda kuralı – Turkish" lang="tr" hreflang="tr" data-title="Borda kuralı" data-language-autonym="Türkçe" data-language-local-name="Turkish" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E6%B3%A2%E9%81%94%E8%A8%88%E6%95%B8%E6%B3%95" title="波達計數法 – Chinese" lang="zh" hreflang="zh" data-title="波達計數法" data-language-autonym="中文" data-language-local-name="Chinese" class="interlanguage-link-target"><span>中文</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/Q576578#sitelinks-wikipedia" title="Edit interlanguage links" class="wbc-editpage">Edit links</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="Namespaces"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" 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.sidebar-title-with-pretitle a{color:var(--color-progressive)!important}}@media print{body.ns-0 .mw-parser-output .sidebar{display:none!important}}</style><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><table class="sidebar 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><span class="nowrap"> </span>(<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_primary" title="Nonpartisan 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 href="/wiki/Schulze_method" title="Schulze method">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 class="mw-selflink selflink">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 href="/wiki/Center_squeeze" title="Center squeeze">Center squeeze</a></li></ul> <hr /> <p><b>Pathological response</b> </p> <ul><li><a href="/wiki/Perverse_response" class="mw-redirect" title="Perverse response">Perverse response</a></li> <li><a href="/wiki/Best-is-worst_paradox" title="Best-is-worst paradox">Best-is-worst paradox</a></li> <li><a href="/wiki/No-show_paradox" title="No-show paradox">No-show paradox</a> <ul><li><a href="/wiki/Multiple_districts_paradox" title="Multiple districts paradox">Multiple districts paradox</a></li></ul></li></ul> <hr /> <p><b><a href="/wiki/Strategic_voting" title="Strategic voting">Strategic voting</a></b> </p> <ul><li><a href="/wiki/Sincere_favorite_criterion" title="Sincere favorite criterion">Lesser evil voting</a></li> <li><a href="/wiki/Strategic_voting#Exaggeration" title="Strategic voting">Exaggeration</a></li> <li><a href="/wiki/Truncation_(voting)" class="mw-redirect" title="Truncation (voting)">Truncation</a></li> <li><a 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 href="/wiki/May%27s_theorem" title="May's theorem">May's theorem</a></li> <li><a href="/wiki/Arrow%27s_theorem#Minimizing" class="mw-redirect" title="Arrow's theorem">Condorcet dominance theorems</a></li> <li><a href="/w/index.php?title=Harsanyi%27s_utilitarian_theorem&action=edit&redlink=1" class="new" title="Harsanyi's utilitarian theorem (page does not exist)">Harsanyi's utilitarian theorem</a></li> <li><a href="/wiki/Vickrey-Clarke-Groves_mechanism" class="mw-redirect" title="Vickrey-Clarke-Groves mechanism">VCG mechanism</a></li> <li><a href="/wiki/Quadratic_voting" title="Quadratic voting">Quadratic voting</a></li></ul></div></div></td> </tr><tr><td class="sidebar-below" style="background: var(--background-color-interactive, #efefef); color: inherit; padding-top:0.2em;"> <div class="hlist"><ul><li><span class="nowrap"><span class="mw-image-border noviewer" typeof="mw:File"><a href="/wiki/File:A_coloured_voting_box.svg" class="mw-file-description"><img alt="icon" src="//upload.wikimedia.org/wikipedia/en/thumb/0/01/A_coloured_voting_box.svg/16px-A_coloured_voting_box.svg.png" decoding="async" width="16" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/0/01/A_coloured_voting_box.svg/24px-A_coloured_voting_box.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/0/01/A_coloured_voting_box.svg/32px-A_coloured_voting_box.svg.png 2x" data-file-width="160" data-file-height="160" /></a></span> </span><a href="/wiki/Portal:Politics" title="Portal:Politics">Politics portal</a></li><li><span class="nowrap"><span class="noviewer" typeof="mw:File"><a 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srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Nuvola_apps_edu_mathematics_blue-p.svg/24px-Nuvola_apps_edu_mathematics_blue-p.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Nuvola_apps_edu_mathematics_blue-p.svg/32px-Nuvola_apps_edu_mathematics_blue-p.svg.png 2x" data-file-width="128" data-file-height="128" /></a></span> </span><a href="/wiki/Portal:Mathematics" title="Portal:Mathematics">Mathematics portal</a></td></tr><tr><td class="sidebar-navbar"><link rel="mw-deduplicated-inline-style" 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>Borda method</b> or <b>order of merit</b> is a <a href="/wiki/Positional_voting" title="Positional voting">positional voting</a> rule that gives each candidate a number of points equal to the number of candidates <a href="/wiki/Ranked_voting" title="Ranked voting">ranked</a> below them: the lowest-ranked candidate gets 0 points, the second-lowest gets 1 point, and so on. The candidate with the most points wins. </p><p>The Borda count has been independently reinvented several times, with the first recorded proposal in 1435 being by <a href="/wiki/Nicholas_of_Cusa#Politics" title="Nicholas of Cusa">Nicholas of Cusa</a> (see <a href="#History">History</a> below),<sup id="cite_ref-Emerson_2016_1-0" class="reference"><a href="#cite_note-Emerson_2016-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-:2_2-0" class="reference"><a href="#cite_note-:2-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> but is named after the 18th-century French mathematician and naval engineer <a href="/wiki/Jean-Charles_de_Borda" title="Jean-Charles de Borda">Jean-Charles de Borda</a>, who devised the system in 1770.<sup id="cite_ref-FOOTNOTEMcLeanUrkenHewitt199581_3-0" class="reference"><a href="#cite_note-FOOTNOTEMcLeanUrkenHewitt199581-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> </p><p>The Borda count is well-known in <a href="/wiki/Social_choice_theory" title="Social choice theory">social choice theory</a> both for its pleasant theoretical properties and its ease of manipulation. In the absence of <a href="/wiki/Strategic_voting" title="Strategic voting">strategic voting</a> and <a href="/wiki/Strategic_nomination" title="Strategic nomination">strategic nomination</a>, the Borda count tends to elect broadly-acceptable options or candidates (rather than consistently following the preferences of a majority);<sup id="cite_ref-Lippman_4-0" class="reference"><a href="#cite_note-Lippman-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> when both voting and nomination patterns are completely random, the Borda count generally has an exceptionally high <a href="/wiki/Social_utility_efficiency" title="Social utility efficiency">social utility efficiency</a>.<sup id="cite_ref-:0_5-0" class="reference"><a href="#cite_note-:0-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> However, the method is highly vulnerable to <a href="/wiki/Spoiler_effect" title="Spoiler effect">spoiler effects</a> when there are clusters of similar candidates; because the effects of more candidates on the election are unbounded, it is possible for any political party to win an election by running enough <a href="/wiki/Independence_of_clones" class="mw-redirect" title="Independence of clones">clones</a>.<sup id="cite_ref-:0_5-1" class="reference"><a href="#cite_note-:0-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> Common implementations of <a href="/wiki/Tied_rank" class="mw-redirect" title="Tied rank">equal-rank</a> or <a href="/w/index.php?title=Truncated_ballot&action=edit&redlink=1" class="new" title="Truncated ballot (page does not exist)">truncated ballots</a> can also incentivize extreme <a href="/wiki/Strategic_voting#Burial" title="Strategic voting">burial</a> when voters are strategic, which allows deeply unpopular <a href="/wiki/Dark_horse" title="Dark horse">dark horse</a> candidates to win by avoiding any attention.<sup id="cite_ref-:02_7-0" class="reference"><a href="#cite_note-:02-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> </p><p>The traditional Borda method is currently used to elect two ethnic minority members of the <a href="/wiki/National_Assembly_of_Slovenia" class="mw-redirect" title="National Assembly of Slovenia">National Assembly of Slovenia</a>,<sup id="cite_ref-:1_10-0" class="reference"><a href="#cite_note-:1-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> in modified forms to determine which candidates are elected to the party list seats in <a href="/wiki/Icelandic_parliamentary_election,_2013#Constituencies" class="mw-redirect" title="Icelandic parliamentary election, 2013">Icelandic parliamentary elections</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. (August 2024)">citation needed</span></a></i>]</sup> and for selecting presidential election candidates in <a href="/wiki/Kiribati" title="Kiribati">Kiribati</a>.<sup id="cite_ref-Reilly2002_11-0" class="reference"><a href="#cite_note-Reilly2002-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> A variant known as the <a href="#Dowdall">Dowdall system</a> is used to elect members of the <a href="/wiki/Parliament_of_Nauru" title="Parliament of Nauru">Parliament of Nauru</a>.<sup id="cite_ref-Fraenkel_Grofman_2014_12-0" class="reference"><a href="#cite_note-Fraenkel_Grofman_2014-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> Until the early 1970s, another variant was used in Finland to select individual candidates within party lists.<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. (August 2024)">citation needed</span></a></i>]</sup> It is also widely used throughout the world by various private organizations and competitions. </p><p> The <a href="/wiki/Quota_Borda_system" title="Quota Borda system">Quota Borda system</a> is a proportional <a href="/wiki/Multiwinner_voting" title="Multiwinner voting">multiwinner</a> variant. <style data-mw-deduplicate="TemplateStyles:r886046785">.mw-parser-output .toclimit-2 .toclevel-1 ul,.mw-parser-output .toclimit-3 .toclevel-2 ul,.mw-parser-output .toclimit-4 .toclevel-3 ul,.mw-parser-output .toclimit-5 .toclevel-4 ul,.mw-parser-output .toclimit-6 .toclevel-5 ul,.mw-parser-output .toclimit-7 .toclevel-6 ul{display:none}</style></p><div class="toclimit-3"><meta property="mw:PageProp/toc" /></div> <div class="mw-heading mw-heading2"><h2 id="Voting_and_counting">Voting and counting</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Borda_count&action=edit&section=1" title="Edit section: Voting and counting"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Ballot">Ballot</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Borda_count&action=edit&section=2" title="Edit section: Ballot"><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></figcaption></figure> <p>The Borda count is a <a href="/wiki/Ranked_voting" title="Ranked voting">ranked voting</a> system: the voter ranks the list of candidates in order of preference. So, for example, the voter gives a <i>1</i> to their most preferred candidate, a <i>2</i> to their second most preferred, and so on. In this respect, it is similar to other ranked voting systems such as <a href="/wiki/Instant-runoff_voting" title="Instant-runoff voting">instant-runoff voting</a>, the <a href="/wiki/Single_transferable_vote" title="Single transferable vote">single transferable vote</a> or <a href="/wiki/Condorcet_method" title="Condorcet method">Condorcet methods</a>. The integer-valued ranks for evaluating the candidates were justified by <a href="/wiki/Laplace" class="mw-redirect" title="Laplace">Laplace</a>, who used a probabilistic model based on the <a href="/wiki/Law_of_large_numbers" title="Law of large numbers">law of large numbers</a>. </p><p>The Borda count is classified as a <a href="/wiki/Positional_voting_system" class="mw-redirect" title="Positional voting system">positional voting system</a>, that is, all preferences are counted but at different values. The other commonly-used positional system is <a href="/wiki/Plurality_voting" title="Plurality voting">plurality voting</a>, which only assigns one point to the top candidate. </p><p>Each candidate is assigned a number of points from each ballot equal to the number of candidates to whom he or she is preferred, so that with <i>n</i> candidates, each one receives <i>n</i> – 1 points for a first preference, <i>n</i> – 2 for a second, and so on.