CINXE.COM

<!DOCTYPE html> <html class="client-nojs vector-feature-language-in-header-enabled vector-feature-language-in-main-page-header-disabled vector-feature-page-tools-pinned-disabled vector-feature-toc-pinned-clientpref-1 vector-feature-main-menu-pinned-disabled vector-feature-limited-width-clientpref-1 vector-feature-limited-width-content-enabled vector-feature-custom-font-size-clientpref-1 vector-feature-appearance-pinned-clientpref-1 vector-feature-night-mode-enabled skin-theme-clientpref-day vector-sticky-header-enabled vector-toc-available" lang="en" dir="ltr"> <head> <meta charset="UTF-8"> <title>Ranked voting - Wikipedia</title> <script>(function(){var className="client-js vector-feature-language-in-header-enabled vector-feature-language-in-main-page-header-disabled vector-feature-page-tools-pinned-disabled vector-feature-toc-pinned-clientpref-1 vector-feature-main-menu-pinned-disabled vector-feature-limited-width-clientpref-1 vector-feature-limited-width-content-enabled vector-feature-custom-font-size-clientpref-1 vector-feature-appearance-pinned-clientpref-1 vector-feature-night-mode-enabled skin-theme-clientpref-day vector-sticky-header-enabled vector-toc-available";var cookie=document.cookie.match(/(?:^|; )enwikimwclientpreferences=([^;]+)/);if(cookie){cookie[1].split('%2C').forEach(function(pref){className=className.replace(new RegExp('(^| )'+pref.replace(/-clientpref-\w+$|[^\w-]+/g,'')+'-clientpref-\\w+( |$)'),'$1'+pref+'$2');});}document.documentElement.className=className;}());RLCONF={"wgBreakFrames":false,"wgSeparatorTransformTable":["",""],"wgDigitTransformTable":["",""],"wgDefaultDateFormat":"dmy", "wgMonthNames":["","January","February","March","April","May","June","July","August","September","October","November","December"],"wgRequestId":"0deb0cea-f39b-4e73-ab99-d51050968a6d","wgCanonicalNamespace":"","wgCanonicalSpecialPageName":false,"wgNamespaceNumber":0,"wgPageName":"Ranked_voting","wgTitle":"Ranked voting","wgCurRevisionId":1276976550,"wgRevisionId":1276976550,"wgArticleId":36968102,"wgIsArticle":true,"wgIsRedirect":false,"wgAction":"view","wgUserName":null,"wgUserGroups":["*"],"wgCategories":["CS1 French-language sources (fr)","Articles with short description","Short description matches Wikidata","Use mdy dates from February 2025","All articles with unsourced statements","Articles with unsourced statements from July 2024","Pages displaying wikidata descriptions as a fallback via Module:Annotated link","Instant-runoff voting","Cardinal electoral systems","Electoral systems","Preferential electoral systems","Proportional representation electoral systems","Psephology", "Public choice theory","Social choice theory"],"wgPageViewLanguage":"en","wgPageContentLanguage":"en","wgPageContentModel":"wikitext","wgRelevantPageName":"Ranked_voting","wgRelevantArticleId":36968102,"wgIsProbablyEditable":true,"wgRelevantPageIsProbablyEditable":true,"wgRestrictionEdit":[],"wgRestrictionMove":[],"wgRedirectedFrom":"Ranked_voting_systems","wgNoticeProject":"wikipedia","wgCiteReferencePreviewsActive":false,"wgFlaggedRevsParams":{"tags":{"status":{"levels":1}}},"wgMediaViewerOnClick":true,"wgMediaViewerEnabledByDefault":true,"wgPopupsFlags":0,"wgVisualEditor":{"pageLanguageCode":"en","pageLanguageDir":"ltr","pageVariantFallbacks":"en"},"wgMFDisplayWikibaseDescriptions":{"search":true,"watchlist":true,"tagline":false,"nearby":true},"wgWMESchemaEditAttemptStepOversample":false,"wgWMEPageLength":30000,"wgInternalRedirectTargetUrl":"/wiki/Ranked_voting","wgEditSubmitButtonLabelPublish":true,"wgULSPosition":"interlanguage","wgULSisCompactLinksEnabled":false, "wgVector2022LanguageInHeader":true,"wgULSisLanguageSelectorEmpty":false,"wgWikibaseItemId":"Q1078003","wgCheckUserClientHintsHeadersJsApi":["brands","architecture","bitness","fullVersionList","mobile","model","platform","platformVersion"],"GEHomepageSuggestedEditsEnableTopics":true,"wgGETopicsMatchModeEnabled":false,"wgGEStructuredTaskRejectionReasonTextInputEnabled":false,"wgGELevelingUpEnabledForUser":false};RLSTATE={"ext.globalCssJs.user.styles":"ready","site.styles":"ready","user.styles":"ready","ext.globalCssJs.user":"ready","user":"ready","user.options":"loading","ext.cite.styles":"ready","skins.vector.search.codex.styles":"ready","skins.vector.styles":"ready","skins.vector.icons":"ready","jquery.makeCollapsible.styles":"ready","ext.wikimediamessages.styles":"ready","ext.visualEditor.desktopArticleTarget.noscript":"ready","ext.uls.interlanguage":"ready","wikibase.client.init":"ready"};RLPAGEMODULES=["mediawiki.action.view.redirect","ext.cite.ux-enhancements", "mediawiki.page.media","ext.scribunto.logs","site","mediawiki.page.ready","jquery.makeCollapsible","mediawiki.toc","skins.vector.js","ext.centralNotice.geoIP","ext.centralNotice.startUp","ext.gadget.ReferenceTooltips","ext.gadget.switcher","ext.urlShortener.toolbar","ext.centralauth.centralautologin","mmv.bootstrap","ext.popups","ext.visualEditor.desktopArticleTarget.init","ext.visualEditor.targetLoader","ext.echo.centralauth","ext.eventLogging","ext.wikimediaEvents","ext.navigationTiming","ext.uls.interface","ext.cx.eventlogging.campaigns","ext.cx.uls.quick.actions","wikibase.client.vector-2022","ext.checkUser.clientHints","ext.growthExperiments.SuggestedEditSession"];</script> <script>(RLQ=window.RLQ||[]).push(function(){mw.loader.impl(function(){return["user.options@12s5i",function($,jQuery,require,module){mw.user.tokens.set({"patrolToken":"+\\","watchToken":"+\\","csrfToken":"+\\"}); }];});});</script> <link rel="stylesheet" href="/w/load.php?lang=en&modules=ext.cite.styles%7Cext.uls.interlanguage%7Cext.visualEditor.desktopArticleTarget.noscript%7Cext.wikimediamessages.styles%7Cjquery.makeCollapsible.styles%7Cskins.vector.icons%2Cstyles%7Cskins.vector.search.codex.styles%7Cwikibase.client.init&only=styles&skin=vector-2022"> <script async="" src="/w/load.php?lang=en&modules=startup&only=scripts&raw=1&skin=vector-2022"></script> <meta name="ResourceLoaderDynamicStyles" content=""> <link rel="stylesheet" href="/w/load.php?lang=en&modules=site.styles&only=styles&skin=vector-2022"> <meta