<sup id="cite_ref-Black_1987_13-0" class="reference"><a href="#cite_note-Black_1987-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> The winner is the candidate with the largest total number of points. For example, in a four-candidate election, the number of points assigned for the preferences expressed by a voter on a single ballot paper might be: </p> <table class="wikitable"> <tbody><tr> <th>Ranking</th> <th>Candidate</th> <th>Formula</th> <th>Points </th></tr> <tr> <th>1st </th> <td>Andrew</td> <td><i>n</i> − 1</td> <td><b>3</b> </td></tr> <tr> <th>2nd </th> <td>Brian</td> <td><i>n</i> − 2</td> <td><b>2</b> </td></tr> <tr> <th>3rd </th> <td>Catherine</td> <td><i>n</i> − 3</td> <td><b>1</b> </td></tr> <tr> <th>4th </th> <td>David</td> <td><i>n</i> − 4</td> <td><b>0</b> </td></tr></tbody></table> <p>Suppose that there are 3 voters, <i>U</i>, <i>V</i> and <i>W</i>, of whom <i>U</i> and <i>V</i> rank the candidates in the order A-B-C-D while <i>W</i> ranks them B-C-D-A. </p> <table class="wikitable"> <tbody><tr> <th>Candidate</th> <th><i>U</i> Points</th> <th><i>V Points</i></th> <th><i>W</i> points</th> <th>Total </th></tr> <tr> <td>Andrew</td> <td>3</td> <td>3</td> <td>0</td> <td>6 </td></tr> <tr> <td>Brian</td> <td>2</td> <td>2</td> <td>3</td> <td>7 </td></tr> <tr> <td>Catherine</td> <td>1</td> <td>1</td> <td>2</td> <td>4 </td></tr> <tr> <td>David</td> <td>0</td> <td>0</td> <td>1</td> <td>1 </td></tr></tbody></table> <p>Thus Brian is elected. </p><p>A longer example, based on a fictitious election for Tennessee state capital, is shown <a href="#tennessee">below</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Properties">Properties</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Borda_count&action=edit&section=3" title="Edit section: Properties"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Elections_as_estimation_procedures">Elections as estimation procedures</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Borda_count&action=edit&section=4" title="Edit section: Elections as estimation procedures"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/Marquis_de_Condorcet" title="Marquis de Condorcet">Condorcet</a> looked at an election as an attempt to combine estimators. Suppose that each candidate has a figure of merit and that each voter has a noisy estimate of the value of each candidate. The ballot paper allows the voter to rank the candidates in order of estimated merit. The aim of the election is to produce a combined estimate of the best candidate. Such an estimator can be more reliable than any of its individual components.<sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> </p><p><a href="/wiki/Peyton_Young" title="Peyton Young">Peyton Young</a> showed that the Borda count gives an approximately <a href="/wiki/Maximum_likelihood_estimation" title="Maximum likelihood estimation">maximum likelihood estimator</a> of the best candidate.<sup id="cite_ref-:0_5-2" class="reference"><a href="#cite_note-:0-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> His theorem assumes that errors are independent, in other words, that if a voter rates a particular candidate highly, then there is no reason to expect her to rate "similar" candidates highly. If this property is absent – if the voter gives correlated rankings to candidates with shared attributes – then the maximum likelihood property is lost, and the Borda count is highly subject to <a href="/wiki/Spoiler_effect" title="Spoiler effect">nomination effects</a>: a candidate is more likely to be elected if there are similar candidates on the ballot. </p> <div class="mw-heading mw-heading3"><h3 id="Effect_of_irrelevant_candidates">Effect of irrelevant candidates<span class="anchor" id="irrelevant"></span></h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Borda_count&action=edit&section=5" title="Edit section: Effect of irrelevant candidates"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-halign-right" typeof="mw:File"><a href="/wiki/File:Borda_(dependence_on_irrelevant_alternatives).png" class="mw-file-description" title="An election under the Borda count"><img alt="An election under the Borda count" src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d0/Borda_%28dependence_on_irrelevant_alternatives%29.png/455px-Borda_%28dependence_on_irrelevant_alternatives%29.png" decoding="async" width="455" height="170" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d0/Borda_%28dependence_on_irrelevant_alternatives%29.png/683px-Borda_%28dependence_on_irrelevant_alternatives%29.png 1.5x, //upload.wikimedia.org/wikipedia/commons/d/d0/Borda_%28dependence_on_irrelevant_alternatives%29.png 2x" data-file-width="910" data-file-height="340" /></a><figcaption>An election under the Borda count</figcaption></figure> <p>The Borda count is particularly susceptible to distortion through the presence of candidates who do not themselves come into consideration, even when the voters lie along a spectrum. Voting systems which satisfy the <a href="/wiki/Condorcet_criterion" class="mw-redirect" title="Condorcet criterion">Condorcet criterion</a> are protected against this weakness since they automatically also satisfy the <a href="/wiki/Median_voter_theorem" title="Median voter theorem">median voter theorem</a>, which says that the winner of an election will be the candidate preferred by the median voter regardless of which other candidates stand. </p><p>Suppose that there are 11 voters whose positions along the spectrum can be written 0, 1, ..., 10, and suppose that there are 2 candidates, Andrew and Brian, whose positions are as shown: </p> <table class="wikitable"> <tbody><tr> <th>Candidate </th> <td>A </td> <td>B </td></tr> <tr> <th>Position </th> <td>5<style data-mw-deduplicate="TemplateStyles:r1154941027">.mw-parser-output .frac{white-space:nowrap}.mw-parser-output .frac .num,.mw-parser-output .frac .den{font-size:80%;line-height:0;vertical-align:super}.mw-parser-output .frac .den{vertical-align:sub}.mw-parser-output .sr-only{border:0;clip:rect(0,0,0,0);clip-path:polygon(0px 0px,0px 0px,0px 0px);height:1px;margin:-1px;overflow:hidden;padding:0;position:absolute;width:1px}</style><span class="frac"><span class="num">1</span>⁄<span class="den">4</span></span> </td> <td>6<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027"><span class="frac"><span class="num">1</span>⁄<span class="den">4</span></span> </td></tr></tbody></table> <p>The median voter Marlene is at position 5, and both candidates are to her right, so we would expect A to be elected. We can verify this for the Borda system by constructing a table to illustrate the count. The main part of the table shows the voters who prefer the first to the second candidate, as given by the row and column headings, while the additional column to the right gives the scores for the first candidate. </p> <table class="wikitable" style="border:none"> <tbody><tr> <th style="background:var(--background-color-neutral,#eaecf0);color:inherit;background:linear-gradient(to top right,var(--background-color-neutral,#eaecf0) 49%,var(--border-color-base,#a2a9b1) 49.5%,var(--border-color-base,#a2a9b1) 50.5%,var(--background-color-neutral,#eaecf0) 51%);line-height:1.2;padding:0.1em 0.4em;"><div style="margin-left:2em;text-align:right">2nd</div><div style="margin-right:2em;text-align:left">1st</div> </th> <th>A</th> <th>B </th> <td rowspan="3" style="border: none; background: white;"> </td> <th>score </th></tr> <tr> <th>A </th> <td data-sort-value="" style="vertical-align:middle; text-align:center" class="table-na">—</td> <td>0–5</td> <td>6 </td></tr> <tr> <th>B </th> <td>6–10</td> <td data-sort-value="" style="vertical-align:middle; text-align:center" class="table-na">—</td> <td>5 </td></tr></tbody></table> <p>A is indeed elected. </p><p>But now suppose that two additional candidates, further to the right, enter the election. </p> <table class="wikitable"> <tbody><tr> <th>Candidate </th> <td>A </td> <td>B </td> <td>C </td> <td>D </td></tr> <tr> <th>Position </th> <td>5<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027"><span class="frac"><span class="num">1</span>⁄<span class="den">4</span></span> </td> <td>6<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027"><span class="frac"><span class="num">1</span>⁄<span class="den">4</span></span> </td> <td>8<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027"><span class="frac"><span class="num">1</span>⁄<span class="den">4</span></span> </td> <td>10<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027"><span class="frac"><span class="num">1</span>⁄<span class="den">4</span></span> </td></tr></tbody></table> <p>The counting table expands as follows: </p> <table class="wikitable" style="border:none"> <tbody><tr> <th style="background:var(--background-color-neutral,#eaecf0);color:inherit;background:linear-gradient(to top right,var(--background-color-neutral,#eaecf0) 49%,var(--border-color-base,#a2a9b1) 49.5%,var(--border-color-base,#a2a9b1) 50.5%,var(--background-color-neutral,#eaecf0) 51%);line-height:1.2;padding:0.1em 0.4em;"><div style="margin-left:2em;text-align:right">2nd</div><div style="margin-right:2em;text-align:left">1st</div> </th> <th>A</th> <th>B</th> <th>C</th> <th>D </th> <td rowspan="5" style="border: none; background: white;"> </td> <th>score </th></tr> <tr> <th>A </th> <td data-sort-value="" style="vertical-align:middle; text-align:center" class="table-na">—</td> <td>0–5</td> <td>0–6</td> <td>0–7</td> <td>21 </td></tr> <tr> <th>B </th> <td>6–10</td> <td data-sort-value="" style="vertical-align:middle; text-align:center" class="table-na">—</td> <td>0–7</td> <td>0–8</td> <td>22 </td></tr> <tr> <th>C </th> <td>7–10</td> <td>8–10</td> <td data-sort-value="" style="vertical-align:middle; text-align:center" class="table-na">—</td> <td>0–9</td> <td>17 </td></tr> <tr> <th>D </th> <td>8–10</td> <td>9–10</td> <td>10</td> <td data-sort-value="" style="vertical-align:middle; text-align:center" class="table-na">—</td> <td>6 </td></tr></tbody></table> <p>The entry of two <a href="/wiki/Dummy_candidate" title="Dummy candidate">dummy candidates</a> allows B to win the election. Similar examples led the Marquis de Condorcet to argue that the Borda count is "bound to lead to error" because it "<a href="/wiki/Independence_of_irrelevant_alternatives" title="Independence of irrelevant alternatives">relies on irrelevant factors</a> to form its judgments".<sup id="cite_ref-Fraenkel_Grofman_2014_12-1" class="reference"><a href="#cite_note-Fraenkel_Grofman_2014-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Other_properties">Other properties</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Borda_count&action=edit&section=6" title="Edit section: Other properties"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>There are a number of formalised <a href="/wiki/Voting_system_criterion" class="mw-redirect" title="Voting system criterion">voting system criteria</a> whose results are summarised in 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.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_15-0" class="reference"><a href="#cite_note-condorcet-iia-incompatibility-15"><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_15-1" class="reference"><a href="#cite_note-condorcet-iia-incompatibility-15"><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_15-2" class="reference"><a href="#cite_note-condorcet-iia-incompatibility-15"><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_15-3" class="reference"><a href="#cite_note-condorcet-iia-incompatibility-15"><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_15-4" class="reference"><a href="#cite_note-condorcet-iia-incompatibility-15"><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_15-5" class="reference"><a href="#cite_note-condorcet-iia-incompatibility-15"><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_15-6" class="reference"><a href="#cite_note-condorcet-iia-incompatibility-15"><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_16-0" class="reference"><a href="#cite_note-MinimaxVarient-16"><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_16-1" class="reference"><a href="#cite_note-MinimaxVarient-16"><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_17-0" class="reference"><a href="#cite_note-semipc-17"><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/Schulze_method" title="Schulze method">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_17-1" class="reference"><a href="#cite_note-semipc-17"><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">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_18-0" class="reference"><a href="#cite_note-IIA_rating_methods-18"><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-19" class="reference"><a href="#cite_note-19"><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_20-0" class="reference"><a href="#cite_note-mjmmc-20"><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_18-1" class="reference"><a href="#cite_note-IIA_rating_methods-18"><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_17-2" class="reference"><a href="#cite_note-semipc-17"><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_18-2" class="reference"><a href="#cite_note-IIA_rating_methods-18"><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/Quadratic_voting" title="Quadratic voting">Quadratic</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:#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;">N/A </td> <td style="vertical-align:middle;">N/A </td> <td style="vertical-align:middle; background-color:#FFC7C7;">No </td> <td data-sort-value="1" style="border-left:2px solid #a0a0a0;">Credits </td></tr> <tr> <th style="font-weight:bold"><a href="/wiki/Random_ballot" title="Random ballot">Random ballot</a><wbr /><sup id="cite_ref-21" class="reference"><a href="#cite_note-21"><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-22" class="reference"><a href="#cite_note-22"><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-15"><span class="mw-cite-backlink">^ <a href="#cite_ref-condorcet-iia-incompatibility_15-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-condorcet-iia-incompatibility_15-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-condorcet-iia-incompatibility_15-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-condorcet-iia-incompatibility_15-3"><sup><i><b>d</b></i></sup></a> <a href="#cite_ref-condorcet-iia-incompatibility_15-4"><sup><i><b>e</b></i></sup></a> <a href="#cite_ref-condorcet-iia-incompatibility_15-5"><sup><i><b>f</b></i></sup></a> <a href="#cite_ref-condorcet-iia-incompatibility_15-6"><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-16"><span class="mw-cite-backlink">^ <a href="#cite_ref-MinimaxVarient_16-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-MinimaxVarient_16-1"><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-17"><span class="mw-cite-backlink">^ <a href="#cite_ref-semipc_17-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-semipc_17-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-semipc_17-2"><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-18"><span class="mw-cite-backlink">^ <a href="#cite_ref-IIA_rating_methods_18-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-IIA_rating_methods_18-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-IIA_rating_methods_18-2"><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-19"><span class="mw-cite-backlink"><b><a href="#cite_ref-19">^</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-20"><span class="mw-cite-backlink"><b><a href="#cite_ref-mjmmc_20-0">^</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-21"><span class="mw-cite-backlink"><b><a href="#cite_ref-21">^</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-22"><span class="mw-cite-backlink"><b><a href="#cite_ref-22">^</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><p>Simulations show that Borda has a high probability of choosing the Condorcet winner when one exists, in the absence of <a href="/wiki/Strategic_voting" title="Strategic voting">strategic voting</a> and with ballots ranking all candidates.<sup id="cite_ref-Emerson_2016_1-1" class="reference"><a href="#cite_note-Emerson_2016-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Fraenkel_Grofman_2014_12-2" class="reference"><a href="#cite_note-Fraenkel_Grofman_2014-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Equal_ranks">Equal ranks</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Borda_count&action=edit&section=7" title="Edit section: Equal ranks"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Several different methods of handling tied ranks have been suggested. They can be illustrated using the 4-candidate election discussed previously. </p> <table class="wikitable"> <tbody><tr> <th>Ranking</th> <th>Candidate</th> <th>Points </th></tr> <tr> <th>1st </th> <td>Andrew</td> <td><b>3</b> </td></tr> <tr> <th>2nd </th> <td>Brian</td> <td><b>2</b> </td></tr> <tr> <th>3rd </th> <td>Catherine</td> <td><b>1</b> </td></tr> <tr> <th>4th </th> <td>David</td> <td><b>0</b> </td></tr></tbody></table> <ul><li><b>Traditional Borda</b>: In Borda's system as originally proposed, each tied candidate was given the minimum number of points. So if a voter marks Andrew as his or her first preference, Brian as his or her second, and leaves Catherine and David unranked, then Andrew will receive 3 points, Brian 2, and Catherine and David none. This is an example of what Narodytska and Walsh call "rounding up".</li> <li><b>Tournament Borda:</b> each candidate receives half a point for every other candidate they are tied with, in addition to a whole point for every candidate they are strictly preferred to. In the example, suppose that a voter is indifferent between Andrew and Brian, preferring both to Catherine and Catherine to David. Then Andrew and Brian will each receive 2<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027"><span class="frac"><span class="num">1</span>⁄<span class="den">2</span></span> points, Catherine will receive 1, and David none. This is referred to as "averaging" by Narodytska and Walsh.<sup id="cite_ref-nina2_23-0" class="reference"><a href="#cite_note-nina2-23"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup></li> <li><span class="anchor" id="Modified_Borda"></span><span class="anchor" id="Modified_Borda_count"></span><b>Modified Borda</b>: again allows ties only at the end of a voter's ranking. It gives no points to unranked candidates, 1 point to the least preferred of the ranked candidates, etc. So if a voter ranks Andrew above Brian and leaves other candidates unranked, Andrew will receive 2 points, Brian will receive 1 point, and Catherine and David will receive none. This is equivalent to "rounding down". The most preferred candidate on a ballot paper will receive a different number of points depending on how many candidates were left unranked.</li></ul> <div class="mw-heading mw-heading3"><h3 id="Effects_on_strategy">Effects on strategy</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Borda_count&action=edit&section=8" title="Edit section: Effects on strategy"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div><p> The modified Borda and tournament Borda methods, as well as methods of Borda that do not allow for equal rankings, are well-known for behaving disastrously in response to tactical voting, a reaction called a <a href="/wiki/Turkey-raising" class="mw-redirect" title="Turkey-raising">turkey election</a>.<sup id="cite_ref-:02_7-1" class="reference"><a href="#cite_note-:02-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> The <a href="/wiki/French_Academy_of_Sciences" title="French Academy of Sciences">French Academy of Sciences</a> (of which Borda was a member) experimented with Borda's system but abandoned it, in part because "the voters found how to manipulate the Borda rule".<sup id="cite_ref-FOOTNOTEMcLeanUrkenHewitt199540_24-0" class="reference"><a href="#cite_note-FOOTNOTEMcLeanUrkenHewitt199540-24"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> In response to the issue of strategic manipulation in the Borda count, M. de Borda said:<sup id="cite_ref-Black_19872_25-0" class="reference"><a href="#cite_note-Black_19872-25"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-FOOTNOTEMcLeanUrkenHewitt199540_24-1" class="reference"><a href="#cite_note-FOOTNOTEMcLeanUrkenHewitt199540-24"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup><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><style data-mw-deduplicate="TemplateStyles:r1244412712">.mw-parser-output .templatequote{overflow:hidden;margin:1em 0;padding:0 32px}.mw-parser-output .templatequotecite{line-height:1.5em;text-align:left;margin-top:0}@media(min-width:500px){.mw-parser-output .templatequotecite{padding-left:1.6em}}</style></p><blockquote class="templatequote"><p><span title="French-language text"><i lang="fr">Mon scrutin n'est fait que pour d'honnêtes gens.</i></span><br /> My scheme is intended for only honest men.</p></blockquote><p>Despite its abandonment, the rounded-down Borda rule has a substantially less severe reaction to tactical voting than the traditional or tournament variants. Tactical voting consists of the relatively mild <a href="/wiki/Bullet_voting" title="Bullet voting">bullet voting</a>, which only causes the race to behave like a cross between a <a href="/wiki/Plurality_voting" title="Plurality voting">plurality vote</a> and an honest Borda count, rather than producing a potential turkey-election. In Slovenia, which uses this form of the rule, roughly 42% of voters rank a second preference.<sup id="cite_ref-Fraenkel_Grofman_20142_27-0" class="reference"><a href="#cite_note-Fraenkel_Grofman_20142-27"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> </p><div class="mw-heading mw-heading3"><h3 id="Forced_truncation">Forced truncation</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Borda_count&action=edit&section=9" title="Edit section: Forced truncation"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Some implementations of Borda voting require voters to truncate their ballots to a certain length: </p> <ul><li>In Kiribati, a variant is employed which uses a traditional Borda formula, but in which voters rank only four candidates, irrespective of how many are standing.<sup id="cite_ref-reilly_28-0" class="reference"><a href="#cite_note-reilly-28"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup></li> <li>In <a href="/wiki/Toastmasters_International" title="Toastmasters International">Toastmasters International</a>, speech contests are truncation-scored as 3, 2, 1 for the top-three ranked candidates. Ties are broken by having a special ballot that is ignored unless there is a tie.<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></li></ul> <div class="mw-heading mw-heading2"><h2 id="Multiple_winners">Multiple winners</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Borda_count&action=edit&section=10" title="Edit section: Multiple winners"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The system invented by Borda was intended for use in elections with a single winner, but it is also possible to conduct a Borda count with more than one winner, by recognizing the desired number of candidates with the most points as the winners. In other words, if there are two seats to be filled, then the two candidates with most points win; in a three-seat election, the three candidates with most points, and so on. In Nauru, which uses the multi-seat variant of the Borda count, parliamentary constituencies of two and four seats are used. </p><p>The <a href="/wiki/Quota_Borda_system" title="Quota Borda system">quota Borda system</a> is a system of <a href="/wiki/Proportional_representation" title="Proportional representation">proportional representation</a> in multi-seat constituencies that uses the Borda count. Chris Geller's STV-B uses vote count quotas to elect, but eliminates the candidate with the lowest Borda score; Geller-STV does not recalculate Borda scores after partial vote transfers, meaning partial-transfer of votes affects voting power for election but not for elimination.