name="generator" content="MediaWiki 1.44.0-wmf.18"> <meta name="referrer" content="origin"> <meta name="referrer" content="origin-when-cross-origin"> <meta name="robots" content="max-image-preview:standard"> <meta name="format-detection" content="telephone=no"> <meta property="og:image" content="https://upload.wikimedia.org/wikipedia/commons/4/4d/Rankballotoval.gif"> <meta property="og:image:width" content="1200"> <meta property="og:image:height" content="1546"> <meta property="og:image" content="https://upload.wikimedia.org/wikipedia/commons/4/4d/Rankballotoval.gif"> <meta property="og:image:width" content="800"> <meta property="og:image:height" content="1030"> <meta property="og:image:width" content="640"> <meta property="og:image:height" content="824"> <meta name="viewport" content="width=1120"> <meta property="og:title" content="Ranked voting - Wikipedia"> <meta property="og:type" content="website"> <link rel="preconnect" href="//upload.wikimedia.org"> <link rel="alternate" media="only screen and (max-width: 640px)" href="//en.m.wikipedia.org/wiki/Ranked_voting"> <link rel="alternate" type="application/x-wiki" title="Edit this page" href="/w/index.php?title=Ranked_voting&action=edit"> <link rel="apple-touch-icon" href="/static/apple-touch/wikipedia.png"> <link rel="icon" href="/static/favicon/wikipedia.ico"> <link rel="search" type="application/opensearchdescription+xml" href="/w/rest.php/v1/search" title="Wikipedia (en)"> <link rel="EditURI" type="application/rsd+xml" href="//en.wikipedia.org/w/api.php?action=rsd"> <link rel="canonical" href="https://en.wikipedia.org/wiki/Ranked_voting"> <link rel="license" href="https://creativecommons.org/licenses/by-sa/4.0/deed.en"> <link rel="alternate" type="application/atom+xml" title="Wikipedia Atom feed" href="/w/index.php?title=Special:RecentChanges&feed=atom"> <link rel="dns-prefetch" href="//meta.wikimedia.org" /> <link rel="dns-prefetch" href="login.wikimedia.org"> </head> <body class="skin--responsive skin-vector skin-vector-search-vue mediawiki ltr sitedir-ltr mw-hide-empty-elt ns-0 ns-subject mw-editable page-Ranked_voting rootpage-Ranked_voting skin-vector-2022 action-view"><a class="mw-jump-link" href="#bodyContent">Jump to content</a> <div class="vector-header-container"> <header class="vector-header mw-header"> <div class="vector-header-start"> <nav class="vector-main-menu-landmark" aria-label="Site"> <div id="vector-main-menu-dropdown" class="vector-dropdown vector-main-menu-dropdown vector-button-flush-left vector-button-flush-right" title="Main menu" > <input type="checkbox" id="vector-main-menu-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-main-menu-dropdown" class="vector-dropdown-checkbox " aria-label="Main menu" > <label id="vector-main-menu-dropdown-label" for="vector-main-menu-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-menu mw-ui-icon-wikimedia-menu"></span> <span class="vector-dropdown-label-text">Main menu</span> </label> <div class="vector-dropdown-content"> <div id="vector-main-menu-unpinned-container" class="vector-unpinned-container"> <div id="vector-main-menu" class="vector-main-menu vector-pinnable-element"> <div class="vector-pinnable-header vector-main-menu-pinnable-header vector-pinnable-header-unpinned" data-feature-name="main-menu-pinned" data-pinnable-element-id="vector-main-menu" data-pinned-container-id="vector-main-menu-pinned-container" data-unpinned-container-id="vector-main-menu-unpinned-container" > <div class="vector-pinnable-header-label">Main menu</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-main-menu.pin">move to sidebar</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-main-menu.unpin">hide</button> </div> <div id="p-navigation" class="vector-menu mw-portlet mw-portlet-navigation" > <div class="vector-menu-heading"> Navigation </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="n-mainpage-description" class="mw-list-item"><a href="/wiki/Main_Page" title="Visit the main page [z]" accesskey="z"><span>Main page</span></a></li><li id="n-contents" class="mw-list-item"><a href="/wiki/Wikipedia:Contents" title="Guides to browsing Wikipedia"><span>Contents</span></a></li><li id="n-currentevents" class="mw-list-item"><a href="/wiki/Portal:Current_events" title="Articles related to current events"><span>Current events</span></a></li><li id="n-randompage" class="mw-list-item"><a href="/wiki/Special:Random" title="Visit a randomly selected article [x]" accesskey="x"><span>Random article</span></a></li><li id="n-aboutsite" class="mw-list-item"><a href="/wiki/Wikipedia:About" title="Learn about Wikipedia and how it works"><span>About Wikipedia</span></a></li><li id="n-contactpage" class="mw-list-item"><a href="//en.wikipedia.org/wiki/Wikipedia:Contact_us" title="How to contact Wikipedia"><span>Contact us</span></a></li> </ul> </div> </div> <div id="p-interaction" class="vector-menu mw-portlet mw-portlet-interaction" > <div class="vector-menu-heading"> Contribute </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="n-help" class="mw-list-item"><a href="/wiki/Help:Contents" title="Guidance on how to use and edit Wikipedia"><span>Help</span></a></li><li id="n-introduction" class="mw-list-item"><a href="/wiki/Help:Introduction" title="Learn how to edit Wikipedia"><span>Learn to edit</span></a></li><li id="n-portal" class="mw-list-item"><a href="/wiki/Wikipedia:Community_portal" title="The hub for editors"><span>Community portal</span></a></li><li id="n-recentchanges" class="mw-list-item"><a href="/wiki/Special:RecentChanges" title="A list of recent changes to Wikipedia [r]" accesskey="r"><span>Recent changes</span></a></li><li id="n-upload" class="mw-list-item"><a href="/wiki/Wikipedia:File_upload_wizard" title="Add images or other media for use on Wikipedia"><span>Upload file</span></a></li><li id="n-specialpages" class="mw-list-item"><a href="/wiki/Special:SpecialPages"><span>Special pages</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> <a href="/wiki/Main_Page" class="mw-logo"> <img class="mw-logo-icon" src="/static/images/icons/wikipedia.png" alt="" aria-hidden="true" height="50" width="50"> <span