<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. (May 2021)">citation needed</span></a></i>]</sup> </p> <div class="mw-heading mw-heading2"><h2 id="Related_systems">Related systems</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Borda_count&action=edit&section=11" title="Edit section: Related systems"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/Nanson%27s_method" title="Nanson's method">Nanson's and Baldwin's methods</a> are Condorcet-consistent voting methods based on the Borda score. Both are run as series of elimination rounds analogous to <a href="/wiki/Instant-runoff_voting" title="Instant-runoff voting">instant-runoff voting</a>. In the first case, in each round every candidate with less than the average Borda score is eliminated; in the second, the candidate with lowest score is eliminated. Unlike the Borda count, Nanson and Baldwin are majoritarian and Condorcet methods because they use the fact that a Condorcet winner always has a higher-than-average Borda score relative to other candidates, and the <a href="/wiki/Condorcet_loser" class="mw-redirect" title="Condorcet loser">Condorcet loser</a> a lower than average Borda score.<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> However they are not monotonic. </p> <div class="mw-heading mw-heading2"><h2 id="Potential_for_tactical_manipulation">Potential for tactical manipulation</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Borda_count&action=edit&section=12" title="Edit section: Potential for tactical manipulation"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1236090951">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">See also: <a href="/wiki/Tactical_voting#Borda" class="mw-redirect" title="Tactical voting">Tactical voting § Borda</a></div> <p>Borda counts are vulnerable to manipulation by both tactical voting and strategic nomination. The Dowdall system may be more resistant, based on observations in Kiribati using the modified Borda count versus Nauru using the Dowdall system,<sup id="cite_ref-Reilly2002_11-1" class="reference"><a href="#cite_note-Reilly2002-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> but little research has been done thus far on the Nauru system. </p> <div class="mw-heading mw-heading3"><h3 id="Tactical_voting">Tactical voting</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Borda_count&action=edit&section=13" title="Edit section: Tactical voting"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Borda counts are unusually vulnerable to <a href="/wiki/Tactical_voting" class="mw-redirect" title="Tactical voting">tactical voting</a>, even compared to most other voting systems.<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> Voters who vote tactically, rather than via their true preference, will be more influential; more alarmingly, if everyone starts voting tactically, the result tends to approach a large tie that will be decided semi-randomly. When a voter utilizes <i>compromising</i>, they insincerely raise the position of a second or third choice candidate over their first choice candidate, in order to help the second choice candidate to beat a candidate they like even less. When a voter utilizes <i>burying</i>, voters can help a more-preferred candidate by insincerely lowering the position of a less-preferred candidate on their ballot. Combining both these strategies can be powerful, especially as the number of candidates in an election increases. For example, if there are two candidates whom a voter considers to be the most likely to win, the voter can maximise his impact on the contest between these front runners by ranking the candidate whom he likes more in first place, and ranking the candidate whom he likes less in last place. If neither front runner is his sincere first or last choice, the voter is employing both the compromising and burying tactics at once; if enough voters employ such strategies, then the result will no longer reflect the sincere preferences of the electorate. </p><p>For an example of how potent tactical voting can be, suppose a trip is being planned by a group of 100 people on the East Coast of North America. They decide to use Borda count to vote on which city they will visit. The three candidates are <a href="/wiki/New_York_City" title="New York City">New York City</a>, <a href="/wiki/Orlando,_Florida" title="Orlando, Florida">Orlando</a>, and <a href="/wiki/Iqaluit" title="Iqaluit">Iqaluit</a>. 48 people prefer Orlando / New York / Iqaluit; 44 people prefer New York / Orlando / Iqaluit; 4 people prefer Iqaluit / New York / Orlando; and 4 people prefer Iqaluit / Orlando / New York. If everyone votes their true preference, the result is: </p> <ol><li>Orlando: <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 (48\times 2)+((44+4)\times 1){=}144}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mn>48</mn> <mo>×</mo> <mn>2</mn> <mo stretchy="false">)</mo> <mo>+</mo> <mo stretchy="false">(</mo> <mo stretchy="false">(</mo> <mn>44</mn> <mo>+</mo> <mn>4</mn> <mo stretchy="false">)</mo> <mo>×</mo> <mn>1</mn> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>=</mo> </mrow> <mn>144</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (48\times 2)+((44+4)\times 1){=}144}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6ea8f6ddc144ffe216fa4a3f16856af62cf2c472" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:30.222ex; height:2.843ex;" alt="{\displaystyle (48\times 2)+((44+4)\times 1){=}144}"></span></li> <li>New York: <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 (44\times 2)+((48+4)\times 1){=}140}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mn>44</mn> <mo>×</mo> <mn>2</mn> <mo stretchy="false">)</mo> <mo>+</mo> <mo stretchy="false">(</mo> <mo stretchy="false">(</mo> <mn>48</mn> <mo>+</mo> <mn>4</mn> <mo stretchy="false">)</mo> <mo>×</mo> <mn>1</mn> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>=</mo> </mrow> <mn>140</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (44\times 2)+((48+4)\times 1){=}140}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/13ada79d060689cec7fa814480b069561e5e29fc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:30.222ex; height:2.843ex;" alt="{\displaystyle (44\times 2)+((48+4)\times 1){=}140}"></span></li> <li>Iqaluit: <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 ((4+4)\times 2){=}16}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mo stretchy="false">(</mo> <mn>4</mn> <mo>+</mo> <mn>4</mn> <mo stretchy="false">)</mo> <mo>×</mo> <mn>2</mn> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>=</mo> </mrow> <mn>16</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle ((4+4)\times 2){=}16}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b17e19815b6907ebdb2600be47d6e428f717fb52" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:16.92ex; height:2.843ex;" alt="{\displaystyle ((4+4)\times 2){=}16}"></span></li></ol> <p>If the New York voters realize that they are likely to lose and all agree to tactically change their stated preference to New York / Iqaluit / Orlando, burying Orlando, then this is enough to change the result in their favor: </p> <ol><li>New York: <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 (44\times 2)+((48+4)\times 1){=}140}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mn>44</mn> <mo>×</mo> <mn>2</mn> <mo stretchy="false">)</mo> <mo>+</mo> <mo stretchy="false">(</mo> <mo stretchy="false">(</mo> <mn>48</mn> <mo>+</mo> <mn>4</mn> <mo stretchy="false">)</mo> <mo>×</mo> <mn>1</mn> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>=</mo> </mrow> <mn>140</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (44\times 2)+((48+4)\times 1){=}140}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/13ada79d060689cec7fa814480b069561e5e29fc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:30.222ex; height:2.843ex;" alt="{\displaystyle (44\times 2)+((48+4)\times 1){=}140}"></span></li> <li>Orlando: <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 (48\times 2)+(4\times 1){=}100}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mn>48</mn> <mo>×</mo> <mn>2</mn> <mo stretchy="false">)</mo> <mo>+</mo> <mo stretchy="false">(</mo> <mn>4</mn> <mo>×</mo> <mn>1</mn> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>=</mo> </mrow> <mn>100</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (48\times 2)+(4\times 1){=}100}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4415d620cd827ba797908b974602124ad9abfd3d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:23.248ex; height:2.843ex;" alt="{\displaystyle (48\times 2)+(4\times 1){=}100}"></span></li> <li>Iqaluit: <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 ((4+4)\times 2)+(44\times 1){=}60}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mo stretchy="false">(</mo> <mn>4</mn> <mo>+</mo> <mn>4</mn> <mo stretchy="false">)</mo> <mo>×</mo> <mn>2</mn> <mo stretchy="false">)</mo> <mo>+</mo> <mo stretchy="false">(</mo> <mn>44</mn> <mo>×</mo> <mn>1</mn> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>=</mo> </mrow> <mn>60</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle ((4+4)\times 2)+(44\times 1){=}60}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/44a61b50f447cf02e9745813e7c7ff062d8015ae" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:27.897ex; height:2.843ex;" alt="{\displaystyle ((4+4)\times 2)+(44\times 1){=}60}"></span></li></ol> <p>In this example, only a few of the New York voters needed to change their preference to tip this result because it was so close – just five voters would have been sufficient had everyone else still voted their true preferences. However, if Orlando voters realize that the New York voters are planning on tactically voting, they too can tactically vote for Orlando / Iqaluit / New York. When all of the New York and all of the Orlando voters do this, however, there is a surprising new result: </p> <ol><li>Iqaluit: <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 ((4+4)\times 2)+((48+44)\times 1){=}108}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mo stretchy="false">(</mo> <mn>4</mn> <mo>+</mo> <mn>4</mn> <mo stretchy="false">)</mo> <mo>×</mo> <mn>2</mn> <mo stretchy="false">)</mo> <mo>+</mo> <mo stretchy="false">(</mo> <mo stretchy="false">(</mo> <mn>48</mn> <mo>+</mo> <mn>44</mn> <mo stretchy="false">)</mo> <mo>×</mo> <mn>1</mn> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>=</mo> </mrow> <mn>108</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle ((4+4)\times 2)+((48+44)\times 1){=}108}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/df1507d09aa1fde47fdef24482bed014839fdb3c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:36.034ex; height:2.843ex;" alt="{\displaystyle ((4+4)\times 2)+((48+44)\times 1){=}108}"></span></li> <li>Orlando: <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 (48\times 2)+(4\times 1){=}100}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mn>48</mn> <mo>×</mo> <mn>2</mn> <mo stretchy="false">)</mo> <mo>+</mo> <mo stretchy="false">(</mo> <mn>4</mn> <mo>×</mo> <mn>1</mn> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>=</mo> </mrow> <mn>100</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (48\times 2)+(4\times 1){=}100}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4415d620cd827ba797908b974602124ad9abfd3d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:23.248ex; height:2.843ex;" alt="{\displaystyle (48\times 2)+(4\times 1){=}100}"></span></li> <li>New York: <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 (44\times 2)+(4\times 