class="mw-logo-container skin-invert"> <img class="mw-logo-wordmark" alt="Wikipedia" src="/static/images/mobile/copyright/wikipedia-wordmark-en.svg" style="width: 7.5em; height: 1.125em;"> <img class="mw-logo-tagline" alt="The Free Encyclopedia" src="/static/images/mobile/copyright/wikipedia-tagline-en.svg" width="117" height="13" style="width: 7.3125em; height: 0.8125em;"> </span> </a> </div> <div class="vector-header-end"> <div id="p-search" role="search" class="vector-search-box-vue vector-search-box-collapses vector-search-box-show-thumbnail vector-search-box-auto-expand-width vector-search-box"> <a href="/wiki/Special:Search" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only search-toggle" title="Search Wikipedia [f]" accesskey="f"><span class="vector-icon mw-ui-icon-search mw-ui-icon-wikimedia-search"></span> <span>Search</span> </a> <div class="vector-typeahead-search-container"> <div class="cdx-typeahead-search cdx-typeahead-search--show-thumbnail cdx-typeahead-search--auto-expand-width"> <form action="/w/index.php" id="searchform" class="cdx-search-input cdx-search-input--has-end-button"> <div id="simpleSearch" class="cdx-search-input__input-wrapper" data-search-loc="header-moved"> <div class="cdx-text-input cdx-text-input--has-start-icon"> <input class="cdx-text-input__input" type="search" name="search" placeholder="Search Wikipedia" aria-label="Search Wikipedia" autocapitalize="sentences" title="Search Wikipedia [f]" accesskey="f" id="searchInput" > <span class="cdx-text-input__icon cdx-text-input__start-icon"></span> </div> <input type="hidden" name="title" value="Special:Search"> </div> <button class="cdx-button cdx-search-input__end-button">Search</button> </form> </div> </div> </div> <nav class="vector-user-links vector-user-links-wide" aria-label="Personal tools"> <div class="vector-user-links-main"> <div id="p-vector-user-menu-preferences" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <div id="p-vector-user-menu-userpage" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <nav class="vector-appearance-landmark" aria-label="Appearance"> <div id="vector-appearance-dropdown" class="vector-dropdown " title="Change the appearance of the page's font size, width, and color" > <input type="checkbox" id="vector-appearance-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-appearance-dropdown" class="vector-dropdown-checkbox " aria-label="Appearance" > <label id="vector-appearance-dropdown-label" for="vector-appearance-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-appearance mw-ui-icon-wikimedia-appearance"></span> <span class="vector-dropdown-label-text">Appearance</span> </label> <div class="vector-dropdown-content"> <div id="vector-appearance-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <div id="p-vector-user-menu-notifications" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <div id="p-vector-user-menu-overflow" class="vector-menu mw-portlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="https://donate.wikimedia.org/?wmf_source=donate&wmf_medium=sidebar&wmf_campaign=en.wikipedia.org&uselang=en" class=""><span>Donate</span></a> </li> <li id="pt-createaccount-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=Special:CreateAccount&returnto=Ranked+voting" title="You are encouraged to create an account and log in; however, it is not mandatory" class=""><span>Create account</span></a> </li> <li id="pt-login-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=Special:UserLogin&returnto=Ranked+voting" title="You're encouraged to log in; however, it's not mandatory. [o]" accesskey="o" class=""><span>Log in</span></a> </li> </ul> </div> </div> </div> <div id="vector-user-links-dropdown" class="vector-dropdown vector-user-menu vector-button-flush-right vector-user-menu-logged-out" title="Log in and more options" > <input type="checkbox" id="vector-user-links-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-user-links-dropdown" class="vector-dropdown-checkbox " aria-label="Personal tools" > <label id="vector-user-links-dropdown-label" for="vector-user-links-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-ellipsis mw-ui-icon-wikimedia-ellipsis"></span> <span class="vector-dropdown-label-text">Personal tools</span> </label> <div class="vector-dropdown-content"> <div id="p-personal" class="vector-menu mw-portlet mw-portlet-personal user-links-collapsible-item" title="User menu" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport" class="user-links-collapsible-item mw-list-item"><a href="https://donate.wikimedia.org/?wmf_source=donate&wmf_medium=sidebar&wmf_campaign=en.wikipedia.org&uselang=en"><span>Donate</span></a></li><li id="pt-createaccount" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Special:CreateAccount&returnto=Ranked+voting" title="You are encouraged to create an account and log in; however, it is not mandatory"><span class="vector-icon mw-ui-icon-userAdd mw-ui-icon-wikimedia-userAdd"></span> <span>Create account</span></a></li><li id="pt-login" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Special:UserLogin&returnto=Ranked+voting" title="You're encouraged to log in; however, it's not mandatory. [o]" accesskey="o"><span class="vector-icon mw-ui-icon-logIn mw-ui-icon-wikimedia-logIn"></span> <span>Log in</span></a></li> </ul> </div> </div> <div id="p-user-menu-anon-editor" class="vector-menu mw-portlet mw-portlet-user-menu-anon-editor" > <div class="vector-menu-heading"> Pages for logged out editors <a href="/wiki/Help:Introduction" aria-label="Learn more about editing"><span>learn more</span></a> </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-anoncontribs" class="mw-list-item"><a href="/wiki/Special:MyContributions" title="A list of edits made from this IP address [y]" accesskey="y"><span>Contributions</span></a></li><li id="pt-anontalk" class="mw-list-item"><a href="/wiki/Special:MyTalk" title="Discussion about edits from this IP address [n]" accesskey="n"><span>Talk</span></a></li> </ul> </div> </div> </div> </div> </nav> </div> </header> </div> <div class="mw-page-container"> <div class="mw-page-container-inner"> <div class="vector-sitenotice-container"> <div id="siteNotice"></div> </div> <div class="vector-column-start"> <div class="vector-main-menu-container"> <div id="mw-navigation"> <nav id="mw-panel" class="vector-main-menu-landmark" aria-label="Site"> <div id="vector-main-menu-pinned-container" class="vector-pinned-container"> </div> </nav> </div> </div> <div class="vector-sticky-pinned-container"> <nav id="mw-panel-toc" aria-label="Contents" data-event-name="ui.sidebar-toc" class="mw-table-of-contents-container vector-toc-landmark"> <div id="vector-toc-pinned-container" class="vector-pinned-container"> <div id="vector-toc" class="vector-toc vector-pinnable-element"> <div class="vector-pinnable-header vector-toc-pinnable-header vector-pinnable-header-pinned" data-feature-name="toc-pinned" data-pinnable-element-id="vector-toc" > <h2 class="vector-pinnable-header-label">Contents</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">move to sidebar</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">hide</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">(Top)</div> </a> </li> <li id="toc-History_of_ranked_voting" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#History_of_ranked_voting"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>History of ranked voting</span> </div> </a> <button aria-controls="toc-History_of_ranked_voting-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 History of ranked voting subsection</span> </button> <ul id="toc-History_of_ranked_voting-sublist" class="vector-toc-list"> <li id="toc-Adoption" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Adoption"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1</span> <span>Adoption</span> </div> </a> <ul id="toc-Adoption-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Equal-ranked_ballots" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Equal-ranked_ballots"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Equal-ranked ballots</span> </div> </a> <ul id="toc-Equal-ranked_ballots-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Theoretical_foundations_of_ranked_voting" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Theoretical_foundations_of_ranked_voting"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Theoretical foundations of ranked voting</span> </div> </a> <button aria-controls="toc-Theoretical_foundations_of_ranked_voting-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 Theoretical foundations of ranked voting subsection</span> </button> <ul id="toc-Theoretical_foundations_of_ranked_voting-sublist" class="vector-toc-list"> <li id="toc-Majority-rule" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Majority-rule"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1</span> <span>Majority-rule</span> </div> </a> <ul id="toc-Majority-rule-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Social_well-being" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Social_well-being"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2</span> <span>Social well-being</span> </div> </a> <ul id="toc-Social_well-being-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Spatial_voting_models" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Spatial_voting_models"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.3</span> <span>Spatial voting models</span> </div> </a> <ul id="toc-Spatial_voting_models-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Other_theorems" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Other_theorems"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.4</span> <span>Other theorems</span> </div> </a> <ul id="toc-Other_theorems-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Examples" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Examples"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Examples</span> </div> </a> <button aria-controls="toc-Examples-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 Examples subsection</span> </button> <ul id="toc-Examples-sublist" class="vector-toc-list"> <li id="toc-Borda_count" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Borda_count"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1</span> <span>Borda count</span> </div> </a> <ul id="toc-Borda_count-sublist" class="vector-toc-list"> <li id="toc-Other_positional_systems" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Other_positional_systems"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1.1</span> <span>Other positional systems</span> </div> </a> <ul id="toc-Other_positional_systems-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Instant-runoff_voting" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Instant-runoff_voting"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.2</span> <span>Instant-runoff voting</span> </div> </a> <ul id="toc-Instant-runoff_voting-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Single_transferable_voting" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Single_transferable_voting"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.3</span> <span>Single transferable voting</span> </div> </a> <ul id="toc-Single_transferable_voting-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Defeat-dropping_Condorcet" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Defeat-dropping_Condorcet"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.4</span> <span>Defeat-dropping Condorcet</span> </div> </a> <ul id="toc-Defeat-dropping_Condorcet-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>References</span> </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</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" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Toggle the table of contents" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Toggle the table of contents</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Ranked voting</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Go to an article in another language. Available in 26 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-26" 