1){=}92}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mn>44</mn> <mo>×</mo> <mn>2</mn> <mo stretchy="false">)</mo> <mo>+</mo> <mo stretchy="false">(</mo> <mn>4</mn> <mo>×</mo> <mn>1</mn> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>=</mo> </mrow> <mn>92</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (44\times 2)+(4\times 1){=}92}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ff69eb015a0619dec349537ff335415098aef00d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:22.085ex; height:2.843ex;" alt="{\displaystyle (44\times 2)+(4\times 1){=}92}"></span></li></ol> <p>The tactical voting has overcorrected, and now the clear last place option is a threat to win, with all three options extremely close. Tactical voting has entirely obscured the true preferences of the group into a large near-tie. </p> <div class="mw-heading mw-heading3"><h3 id="Strategic_nomination">Strategic nomination</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Borda_count&action=edit&section=14" title="Edit section: Strategic nomination"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The Borda count is highly vulnerable to a form of <a href="/wiki/Strategic_nomination" title="Strategic nomination">strategic nomination</a> called <i>teaming</i> or <i>cloning</i>. This means that when more candidates run with similar ideologies, the probability of one of those candidates winning increases. This is illustrated by the example <a href="#irrelevant">'Effect of irrelevant alternatives'</a> above. Therefore, under the Borda count, it is to a faction's advantage to run as many candidates as it can. For example, even in a single-seat election, it would be to the advantage of a political party to stand as many candidates as possible in an election. In this respect, the Borda count differs from many other single-winner systems, such as the '<a href="/wiki/Plurality_voting_system" class="mw-redirect" title="Plurality voting system">first past the post</a>' plurality system, in which a political faction is disadvantaged by running too many candidates. Under systems such as plurality, '<a href="/wiki/Vote_splitting" class="mw-redirect" title="Vote splitting">splitting</a>' a party's vote in this way can lead to the <a href="/wiki/Spoiler_effect" title="Spoiler effect">spoiler effect</a>, which harms the chances of any of a faction's candidates being elected. </p><p>Strategic nomination is used in Nauru, according to MP <a href="/wiki/Roland_Kun" title="Roland Kun">Roland Kun</a>, with factions running multiple "buffer candidates" who are not expected to win, to lower the tallies of their main competitors.<sup id="cite_ref-Fraenkel_Grofman_2014_12-3" class="reference"><a href="#cite_note-Fraenkel_Grofman_2014-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> However, the effect of this strategic nomination is greatly reduced by the use of a <a href="/wiki/Harmonic_progression_(mathematics)" title="Harmonic progression (mathematics)">harmonic progression</a> rather than a simple <a href="/wiki/Arithmetic_progression" title="Arithmetic progression">arithmetic progression</a>. Because the <a href="/wiki/Harmonic_series_(mathematics)" title="Harmonic series (mathematics)">harmonic series</a> is unbounded, it is theoretically possible to elect any candidate (no matter how unpopular) by nominating enough clones. In practice, the number of clones required to do so would likely exceed the total population of Nauru. </p> <div class="mw-heading mw-heading2"><h2 id="Example">Example<span class="anchor" id="tennessee"></span></h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Borda_count&action=edit&section=15" title="Edit section: Example"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><span class="anchor" id="Tennessee"></span> </p> <div style="float: left;"> <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:Tenn_voting_example" title="Template:Tenn voting example"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Tenn_voting_example" title="Template talk:Tenn voting example"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Tenn_voting_example" title="Special:EditPage/Template:Tenn voting example"><abbr title="Edit this template">e</abbr></a></li></ul></div></div> <p><span typeof="mw:File"><a href="/wiki/File:Tennessee_map_for_voting_example.svg" class="mw-file-description"><img alt="Tennessee and its four major cities: Memphis in the far west; Nashville in the center; Chattanooga in the east; and Knoxville in the far northeast" src="//upload.wikimedia.org/wikipedia/commons/thumb/8/88/Tennessee_map_for_voting_example.svg/500px-Tennessee_map_for_voting_example.svg.png" decoding="async" width="500" height="122" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/88/Tennessee_map_for_voting_example.svg/750px-Tennessee_map_for_voting_example.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/88/Tennessee_map_for_voting_example.svg/1000px-Tennessee_map_for_voting_example.svg.png 2x" data-file-width="780" data-file-height="190" /></a></span> </p><p>Suppose that <a href="/wiki/Tennessee" title="Tennessee">Tennessee</a> is holding an election on the location of its <a href="/wiki/Capital_city" title="Capital city">capital</a>. The population is concentrated around four major cities. <a href="/wiki/Spatial_voting" title="Spatial voting">All voters want the capital to be as close to them as possible.</a> The options are: </p> <ul><li><a href="/wiki/Memphis,_Tennessee" title="Memphis, Tennessee">Memphis</a>, the largest city, but far from the others (42% of voters)</li> <li><a href="/wiki/Nashville,_Tennessee" title="Nashville, Tennessee">Nashville</a>, near the center of the state (26% of voters)</li> <li><a href="/wiki/Chattanooga,_Tennessee" title="Chattanooga, Tennessee">Chattanooga</a>, somewhat east (15% of voters)</li> <li><a href="/wiki/Knoxville,_Tennessee" title="Knoxville, Tennessee">Knoxville</a>, far to the northeast (17% of voters)</li></ul> <p>The preferences of each region's voters are: </p> <table class="wikitable"> <tbody><tr> <th width="25%" style="background-color: #ffdddd">42% of voters<br /><small>Far-West</small> </th> <th width="25%" style="background-color: #ccffcc">26% of voters<br /><small>Center</small> </th> <th width="25%" style="background-color: #ddddff">15% of voters<br /><small>Center-East</small> </th> <th width="25%" style="background-color: #ffeedd">17% of voters<br /><small>Far-East</small> </th></tr> <tr> <td> <ol style="margin-left: 1.5em;"> <li> <b>Memphis</b> </li><li> Nashville </li><li> Chattanooga </li><li> Knoxville </li></ol> </td> <td> <ol style="margin-left: 1.5em;"> <li> <b>Nashville</b> </li><li> Chattanooga </li><li> Knoxville </li><li> Memphis </li></ol> </td> <td> <ol style="margin-left: 1.5em;"> <li> <b>Chattanooga</b> </li><li> Knoxville </li><li> Nashville </li><li> Memphis </li></ol> </td> <td> <ol style="margin-left: 1.5em;"> <li> <b>Knoxville</b> </li><li> Chattanooga </li><li> Nashville </li><li> Memphis </li></ol> </td></tr></tbody></table> <p><br /> Thus voters are assumed to prefer candidates in order of proximity to their home town. We get the following point counts per 100 voters: </p> <table class="wikitable" style="border:none"> <tbody><tr> <th style="background:var(--background-color-neutral,#eaecf0);color:inherit;background:linear-gradient(to top right,var(--background-color-neutral,#eaecf0) 49%,var(--border-color-base,#a2a9b1) 49.5%,var(--border-color-base,#a2a9b1) 50.5%,var(--background-color-neutral,#eaecf0) 51%);line-height:1.2;padding:0.1em 0.4em;"><div style="margin-left:2em;text-align:right">Voters</div><div style="margin-right:2em;text-align:left">Candidate</div></th> <th>Memphis</th> <th>Nashville</th> <th>Knoxville</th> <th>Chattanooga </th> <td rowspan="5" style="border: none; background: white;"> </td> <th>Score </th></tr> <tr> <th>Memphis </th> <td>42×3=126</td> <td>0</td> <td>0</td> <td>0</td> <td>126 </td></tr> <tr> <th>Nashville </th> <td>42×2 = 84</td> <td>26×3 = 78</td> <td>17×1 = 17</td> <td>15×1 = 15</td> <td>194 </td></tr> <tr> <th>Knoxville </th> <td>0</td> <td>26×1 = 26</td> <td>17×3 = 51</td> <td>15×2 = 30</td> <td>107 </td></tr> <tr> <th>Chattanooga </th> <td>42×1 = 42</td> <td>26×2 = 52</td> <td>17×2 = 34</td> <td>15×3 = 45</td> <td>173 </td></tr></tbody></table> <p>Accordingly Nashville is elected. </p> <div class="mw-heading mw-heading3"><h3 id="Dowdall">Dowdall</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Borda_count&action=edit&section=16" title="Edit section: Dowdall"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Under Dowdall rules the table would be as follows </p> <table class="wikitable" style="border:none"> <tbody><tr> <th style="background:var(--background-color-neutral,#eaecf0);color:inherit;background:linear-gradient(to top right,var(--background-color-neutral,#eaecf0) 49%,var(--border-color-base,#a2a9b1) 49.5%,var(--border-color-base,#a2a9b1) 50.5%,var(--background-color-neutral,#eaecf0) 51%);line-height:1.2;padding:0.1em 0.4em;"><div style="margin-left:2em;text-align:right">Voters</div><div style="margin-right:2em;text-align:left">Candidate</div> </th> <th>Memphis </th> <th>Nashville </th> <th>Knoxville </th> <th>Chattanooga </th> <td rowspan="5" style="border: none; background: white;"> </td> <th>Score </th></tr> <tr> <th>Memphis </th> <td>42×1=42 </td> <td>26×1/4 = 6.5 </td> <td>17×1/4 = 4.25 </td> <td>15×1/4 = 3.75 </td> <td>56.5 </td></tr> <tr> <th>Nashville </th> <td>42×1/2 = 21 </td> <td>26×1 = 26 </td> <td>17×1/3 = 5.6667... </td> <td>15×1/3 = 5 </td> <td>57.667... </td></tr> <tr> <th>Knoxville </th> <td>42×1/4 = 10.5 </td> <td>26×1/3 = 8.333... </td> <td>17×1 = 17 </td> <td>15×1/2 = 7.5 </td> <td>43.667... </td></tr> <tr> <th>Chattanooga </th> <td>42×1/3 = 14 </td> <td>26×1/2 = 13 </td> <td>17×1/2 = 8.5 </td> <td>15×1 = 15 </td> <td>50.5 </td></tr></tbody></table> <p>Just like normal Borda rules, Nashville would win. </p> <div class="mw-heading mw-heading2"><h2 id="Current_uses">Current uses</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Borda_count&action=edit&section=17" title="Edit section: Current uses"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Political_uses">Political uses</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Borda_count&action=edit&section=18" title="Edit section: Political uses"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The Borda count is used for certain political elections in <a href="/wiki/Slovenia" title="Slovenia">Slovenia</a> and the <a href="/wiki/Micronesia" title="Micronesia">Micronesian</a> nation of <a href="/wiki/Kiribati" title="Kiribati">Kiribati</a>. A <a href="/wiki/Dowdall_system" class="mw-redirect" title="Dowdall system">similar rule</a> is used in <a href="/wiki/Nauru" title="Nauru">Nauru</a>. </p><p>In Slovenia, the Borda count is used to elect two of the ninety members of the National Assembly: one member represents a constituency of ethnic Italians, the other a constituency of the Hungarian minority. </p><p>Members of the Parliament of Nauru are elected based on a variant of the Borda count that involves two departures from the normal practice: </p> <ol><li>multi-seat constituencies, of either two or four seats</li> <li>a point-allocation formula that involves increasingly small fractions of points for each ranking, rather than whole points.</li></ol> <p>In Kiribati, the president (or <i><a href="/wiki/Beretitenti" class="mw-redirect" title="Beretitenti">Beretitenti</a></i>) is elected by the plurality system, but a variant of the Borda count is used to select either three or four candidates to stand in the election. The constituency consists of members of the legislature (<i><a href="/wiki/Maneaba" title="Maneaba">Maneaba</a></i>). Voters in the legislature rank only four candidates, with all other candidates receiving zero points. Since at least 1991, tactical voting has been an important feature of the nominating process. </p><p>The <a href="/wiki/Republic_of_Nauru" class="mw-redirect" title="Republic of Nauru">Republic of Nauru</a> became independent from <a href="/wiki/Australia" title="Australia">Australia</a> in 1968. Before independence, and for three years afterwards, Nauru used instant-runoff voting, importing the system from Australia, but since 1971, a variant of the Borda count has been used. </p><p>The modified Borda count has been used by the <a href="/wiki/Green_Party_(Ireland)" title="Green Party (Ireland)">Green Party of Ireland</a> to elect its chairperson.