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">26 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%A7%D9%82%D8%AA%D8%B1%D8%A7%D8%B9_%D8%AA%D8%B1%D8%A7%D8%AA%D8%A8%D9%8A" title="اقتراع تراتبي – Arabic" lang="ar" hreflang="ar" data-title="اقتراع تراتبي" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%9F%D1%80%D0%B5%D1%84%D0%B5%D1%80%D0%B5%D0%BD%D1%86%D0%B8%D0%B0%D0%BB%D0%BD%D0%BE_%D0%B3%D0%BB%D0%B0%D1%81%D1%83%D0%B2%D0%B0%D0%BD%D0%B5" title="Преференциално гласуване – Bulgarian" lang="bg" hreflang="bg" data-title="Преференциално гласуване" data-language-autonym="Български" data-language-local-name="Bulgarian" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Po%C5%99adov%C3%A9_volby" title="Pořadové volby – Czech" lang="cs" hreflang="cs" data-title="Pořadové volby" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-cy mw-list-item"><a href="https://cy.wikipedia.org/wiki/Pleidleisio_ffafriol" title="Pleidleisio ffafriol – Welsh" lang="cy" hreflang="cy" data-title="Pleidleisio ffafriol" data-language-autonym="Cymraeg" data-language-local-name="Welsh" class="interlanguage-link-target"><span>Cymraeg</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Pr%C3%A4ferenzwahl" title="Präferenzwahl – German" lang="de" hreflang="de" data-title="Präferenzwahl" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%A8%CE%AE%CF%86%CE%BF%CF%82_%CE%BC%CE%B5_%CF%83%CE%B5%CE%B9%CF%81%CE%AC_%CF%80%CF%81%CE%BF%CF%84%CE%AF%CE%BC%CE%B7%CF%83%CE%B7%CF%82" title="Ψήφος με σειρά προτίμησης – Greek" lang="el" hreflang="el" data-title="Ψήφος με σειρά προτίμησης" data-language-autonym="Ελληνικά" data-language-local-name="Greek" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Voto_por_orden_de_preferencia" title="Voto por orden de preferencia – Spanish" lang="es" hreflang="es" data-title="Voto por orden de preferencia" 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/%D9%86%D8%B8%D8%A7%D9%85_%D8%A7%D9%86%D8%AA%D8%AE%D8%A7%D8%A8%D8%A7%D8%AA%DB%8C_%D8%AA%D8%B1%D8%AC%DB%8C%D8%AD%DB%8C" title="نظام انتخاباتی ترجیحی – Persian" lang="fa" hreflang="fa" data-title="نظام انتخاباتی ترجیحی" 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/Vote_pr%C3%A9f%C3%A9rentiel" title="Vote préférentiel – French" lang="fr" hreflang="fr" data-title="Vote préférentiel" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%84%A0%ED%98%B8%ED%88%AC%ED%91%9C%EC%A0%9C" title="선호투표제 – Korean" lang="ko" hreflang="ko" data-title="선호투표제" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%B0%E0%A5%88%E0%A4%82%E0%A4%95%E0%A4%BF%E0%A4%82%E0%A4%97_%E0%A4%B5%E0%A5%8B%E0%A4%9F%E0%A4%BF%E0%A4%82%E0%A4%97" title="रैंकिंग वोटिंग – Hindi" lang="hi" hreflang="hi" data-title="रैंकिंग वोटिंग" data-language-autonym="हिन्दी" data-language-local-name="Hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Prioritetinis_balsavimas" title="Prioritetinis balsavimas – Lithuanian" lang="lt" hreflang="lt" data-title="Prioritetinis balsavimas" data-language-autonym="Lietuvių" data-language-local-name="Lithuanian" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Preferenci%C3%A1lis_szavaz%C3%A1s" title="Preferenciális szavazás – Hungarian" lang="hu" hreflang="hu" data-title="Preferenciális szavazás" data-language-autonym="Magyar" data-language-local-name="Hungarian" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Gerangschikt_stemmen" title="Gerangschikt stemmen – Dutch" lang="nl" hreflang="nl" data-title="Gerangschikt stemmen" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E9%81%B8%E5%A5%BD%E6%8A%95%E7%A5%A8" title="選好投票 – Japanese" lang="ja" hreflang="ja" data-title="選好投票" 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/Preferansevalg" title="Preferansevalg – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Preferansevalg" 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-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Preferanseval" title="Preferanseval – Norwegian Nynorsk" lang="nn" hreflang="nn" data-title="Preferanseval" data-language-autonym="Norsk nynorsk" data-language-local-name="Norwegian Nynorsk" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Preferensial_ovoz_berish" title="Preferensial ovoz berish – Uzbek" lang="uz" hreflang="uz" data-title="Preferensial ovoz berish" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="Uzbek" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Ordynacja_preferencyjna" title="Ordynacja preferencyjna – Polish" lang="pl" hreflang="pl" data-title="Ordynacja preferencyjna" 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/Voto_preferencial" title="Voto preferencial – Portuguese" lang="pt" hreflang="pt" data-title="Voto preferencial" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Vot_preferen%C8%9Bial" title="Vot preferențial – Romanian" lang="ro" hreflang="ro" data-title="Vot preferențial" data-language-autonym="Română" data-language-local-name="Romanian" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%9F%D1%80%D0%B5%D1%84%D0%B5%D1%80%D0%B5%D0%BD%D1%86%D0%B8%D0%B0%D0%BB%D1%8C%D0%BD%D0%BE%D0%B5_%D0%B3%D0%BE%D0%BB%D0%BE%D1%81%D0%BE%D0%B2%D0%B0%D0%BD%D0%B8%D0%B5" title="Преференциальное голосование – Russian" lang="ru" hreflang="ru" data-title="Преференциальное голосование" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Painotettu_vaalitapa" title="Painotettu vaalitapa – Finnish" lang="fi" hreflang="fi" data-title="Painotettu vaalitapa" data-language-autonym="Suomi" data-language-local-name="Finnish" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%81%E0%B8%B2%E0%B8%A3%E0%B8%A5%E0%B8%87%E0%B8%84%E0%B8%B0%E0%B9%81%E0%B8%99%E0%B8%99%E0%B9%81%E0%B8%9A%E0%B8%9A%E0%B8%88%E0%B8%B1%E0%B8%94%E0%B8%A5%E0%B8%B3%E0%B8%94%E0%B8%B1%E0%B8%9A" title="การลงคะแนนแบบจัดลำดับ – Thai" lang="th" hreflang="th" data-title="การลงคะแนนแบบจัดลำดับ" data-language-autonym="ไทย" data-language-local-name="Thai" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E5%81%8F%E5%A5%BD%E6%8A%95%E7%A5%A8%E5%88%B6" title="偏好投票制 – Cantonese" lang="yue" hreflang="yue" data-title="偏好投票制" data-language-autonym="粵語" data-language-local-name="Cantonese" class="interlanguage-link-target"><span>粵語</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E6%8E%92%E5%BA%8F%E6%8A%95%E7%A5%A8%E5%88%B6" title="排序投票制 – Chinese" lang="zh" hreflang="zh" data-title="排序投票制" 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/Q1078003#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" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-nstab-main" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/Ranked_voting" title="View the content page [c]" accesskey="c"><span>Article</span></a></li><li id="ca-talk" class="vector-tab-noicon mw-list-item"><a href="/wiki/Talk:Ranked_voting" rel="discussion" title="Discuss improvements to the content page [t]" accesskey="t"><span>Talk</span></a></li> </ul> </div> </div> <div id="vector-variants-dropdown" class="vector-dropdown emptyPortlet" > <input type="checkbox" id="vector-variants-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-variants-dropdown" class="vector-dropdown-checkbox " aria-label="Change language variant" > <label id="vector-variants-dropdown-label" for="vector-variants-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">English</span> </label> <div class="vector-dropdown-content"> <div id="p-variants" class="vector-menu mw-portlet mw-portlet-variants emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> </div> </div> </nav> </div> <div id="right-navigation" class="vector-collapsible"> <nav aria-label="Views"> <div id="p-views" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-views" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-view" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/Ranked_voting"><span>Read</span></a></li><li id="ca-edit" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Ranked_voting&action=edit" title="Edit this page [e]" accesskey="e"><span>Edit</span></a></li><li id="ca-history" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Ranked_voting&action=history" title="Past revisions of this page [h]" accesskey="h"><span>View history</span></a></li> </ul> </div> </div> </nav> <nav class="vector-page-tools-landmark" aria-label="Page tools"> <div id="vector-page-tools-dropdown" class="vector-dropdown vector-page-tools-dropdown" > <input type="checkbox" id="vector-page-tools-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-tools-dropdown" class="vector-dropdown-checkbox " aria-label="Tools" > <label id="vector-page-tools-dropdown-label" for="vector-page-tools-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">Tools</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-tools-unpinned-container" class="vector-unpinned-container"> <div id="vector-page-tools" class="vector-page-tools vector-pinnable-element"> <div class="vector-pinnable-header vector-page-tools-pinnable-header vector-pinnable-header-unpinned" data-feature-name="page-tools-pinned" data-pinnable-element-id="vector-page-tools" data-pinned-container-id="vector-page-tools-pinned-container" data-unpinned-container-id="vector-page-tools-unpinned-container" > <div class="vector-pinnable-header-label">Tools</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-page-tools.pin">move to sidebar</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-page-tools.unpin">hide</button> </div> <div id="p-cactions" class="vector-menu mw-portlet mw-portlet-cactions emptyPortlet vector-has-collapsible-items" title="More options" > <div class="vector-menu-heading"> Actions </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-more-view" class="selected vector-more-collapsible-item mw-list-item"><a href="/wiki/Ranked_voting"><span>Read</span></a></li><li id="ca-more-edit" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Ranked_voting&action=edit" title="Edit this page [e]" accesskey="e"><span>Edit</span></a></li><li id="ca-more-history" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Ranked_voting&action=history"><span>View history</span></a></li> </ul> </div> </div> <div id="p-tb" class="vector-menu mw-portlet mw-portlet-tb" > <div class="vector-menu-heading"> General </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-whatlinkshere" class="mw-list-item"><a href="/wiki/Special:WhatLinksHere/Ranked_voting" title="List of all English Wikipedia pages containing links to this page [j]" accesskey="j"><span>What links here</span></a></li><li id="t-recentchangeslinked" class="mw-list-item"><a href="/wiki/Special:RecentChangesLinked/Ranked_voting" rel="nofollow" title="Recent changes in pages linked from this page [k]" accesskey="k"><span>Related changes</span></a></li><li id="t-upload" class="mw-list-item"><a href="//en.wikipedia.org/wiki/Wikipedia:File_Upload_Wizard" title="Upload files [u]" accesskey="u"><span>Upload file</span></a></li><li id="t-permalink" class="mw-list-item"><a href="/w/index.php?title=Ranked_voting&oldid=1276976550" title="Permanent link to this revision of this page"><span>Permanent link</span></a></li><li id="t-info" class="mw-list-item"><a href="/w/index.php?title=Ranked_voting&action=info" title="More information about this page"><span>Page information</span></a></li><li id="t-cite" class="mw-list-item"><a href="/w/index.php?title=Special:CiteThisPage&page=Ranked_voting&id=1276976550&wpFormIdentifier=titleform" title="Information on how to cite this page"><span>Cite this page</span></a></li><li id="t-urlshortener" class="mw-list-item"><a href="/w/index.php?title=Special:UrlShortener&url=https%3A%2F%2Fen.wikipedia.org%2Fwiki%2FRanked_voting"><span>Get shortened URL</span></a></li><li id="t-urlshortener-qrcode" class="mw-list-item"><a href="/w/index.php?title=Special:QrCode&url=https%3A%2F%2Fen.wikipedia.org%2Fwiki%2FRanked_voting"><span>Download QR code</span></a></li> </ul> </div> </div> <div id="p-coll-print_export" class="vector-menu mw-portlet mw-portlet-coll-print_export" > <div class="vector-menu-heading"> Print/export </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="coll-download-as-rl" class="mw-list-item"><a href="/w/index.php?title=Special:DownloadAsPdf&page=Ranked_voting&action=show-download-screen" title="Download this page as a PDF file"><span>Download as PDF</span></a></li><li id="t-print" class="mw-list-item"><a