<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><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> </p><p>The Borda count has been used for non-governmental purposes at certain peace conferences in Northern Ireland, where it has been used to help achieve consensus between participants including members of <a href="/wiki/Sinn_F%C3%A9in" title="Sinn Féin">Sinn Féin</a>, the <a href="/wiki/Ulster_Unionists" class="mw-redirect" title="Ulster Unionists">Ulster Unionists</a>, and the political wing of the <a href="/wiki/Ulster_Defence_Association" title="Ulster Defence Association">UDA</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. (July 2021)">citation needed</span></a></i>]</sup> </p> <div class="mw-heading mw-heading3"><h3 id="Other_uses">Other uses</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Borda_count&action=edit&section=19" title="Edit section: Other uses"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The Borda count is used in elections by some educational institutions in the United States: </p> <ul><li><a href="/wiki/University_of_Michigan" title="University of Michigan">University of Michigan</a> <ul><li>Central Student Government</li> <li>Student Government of the College of Literature, Science and the Arts (LSASG)</li></ul></li> <li><a href="/wiki/University_of_Missouri" title="University of Missouri">University of Missouri</a>: officers of the Graduate-Professional Council</li> <li><a href="/wiki/University_of_California_Los_Angeles" class="mw-redirect" title="University of California Los Angeles">University of California Los Angeles</a>: officers of the Graduate Student Association</li> <li><a href="/wiki/Harvard_University" title="Harvard University">Harvard University</a>: members of the Undergraduate Council, as of 2018<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><a href="/wiki/Southern_Illinois_University" title="Southern Illinois University">Southern Illinois University</a> at <a href="/wiki/Carbondale,_Illinois" title="Carbondale, Illinois">Carbondale</a>: officers of the Faculty Senate,</li> <li><a href="/wiki/Arizona_State_University" title="Arizona State University">Arizona State University</a>: officers of the Department of Mathematics and Statistics assembly.</li> <li><a href="/wiki/Wheaton_College,_Massachusetts" class="mw-redirect" title="Wheaton College, Massachusetts">Wheaton College, Massachusetts</a>: faculty members of committees.</li> <li><a href="/wiki/College_of_William_and_Mary" class="mw-redirect" title="College of William and Mary">College of William and Mary</a>: members of the faculty personnel committee of the School of Business Administration (tie-breaker).</li></ul> <p>The Borda count is used in elections by some professional and technical societies: </p> <ul><li><a href="/wiki/International_Society_for_Cryobiology" class="mw-redirect" title="International Society for Cryobiology">International Society for Cryobiology</a>: Board of Governors.</li> <li><a href="/wiki/U.S._Wheat_and_Barley_Scab_Initiative" title="U.S. Wheat and Barley Scab Initiative">U.S. Wheat and Barley Scab Initiative</a>: members of Research Area Committees.</li> <li><a href="/wiki/X.Org_Foundation" title="X.Org Foundation">X.Org Foundation</a>: Board of Directors.</li></ul> <p>The <a href="/wiki/OpenGL" title="OpenGL">OpenGL</a> Architecture Review Board uses the Borda count as one of the feature-selection methods. </p><p>The Borda count is used to determine winners for the <a href="/wiki/World_Champion_of_Public_Speaking" class="mw-redirect" title="World Champion of Public Speaking">World Champion of Public Speaking</a> contest organized by <a href="/wiki/Toastmasters_International" title="Toastmasters International">Toastmasters International</a>. Judges offer a ranking of their top three speakers, awarding them three points, two points, and one point, respectively. All unranked candidates receive zero points. </p><p>The modified Borda count is used to elect the President for the United States member committee of <a href="/wiki/AIESEC" title="AIESEC">AIESEC</a>. </p><p>The <a href="/wiki/Eurovision_Song_Contest" title="Eurovision Song Contest">Eurovision Song Contest</a> uses a heavily modified form of the Borda count, with a different distribution of points: only the top ten entries are considered in each ballot, the favorite entry receiving 12 points, the second-placed entry receiving 10 points, and the other eight entries getting points from 8 to 1. Although designed to favor a clear winner, it has produced very close races and even a tie. </p><p>The Borda count is used for wine trophy judging by the <a href="/wiki/Australian_Society_of_Viticulture_and_Oenology" title="Australian Society of Viticulture and Oenology">Australian Society of Viticulture and Oenology</a>, and by the <a href="/wiki/RoboCup" title="RoboCup">RoboCup</a> autonomous robot soccer competition at the Center for Computing Technologies, in the <a href="/wiki/University_of_Bremen" title="University of Bremen">University of Bremen</a> in <a href="/wiki/Germany" title="Germany">Germany</a>. </p><p>The Finnish Associations Act lists three different modifications of the Borda count for holding a proportional election. All the modifications use fractions, as in Nauru. A Finnish association may choose to use other methods of election, as well.<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> </p> <div class="mw-heading mw-heading4"><h4 id="Sports_awards">Sports awards</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Borda_count&action=edit&section=20" title="Edit section: Sports awards"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The Borda count is a popular method for granting sports awards. American uses include: </p> <ul><li><a href="/wiki/MLB_Most_Valuable_Player_Award" class="mw-redirect" title="MLB Most Valuable Player Award">MLB Most Valuable Player Award</a> (baseball)</li> <li><a href="/wiki/Heisman_Trophy" title="Heisman Trophy">Heisman Trophy</a> (college football)<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> <li>Ranking of <a href="/wiki/National_Collegiate_Athletic_Association" title="National Collegiate Athletic Association">NCAA</a> college teams, including in the <a href="/wiki/AP_Poll" class="mw-redirect" title="AP Poll">AP Poll</a> and <a href="/wiki/Coaches_Poll" title="Coaches Poll">Coaches Poll</a></li></ul> <div class="mw-heading mw-heading3"><h3 id="In_information_retrieval">In information retrieval</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Borda_count&action=edit&section=21" title="Edit section: In information retrieval"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The Borda count has been proposed as a rank aggregation method in <a href="/wiki/Information_retrieval" title="Information retrieval">information retrieval</a>, in which documents are <a href="/wiki/Ranking_(information_retrieval)" title="Ranking (information retrieval)">ranked</a> according to multiple criteria and the resulting rankings are then combined into a composite ranking. In this method, the ranking criteria are treated as voters, and the aggregate ranking is the result of applying the Borda count to their "ballots".<sup id="cite_ref-dwork-www10_37-0" class="reference"><a href="#cite_note-dwork-www10-37"><span class="cite-bracket">[</span>29<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Analogy_with_sporting_tournaments">Analogy with sporting tournaments</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Borda_count&action=edit&section=22" title="Edit section: Analogy with sporting tournaments"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Sporting tournaments frequently seek to produce a ranking of competitors from pairwise matches, in each of which a single point is awarded for a win, half a point for a draw, and no points for a loss. (Sometimes the scores are doubled as 2/1/0.) This is analogous to a Borda count in which each preference expressed by a single voter between two candidates is equivalent to a sporting fixture; it is also analogous to <a href="/wiki/Copeland%27s_method" title="Copeland's method">Copeland's method</a> supposing that the electorate's overall preference between two candidates takes the place of a sporting fixture. This scoring system was adopted for international chess around the middle of the nineteenth century and by the <a href="/wiki/English_Football_League" title="English Football League">English Football League</a> in 1888–1889. </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=Borda_count&action=edit&section=23" title="Edit section: History"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The Borda count is thought to have been developed independently at least four times: </p> <ul><li><a href="/wiki/Ramon_Llull" title="Ramon Llull">Ramon Llull</a> (1232–1315/16) described the election of an abbess in the 1283 novel <i><a href="/wiki/Blanquerna" title="Blanquerna">Blanquerna</a></i>. The election process is equivalent to the second of Borda's two equivalent definitions of the Borda count.<sup id="cite_ref-FOOTNOTEMcLean1990102_38-0" class="reference"><a href="#cite_note-FOOTNOTEMcLean1990102-38"><span class="cite-bracket">[</span>30<span class="cite-bracket">]</span></a></sup></li> <li><a href="/wiki/Nicholas_of_Cusa" title="Nicholas of Cusa">Nicholas of Cusa</a> (1401–1464) in his "De Concordantia Catholica" (1433) provided the first description of the Borda count and argued unsuccessfully for its use in the election of the <a href="/wiki/Holy_Roman_Emperor" title="Holy Roman Emperor">Holy Roman Emperor</a>. Cusa is known to have read another of Llull's pamphlets but presents a different definition and appears either to have been unaware of the <i>Blanquerna</i> method or not to realized it was equivalent.<sup id="cite_ref-FOOTNOTEMcLean1990105–106_39-0" class="reference"><a href="#cite_note-FOOTNOTEMcLean1990105–106-39"><span class="cite-bracket">[</span>31<span class="cite-bracket">]</span></a></sup></li> <li><a href="/wiki/Jean-Charles_de_Borda" title="Jean-Charles de Borda">Jean-Charles de Borda</a> (1733–1799) devised the system as a fair way to elect members to the <a href="/wiki/French_Academy_of_Sciences" title="French Academy of Sciences">French Academy of Sciences</a> in a paper presented to the Academy in 1784 and published as <a rel="nofollow" class="external text" href="http://gerardgreco.free.fr/spip.php?article28">"Mémoire sur les élections au scrutin"</a> in <i>Histoire de l'Académie Royale des Sciences, Paris</i>.<sup id="cite_ref-40" class="reference"><a href="#cite_note-40"><span class="cite-bracket">[</span>note 1<span class="cite-bracket">]</span></a></sup> The Borda count was the sole method used for membership election to the Academy from 1795 until 1800, when it was supplemented by other methods at the urging of <a href="/wiki/Napoleon" title="Napoleon">Napoleon</a>.</li> <li><a href="/wiki/Charles_L._Dodgson" class="mw-redirect" title="Charles L. Dodgson">Charles L. Dodgson</a> (Lewis Carroll, 1832–1898) proposed a version of the Borda count in "A discussion of the various methods of procedure in conducting elections" (1783) for a vote to assign a fellowship at <a href="/wiki/Christ_Church,_Oxford" title="Christ Church, Oxford">Christ Church, Oxford</a>. The fellows voted using the method, realized that there was a Condorcet winner who did not win (a violation of the <a href="/wiki/Condorcet_Criterion" class="mw-redirect" title="Condorcet Criterion">Condorcet Criterion</a>), rejected the results, and awarded the fellowship to the Condorcet winner.