href="/w/index.php?title=Ranked_voting&printable=yes" title="Printable version of this page [p]" accesskey="p"><span>Printable version</span></a></li> </ul> </div> </div> <div id="p-wikibase-otherprojects" class="vector-menu mw-portlet mw-portlet-wikibase-otherprojects" > <div class="vector-menu-heading"> In other projects </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="wb-otherproject-link wb-otherproject-commons mw-list-item"><a href="https://commons.wikimedia.org/wiki/Category:Ranked_voting" hreflang="en"><span>Wikimedia Commons</span></a></li><li id="t-wikibase" class="wb-otherproject-link wb-otherproject-wikibase-dataitem mw-list-item"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q1078003" title="Structured data on this page hosted by Wikidata [g]" accesskey="g"><span>Wikidata item</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> </div> </div> </div> <div class="vector-column-end"> <div class="vector-sticky-pinned-container"> <nav class="vector-page-tools-landmark" aria-label="Page tools"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="Appearance"> <div id="vector-appearance-pinned-container" class="vector-pinned-container"> <div id="vector-appearance" class="vector-appearance vector-pinnable-element"> <div class="vector-pinnable-header vector-appearance-pinnable-header vector-pinnable-header-pinned" data-feature-name="appearance-pinned" data-pinnable-element-id="vector-appearance" data-pinned-container-id="vector-appearance-pinned-container" data-unpinned-container-id="vector-appearance-unpinned-container" > <div class="vector-pinnable-header-label">Appearance</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">move to sidebar</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">hide</button> </div> </div> </div> </nav> </div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">From Wikipedia, the free encyclopedia</div> </div> <div id="contentSub"><div id="mw-content-subtitle"><span class="mw-redirectedfrom">(Redirected from <a href="/w/index.php?title=Ranked_voting_systems&redirect=no" class="mw-redirect" title="Ranked voting systems">Ranked voting systems</a>)</span></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Voting systems that use ranked ballots</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">For the voting system often called <i>ranked-choice voting</i> in the United States, see <a href="/wiki/Instant-runoff_voting" title="Instant-runoff voting">Instant-runoff voting</a>.</div> <p class="mw-empty-elt"> </p> <style data-mw-deduplicate="TemplateStyles:r1273380762/mw-parser-output/.tmulti">.mw-parser-output .tmulti .multiimageinner{display:flex;flex-direction:column}.mw-parser-output .tmulti .trow{display:flex;flex-direction:row;clear:left;flex-wrap:wrap;width:100%;box-sizing:border-box}.mw-parser-output .tmulti .tsingle{margin:1px;float:left}.mw-parser-output .tmulti .theader{clear:both;font-weight:bold;text-align:center;align-self:center;background-color:transparent;width:100%}.mw-parser-output .tmulti .thumbcaption{background-color:transparent}.mw-parser-output .tmulti .text-align-left{text-align:left}.mw-parser-output .tmulti .text-align-right{text-align:right}.mw-parser-output .tmulti .text-align-center{text-align:center}@media all and (max-width:720px){.mw-parser-output .tmulti .thumbinner{width:100%!important;box-sizing:border-box;max-width:none!important;align-items:center}.mw-parser-output .tmulti .trow{justify-content:center}.mw-parser-output .tmulti .tsingle{float:none!important;max-width:100%!important;box-sizing:border-box;text-align:center}.mw-parser-output .tmulti .tsingle .thumbcaption{text-align:left}.mw-parser-output .tmulti .trow>.thumbcaption{text-align:center}}@media screen{html.skin-theme-clientpref-night .mw-parser-output .tmulti .multiimageinner span:not(.skin-invert-image):not(.skin-invert):not(.bg-transparent) img{background-color:white}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .tmulti .multiimageinner span:not(.skin-invert-image):not(.skin-invert):not(.bg-transparent) img{background-color:white}}</style><div class="thumb tmulti tright"><div class="thumbinner multiimageinner" style="width:492px;max-width:492px"><div class="trow"><div class="tsingle" style="width:162px;max-width:162px"><div class="thumbimage"><span typeof="mw:File"><a href="/wiki/File:Rankballotoval.gif" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4d/Rankballotoval.gif/160px-Rankballotoval.gif" decoding="async" width="160" height="206" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4d/Rankballotoval.gif/240px-Rankballotoval.gif 1.5x, //upload.wikimedia.org/wikipedia/commons/4/4d/Rankballotoval.gif 2x" data-file-width="243" data-file-height="313" /></a></span></div><div class="thumbcaption">Ovals</div></div><div class="tsingle" style="width:162px;max-width:162px"><div class="thumbimage"><span typeof="mw:File"><a href="/wiki/File:Rankballotname2.gif" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/1/15/Rankballotname2.gif/160px-Rankballotname2.gif" decoding="async" width="160" height="202" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/15/Rankballotname2.gif/240px-Rankballotname2.gif 1.5x, //upload.wikimedia.org/wikipedia/commons/1/15/Rankballotname2.gif 2x" data-file-width="246" data-file-height="311" /></a></span></div><div class="thumbcaption">Names</div></div><div class="tsingle" style="width:162px;max-width:162px"><div class="thumbimage"><span typeof="mw:File"><a href="/wiki/File:Preferential_ballot.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/1/18/Preferential_ballot.svg/160px-Preferential_ballot.svg.png" decoding="async" width="160" height="207" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/18/Preferential_ballot.svg/240px-Preferential_ballot.