<sup id="cite_ref-FOOTNOTEMcLean2019_41-0" class="reference"><a href="#cite_note-FOOTNOTEMcLean2019-41"><span class="cite-bracket">[</span>32<span class="cite-bracket">]</span></a></sup> The next year, Dodgson proposed replacing his Borda count method with one similar to <a href="/wiki/Copeland%27s_method" title="Copeland's method">Copeland's method</a>, then in 1876 proposed a hybrid of the two in "A method of taking votes on more than two issues". He appears to have been unaware of either Borda or Condorcet's work.<sup id="cite_ref-FOOTNOTEMcLean2019123–124_42-0" class="reference"><a href="#cite_note-FOOTNOTEMcLean2019123–124-42"><span class="cite-bracket">[</span>33<span class="cite-bracket">]</span></a></sup></li></ul> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Borda_count&action=edit&section=24" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1266661725">.mw-parser-output .portalbox{padding:0;margin:0.5em 0;display:table;box-sizing:border-box;max-width:175px;list-style:none}.mw-parser-output .portalborder{border:1px solid var(--border-color-base,#a2a9b1);padding:0.1em;background:var(--background-color-neutral-subtle,#f8f9fa)}.mw-parser-output .portalbox-entry{display:table-row;font-size:85%;line-height:110%;height:1.9em;font-style:italic;font-weight:bold}.mw-parser-output .portalbox-image{display:table-cell;padding:0.2em;vertical-align:middle;text-align:center}.mw-parser-output .portalbox-link{display:table-cell;padding:0.2em 0.2em 0.2em 0.3em;vertical-align:middle}@media(min-width:720px){.mw-parser-output .portalleft{margin:0.5em 1em 0.5em 0}.mw-parser-output .portalright{clear:right;float:right;margin:0.5em 0 0.5em 1em}}</style><ul role="navigation" aria-label="Portals" class="noprint portalbox portalborder portalright"> <li class="portalbox-entry"><span class="portalbox-image"><span class="mw-image-border noviewer" typeof="mw:File"><a href="/wiki/File:A_coloured_voting_box.svg" class="mw-file-description"><img alt="icon" src="//upload.wikimedia.org/wikipedia/en/thumb/0/01/A_coloured_voting_box.svg/28px-A_coloured_voting_box.svg.png" decoding="async" width="28" height="28" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/0/01/A_coloured_voting_box.svg/42px-A_coloured_voting_box.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/0/01/A_coloured_voting_box.svg/56px-A_coloured_voting_box.svg.png 2x" data-file-width="160" data-file-height="160" /></a></span></span><span class="portalbox-link"><a href="/wiki/Portal:Politics" title="Portal:Politics">Politics portal</a></span></li></ul> <ul><li><a href="/wiki/Comparison_of_electoral_systems" class="mw-redirect" title="Comparison of electoral systems">Comparison of electoral systems</a></li> <li><a href="/wiki/Copeland%27s_method" title="Copeland's method">Copeland's method</a></li> <li><a href="/wiki/Nanson%27s_method" title="Nanson's method">Nanson's method</a></li> <li><a href="/wiki/Arrow%27s_impossibility_theorem" title="Arrow's impossibility theorem">Arrow's impossibility theorem</a></li> <li><a href="/wiki/Oklahoma_primary_electoral_system" title="Oklahoma primary electoral system">Oklahoma primary electoral system</a></li></ul> <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=Borda_count&action=edit&section=25" title="Edit section: Notes"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-40"><span class="mw-cite-backlink"><b><a href="#cite_ref-40">^</a></b></span> <span class="reference-text">The article appeared in the 1781 edition of the <i>Histoire</i>, and Borda himself asserted he had publicized these ideas as early as 1770, but 1784 appears to be the correct date of attribution. Brian, É, <a rel="nofollow" class="external text" href="https://www.jehps.net/juin2008/Brian.pdf">"Condorcet and Borda in 1784. Misfits and Documents"</a>, <i>Electronic Journal for History of Probability and Statistics',' Vol. 4, No. 1 (June 2008).</i></span> </li> </ol></div> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Borda_count&action=edit&section=26" title="Edit section: References"><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-Emerson_2016-1"><span class="mw-cite-backlink">^ <a href="#cite_ref-Emerson_2016_1-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Emerson_2016_1-1"><sup><i><b>b</b></i></sup></a></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="CITEREFEmerson2016" class="citation book cs1">Emerson, Peter (16 January 2016). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=6txlCwAAQBAJ"><i>From Majority Rule to Inclusive Politics</i></a>. Springer. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-3-319-23500-4" title="Special:BookSources/978-3-319-23500-4"><bdi>978-3-319-23500-4</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=From+Majority+Rule+to+Inclusive+Politics&rft.pub=Springer&rft.date=2016-01-16&rft.isbn=978-3-319-23500-4&rft.aulast=Emerson&rft.aufirst=Peter&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3D6txlCwAAQBAJ&rfr_id=info%3Asid%2Fen.wikipedia.org%3ABorda+count" class="Z3988"></span></span> </li> <li id="cite_note-:2-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-:2_2-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFEmerson2013" class="citation journal cs1">Emerson, Peter (1 February 2013). 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Retrieved <span class="nowrap">26 June</span> 2011</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Finnish+Associations+Act&rft.pub=National+Board+of+Patents+and+Registration+of+Finland&rft_id=http%3A%2F%2Fwww.prh.fi%2Fen%2Fyhdistysrekisteri%2Fyhdistyslaki.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ABorda+count" class="Z3988"></span></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 class="citation web cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20090920205108/http://www.heisman.com/history/balloting.html">"Heisman Trophy Balloting"</a>. Heisman Trophy. Archived from <a rel="nofollow" class="external text" href="http://www.heisman.com/history/balloting.html">the original</a> on 20 September 2009.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Heisman+Trophy+Balloting&rft.pub=Heisman+Trophy&rft_id=http%3A%2F%2Fwww.heisman.com%2Fhistory%2Fballoting.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ABorda+count" class="Z3988"></span></span> </li> <li id="cite_note-dwork-www10-37"><span class="mw-cite-backlink"><b><a href="#cite_ref-dwork-www10_37-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDworkKumarNaorSivakumar2001" class="citation book cs1"><a href="/wiki/Cynthia_Dwork" title="Cynthia Dwork">Dwork, Cynthia</a>; Kumar, Ravi; <a href="/wiki/Moni_Naor" title="Moni Naor">Naor, Moni</a>; Sivakumar, D. (May 2001). "Rank aggregation methods for the Web". <i>Proceedings of the 10th international conference on World Wide Web</i>. pp. <span class="nowrap">613–</span>622. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1145%2F371920.372165">10.1145/371920.372165</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/1-58113-348-0" title="Special:BookSources/1-58113-348-0"><bdi>1-58113-348-0</bdi></a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:8393813">8393813</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Rank+aggregation+methods+for+the+Web&rft.btitle=Proceedings+of+the+10th+international+conference+on+World+Wide+Web&rft.pages=%3Cspan+class%3D%22nowrap%22%3E613-%3C%2Fspan%3E622&rft.date=2001-05&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A8393813%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1145%2F371920.372165&rft.isbn=1-58113-348-0&rft.aulast=Dwork&rft.aufirst=Cynthia&rft.au=Kumar%2C+Ravi&rft.au=Naor%2C+Moni&rft.au=Sivakumar%2C+D.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ABorda+count" class="Z3988"></span></span> </li> <li id="cite_note-FOOTNOTEMcLean1990102-38"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEMcLean1990102_38-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFMcLean1990">McLean 1990</a>, p. 102.</span> </li> <li id="cite_note-FOOTNOTEMcLean1990105–106-39"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEMcLean1990105–106_39-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFMcLean1990">McLean 1990</a>, pp. 105–106.</span> </li> <li id="cite_note-FOOTNOTEMcLean2019-41"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEMcLean2019_41-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFMcLean2019">McLean 2019</a>.</span> </li> <li id="cite_note-FOOTNOTEMcLean2019123–124-42"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEMcLean2019123–124_42-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFMcLean2019">McLean 2019</a>, pp. 123–124.</span> </li> </ol></div> <div class="mw-heading mw-heading3"><h3 id="Works_cited">Works cited</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Borda_count&action=edit&section=27" title="Edit section: Works cited"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMcLean1990" class="citation journal cs1">McLean, Iain (April 1990). "The Borda and Condorcet Principles: Three Medieval Applications". <i>Social Choice and Welfare</i>. <b>7</b> (2): <span class="nowrap">99–</span>108. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2FBF01560577">10.1007/BF01560577</a>. <a href="/wiki/JSTOR_(identifier)" class="mw-redirect" title="JSTOR (identifier)">JSTOR</a> <a rel="nofollow" class="external text" href="https://www.jstor.org/stable/41105942">41105942</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:120618785">120618785</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Social+Choice+and+Welfare&rft.atitle=The+Borda+and+Condorcet+Principles%3A+Three+Medieval+Applications&rft.volume=7&rft.issue=2&rft.pages=%3Cspan+class%3D%22nowrap%22%3E99-%3C%2Fspan%3E108&rft.date=1990-04&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A120618785%23id-name%3DS2CID&rft_id=https%3A%2F%2Fwww.jstor.org%2Fstable%2F41105942%23id-name%3DJSTOR&rft_id=info%3Adoi%2F10.1007%2FBF01560577&rft.aulast=McLean&rft.aufirst=Iain&rfr_id=info%3Asid%2Fen.wikipedia.org%3ABorda+count" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMcLeanUrkenHewitt1995" class="citation book cs1">McLean, Iain; Urken, Arnold B.; Hewitt, Fiona (1995). <i>Classics of Social Choice</i>. University of Michigan Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-472-10450-5" title="Special:BookSources/978-0-472-10450-5"><bdi>978-0-472-10450-5</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Classics+of+Social+Choice&rft.pub=University+of+Michigan+Press&rft.date=1995&rft.isbn=978-0-472-10450-5&rft.aulast=McLean&rft.aufirst=Iain&rft.au=Urken%2C+Arnold+B.&rft.au=Hewitt%2C+Fiona&rfr_id=info%3Asid%2Fen.wikipedia.org%3ABorda+count" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMcLean2019" class="citation book cs1">McLean, Iain (2019). "Voting". In Wilson, Robin; Moktefi, Amirouche (eds.). <i>The Mathematical World of Charles L. Dodgson (Lewis Carroll)</i>. Oxford University Press.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Voting&rft.btitle=The+Mathematical+World+of+Charles+L.+Dodgson+%28Lewis+Carroll%29&rft.pub=Oxford+University+Press&rft.date=2019&rft.aulast=McLean&rft.aufirst=Iain&rfr_id=info%3Asid%2Fen.wikipedia.org%3ABorda+count" class="Z3988"></span></li></ul> <div class="mw-heading mw-heading2"><h2 id="Further_reading">Further reading</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Borda_count&action=edit&section=28" title="Edit section: Further reading"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSzpiro2010" class="citation book cs1"><a href="/wiki/George_Szpiro" title="George Szpiro">Szpiro, George G.</a> (2010). <i>Numbers Rule: The Vexing Mathematics of Democracy, from Plato to the Present</i></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Numbers+Rule%3A+The+Vexing+Mathematics+of+Democracy%2C+from+Plato+to+the+Present&rft.date=2010&rft.aulast=Szpiro&rft.aufirst=George+G.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ABorda+count" class="Z3988"></span>: a popular account of the history of the study of voting methods.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFEmerson2007" class="citation book cs1">Emerson, Peter (2007). <i>Designing an All-Inclusive Democracy: Consensual Voting Procedures for use in Parliaments, Councils and Committees</i>. Springer-Verlag</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Designing+an+All-Inclusive+Democracy%3A+Consensual+Voting+Procedures+for+use+in+Parliaments%2C+Councils+and+Committees&rft.pub=Springer-Verlag&rft.date=2007&rft.aulast=Emerson&rft.aufirst=Peter&rfr_id=info%3Asid%2Fen.wikipedia.org%3ABorda+count" class="Z3988"></span> <ul><li><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/978-3-540-33163-6" title="Special:BookSources/978-3-540-33163-6">978-3-540-33163-6</a> (Print)</li> <li><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/978-3-540-33164-3" title="Special:BookSources/978-3-540-33164-3">978-3-540-33164-3</a> (online)</li></ul></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFReilly2002" class="citation journal cs1">Reilly, Benjamin (2002). "Social Choice in the South Seas: Electoral Innovation and the Borda Count in the Pacific Island Countries". <i><a href="/wiki/International_Political_Science_Review" title="International Political Science Review">International Political Science Review</a></i>. <b>23</b> (4): <span class="nowrap">355–</span>372. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1177%2F0192512102023004002">10.1177/0192512102023004002</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:3213336">3213336</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=International+Political+Science+Review&rft.atitle=Social+Choice+in+the+South+Seas%3A+Electoral+Innovation+and+the+Borda+Count+in+the+Pacific+Island+Countries&rft.volume=23&rft.issue=4&rft.pages=%3Cspan+class%3D%22nowrap%22%3E355-%3C%2Fspan%3E372&rft.date=2002&rft_id=info%3Adoi%2F10.1177%2F0192512102023004002&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A3213336%23id-name%3DS2CID&rft.aulast=Reilly&rft.aufirst=Benjamin&rfr_id=info%3Asid%2Fen.wikipedia.org%3ABorda+count" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSaari2000" class="citation journal cs1"><a href="/wiki/Donald_G._Saari" title="Donald G. Saari">Saari, Donald G.</a> (2000). "Mathematical Structure of Voting Paradoxes: II. Positional Voting". <i><a href="/wiki/Journal_of_Economic_Theory" title="Journal of Economic Theory">Journal of Economic Theory</a></i>. <b>15</b> (1): <span class="nowrap">511–</span>528. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2Fs001990050002">10.1007/s001990050002</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:195227181">195227181</a>. <a href="/wiki/SSRN_(identifier)" class="mw-redirect" title="SSRN (identifier)">SSRN</a> <a rel="nofollow" class="external text" href="https://papers.ssrn.com/sol3/papers.cfm?abstract_id=195769">195769</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+Economic+Theory&rft.atitle=Mathematical+Structure+of+Voting+Paradoxes%3A+II.+Positional+Voting&rft.volume=15&rft.issue=1&rft.pages=%3Cspan+class%3D%22nowrap%22%3E511-%3C%2Fspan%3E528&rft.date=2000&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A195227181%23id-name%3DS2CID&rft_id=https%3A%2F%2Fpapers.ssrn.com%2Fsol3%2Fpapers.cfm%3Fabstract_id%3D195769%23id-name%3DSSRN&rft_id=info%3Adoi%2F10.1007%2Fs001990050002&rft.aulast=Saari&rft.aufirst=Donald+G.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ABorda+count" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSaari2001" class="citation book cs1">Saari, Donald G. (2001). <span class="id-lock-registration" title="Free registration required"><a rel="nofollow" class="external text" href="https://archive.org/details/chaoticelections0000saar"><i>Chaotic Elections!</i></a></span>. Providence, RI: American Mathematical Society. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-8218-2847-2" title="Special:BookSources/978-0-8218-2847-2"><bdi>978-0-8218-2847-2</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Chaotic+Elections%21&rft.place=Providence%2C+RI&rft.pub=American+Mathematical+Society&rft.date=2001&rft.isbn=978-0-8218-2847-2&rft.aulast=Saari&rft.aufirst=Donald+G.&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fchaoticelections0000saar&rfr_id=info%3Asid%2Fen.wikipedia.org%3ABorda+count" class="Z3988"></span>: Describes various voting systems using a mathematical model, and supports the use of the Borda count.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSaari2008" class="citation book cs1">Saari, Donald G. (2008). <a rel="nofollow" class="external text" href="http://a.co/43K4kLO"><i>Disposing Dictators, Demystifying Voting Paradoxes: Social Choice Analysis</i></a>. Cambridge University Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-521-51605-1" title="Special:BookSources/978-0-521-51605-1"><bdi>978-0-521-51605-1</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Disposing+Dictators%2C+Demystifying+Voting+Paradoxes%3A+Social+Choice+Analysis&rft.pub=Cambridge+University+Press&rft.date=2008&rft.isbn=978-0-521-51605-1&rft.aulast=Saari&rft.aufirst=Donald+G.&rft_id=http%3A%2F%2Fa.co%2F43K4kLO&rfr_id=info%3Asid%2Fen.wikipedia.org%3ABorda+count" class="Z3988"></span>: This expository, largely non-technical book is the first to find positive results showing that the situation is not anywhere as dire and negative as we have been led to believe.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFToplak2006" class="citation journal cs1"><a href="/wiki/Jurij_Toplak" title="Jurij Toplak">Toplak, Jurij</a> (2006). "The parliamentary election in Slovenia, October 2004". <i><a href="/wiki/Electoral_Studies" title="Electoral Studies">Electoral Studies</a></i>. <b>25</b> (4): <span class="nowrap">825–</span>831. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2Fj.electstud.2005.12.006">10.1016/j.electstud.2005.12.006</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Electoral+Studies&rft.atitle=The+parliamentary+election+in+Slovenia%2C+October+2004&rft.volume=25&rft.issue=4&rft.pages=%3Cspan+class%3D%22nowrap%22%3E825-%3C%2Fspan%3E831&rft.date=2006&rft_id=info%3Adoi%2F10.1016%2Fj.electstud.2005.12.006&rft.aulast=Toplak&rft.aufirst=Jurij&rfr_id=info%3Asid%2Fen.wikipedia.org%3ABorda+count" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAdelsmanWhinston1977" class="citation journal cs1">Adelsman, Rony M.; Whinston, Andrew B. (1977). "Sophisticated Voting with Information for Two Voting Functions". <i><a href="/wiki/Journal_of_Economic_Theory" title="Journal of Economic Theory">Journal of Economic Theory</a></i>. <b>15</b> (1): <span class="nowrap">145–</span>159. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2F0022-0531%2877%2990073-4">10.1016/0022-0531(77)90073-4</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+Economic+Theory&rft.atitle=Sophisticated+Voting+with+Information+for+Two+Voting+Functions&rft.volume=15&rft.issue=1&rft.pages=%3Cspan+class%3D%22nowrap%22%3E145-%3C%2Fspan%3E159&rft.date=1977&rft_id=info%3Adoi%2F10.1016%2F0022-0531%2877%2990073-4&rft.aulast=Adelsman&rft.aufirst=Rony+M.&rft.au=Whinston%2C+Andrew+B.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ABorda+count" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHulkowerNeatrour2019" class="citation journal cs1">Hulkower, Neal D.; Neatrour, John (2019). <a rel="nofollow" class="external text" href="https://doi.org/10.1177%2F2158244019837468">"The Power of None"</a>. <i>SAGE Open</i>. <b>9</b> (1). <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1177%2F2158244019837468">10.1177/2158244019837468</a></span>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/2158-2440">2158-2440</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:151079205">151079205</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=SAGE+Open&rft.atitle=The+Power+of+None&rft.volume=9&rft.issue=1&rft.date=2019&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A151079205%23id-name%3DS2CID&rft.issn=2158-2440&rft_id=info%3Adoi%2F10.1177%2F2158244019837468&rft.aulast=Hulkower&rft.aufirst=Neal+D.&rft.au=Neatrour%2C+John&rft_id=https%3A%2F%2Fdoi.org%2F10.1177%252F2158244019837468&rfr_id=info%3Asid%2Fen.wikipedia.org%3ABorda+count" class="Z3988"></span>: This paper looks at adding None of the candidates as a binding option for the Borda Count and proves that it uniquely satisfies five rational properties.</li></ul> <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=Borda_count&action=edit&section=29" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a rel="nofollow" class="external text" href="https://plato.stanford.edu/archives/fall2019/entries/voting-methods/">Eric Pacuit, "Voting Methods", The Stanford Encyclopedia of Philosophy (Fall 2019 Edition), Edward N. Zalta (ed.)</a></li> <li><a rel="nofollow" class="external text" href="http://www.deborda.org/">The de Borda Institute, Northern Ireland</a></li> <li><a rel="nofollow" class="external text" href="https://voterschoose.info/">Voters Choose, USA</a>: A Borda Count advocacy and research group based in the United States</li> <li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20080228102001/https://ritdml.rit.edu/dspace/bitstream/1850/4923/1/NRussellThesis07-2007.pdf">Complexity of Control of Borda Count Elections</a>: thesis by Nathan F. Russell</li> <li><a rel="nofollow" class="external text" href="http://pareto.uab.cat/wp/2004/61704.pdf">Scoring Rules on Dichotomous Preferences</a>: article by Marc Vorsatz, mathematically comparing the Borda count to <a href="/wiki/Approval_voting" title="Approval voting">approval voting</a> under specific conditions.</li> <li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20120212035813/http://www.nuff.ox.ac.uk/Users/McLean/A%20program%20to%20implement%20the%20Condorcet%20and%20Borda%20rules%20in%20a%20small.pdf">A program to implement the Condorcet and Borda rules in a small-n election</a>: article by Iain McLean and Neil Shephard.</li> <li><span class="languageicon">(in French)</span> <a rel="nofollow" class="external text" href="http://gerardgreco.free.fr/spip.php?article28"><i>Élections au scrutin</i></a>: Borda's original French text (1781) in a high definition PDF file.</li> <li><a rel="nofollow" class="external text" href="https://ewanchelley.github.io/voting/borda">QuickVote</a> – A website that calculates Borda count results. For comparison, it also calculates the winner according to plurality, instant-runoff, Kemeny–Young , and other voting methods.</li></ul> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><style data-mw-deduplicate="TemplateStyles:r1236075235">.mw-parser-output .navbox{box-sizing:border-box;border:1px solid #a2a9b1;width:100%;clear:both;font-size:88%;text-align:center;padding:1px;margin:1em auto 0}.mw-parser-output .navbox .navbox{margin-top:0}.mw-parser-output .navbox+.navbox,.mw-parser-output .navbox+.navbox-styles+.navbox{margin-top:-1px}.mw-parser-output .navbox-inner,.mw-parser-output .navbox-subgroup{width:100%}.mw-parser-output .navbox-group,.mw-parser-output .navbox-title,.mw-parser-output .navbox-abovebelow{padding:0.25em 1em;line-height:1.5em;text-align:center}.mw-parser-output .navbox-group{white-space:nowrap;text-align:right}.mw-parser-output .navbox,.mw-parser-output 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dl,.mw-parser-output .navbox td.hlist ol,.mw-parser-output .navbox td.hlist ul{padding:0.125em 0}.mw-parser-output .navbox .navbar{display:block;font-size:100%}.mw-parser-output .navbox-title .navbar{float:left;text-align:left;margin-right:0.5em}body.skin--responsive .mw-parser-output .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_systems390" 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_systems390" 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 class="mw-selflink selflink">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 href="/wiki/Schulze_method" title="Schulze method">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" class="mw-redirect" 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?useformat=desktop&type=1x1&usesul3=0" alt="" width="1" height="1" style="border: none; position: 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