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/18/Preferential_ballot.svg/320px-Preferential_ballot.svg.png 2x" data-file-width="765" data-file-height="990" /></a></span></div><div class="thumbcaption">Numbers</div></div></div><div class="trow" style="display:flex"><div class="thumbcaption">Various types of ranked voting ballot</div></div></div></div> <style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output .hlist.inline ul,.mw-parser-output .hlist dl dl,.mw-parser-output .hlist dl ol,.mw-parser-output .hlist dl ul,.mw-parser-output .hlist ol dl,.mw-parser-output .hlist ol ol,.mw-parser-output .hlist ol ul,.mw-parser-output .hlist ul dl,.mw-parser-output .hlist ul ol,.mw-parser-output .hlist ul ul{display:inline}.mw-parser-output .hlist .mw-empty-li{display:none}.mw-parser-output .hlist dt::after{content:": "}.mw-parser-output .hlist dd::after,.mw-parser-output .hlist li::after{content:" · ";font-weight:bold}.mw-parser-output .hlist dd:last-child::after,.mw-parser-output .hlist dt:last-child::after,.mw-parser-output .hlist li:last-child::after{content:none}.mw-parser-output .hlist dd dd:first-child::before,.mw-parser-output .hlist dd dt:first-child::before,.mw-parser-output .hlist dd li:first-child::before,.mw-parser-output .hlist dt dd:first-child::before,.mw-parser-output .hlist dt dt:first-child::before,.mw-parser-output .hlist dt li:first-child::before,.mw-parser-output .hlist li dd:first-child::before,.mw-parser-output .hlist li dt:first-child::before,.mw-parser-output .hlist li li:first-child::before{content:" (";font-weight:normal}.mw-parser-output .hlist dd dd:last-child::after,.mw-parser-output .hlist dd dt:last-child::after,.mw-parser-output .hlist dd li:last-child::after,.mw-parser-output .hlist dt dd:last-child::after,.mw-parser-output .hlist dt dt:last-child::after,.mw-parser-output .hlist dt li:last-child::after,.mw-parser-output .hlist li dd:last-child::after,.mw-parser-output .hlist li dt:last-child::after,.mw-parser-output .hlist li li:last-child::after{content:")";font-weight:normal}.mw-parser-output .hlist ol{counter-reset:listitem}.mw-parser-output .hlist ol>li{counter-increment:listitem}.mw-parser-output .hlist ol>li::before{content:" "counter(listitem)"\a0 "}.mw-parser-output .hlist dd ol>li:first-child::before,.mw-parser-output .hlist dt ol>li:first-child::before,.mw-parser-output .hlist li ol>li:first-child::before{content:" ("counter(listitem)"\a0 "}</style><style data-mw-deduplicate="TemplateStyles:r1246091330">.mw-parser-output .sidebar{width:22em;float:right;clear:right;margin:0.5em 0 1em 1em;background:var(--background-color-neutral-subtle,#f8f9fa);border:1px solid var(--border-color-base,#a2a9b1);padding:0.2em;text-align:center;line-height:1.4em;font-size:88%;border-collapse:collapse;display:table}body.skin-minerva .mw-parser-output .sidebar{display:table!important;float:right!important;margin:0.5em 0 1em 1em!important}.mw-parser-output .sidebar-subgroup{width:100%;margin:0;border-spacing:0}.mw-parser-output .sidebar-left{float:left;clear:left;margin:0.5em 1em 1em 0}.mw-parser-output .sidebar-none{float:none;clear:both;margin:0.5em 1em 1em 0}.mw-parser-output .sidebar-outer-title{padding:0 0.4em 0.2em;font-size:125%;line-height:1.2em;font-weight:bold}.mw-parser-output .sidebar-top-image{padding:0.4em}.mw-parser-output .sidebar-top-caption,.mw-parser-output .sidebar-pretitle-with-top-image,.mw-parser-output .sidebar-caption{padding:0.2em 0.4em 0;line-height:1.2em}.mw-parser-output .sidebar-pretitle{padding:0.4em 0.4em 0;line-height:1.2em}.mw-parser-output .sidebar-title,.mw-parser-output .sidebar-title-with-pretitle{padding:0.2em 0.8em;font-size:145%;line-height:1.2em}.mw-parser-output .sidebar-title-with-pretitle{padding:0.1em 0.4em}.mw-parser-output .sidebar-image{padding:0.2em 0.4em 0.4em}.mw-parser-output .sidebar-heading{padding:0.1em 0.4em}.mw-parser-output .sidebar-content{padding:0 0.5em 0.4em}.mw-parser-output .sidebar-content-with-subgroup{padding:0.1em 0.4em 0.2em}.mw-parser-output .sidebar-above,.mw-parser-output .sidebar-below{padding:0.3em 0.8em;font-weight:bold}.mw-parser-output .sidebar-collapse .sidebar-above,.mw-parser-output .sidebar-collapse .sidebar-below{border-top:1px solid #aaa;border-bottom:1px solid #aaa}.mw-parser-output .sidebar-navbar{text-align:right;font-size:115%;padding:0 0.4em 0.4em}.mw-parser-output .sidebar-list-title{padding:0 0.4em;text-align:left;font-weight:bold;line-height:1.6em;font-size:105%}.mw-parser-output .sidebar-list-title-c{padding:0 0.4em;text-align:center;margin:0 3.3em}@media(max-width:640px){body.mediawiki .mw-parser-output .sidebar{width:100%!important;clear:both;float:none!important;margin-left:0!important;margin-right:0!important}}body.skin--responsive .mw-parser-output .sidebar a>img{max-width:none!important}@media screen{html.skin-theme-clientpref-night .mw-parser-output .sidebar:not(.notheme) .sidebar-list-title,html.skin-theme-clientpref-night .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle{background:transparent!important}html.skin-theme-clientpref-night .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle a{color:var(--color-progressive)!important}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .sidebar:not(.notheme) .sidebar-list-title,html.skin-theme-clientpref-os .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle{background:transparent!important}html.skin-theme-clientpref-os .mw-parser-output .sidebar:not(.notheme) .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 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/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 href="/wiki/Borda_count" title="Borda count">Borda count</a> (<abbr style="font-size:85%" title=""><a href="/wiki/Sequential_elimination_method" title="Sequential elimination method">el.</a></abbr> <a href="/wiki/Baldwin%27s_method" class="mw-redirect" title="Baldwin's method">Baldwin</a>)</li> <li><a href="/wiki/Anti-plurality_voting" title="Anti-plurality voting">Antiplurality</a> (<abbr style="font-size:85%" title=""><a href="/wiki/Sequential_elimination_method" title="Sequential elimination method">el.</a></abbr> <a href="/wiki/Coombs_method" class="mw-redirect" title="Coombs method">Coombs</a>)</li></ul> <hr /> <p><b><a href="/wiki/Rated_voting" title="Rated voting">Cardinal voting</a></b> </p> <ul><li><a href="/wiki/Score_voting" title="Score voting">Score voting</a></li> <li><a href="/wiki/Approval_voting" title="Approval voting">Approval voting</a></li> <li><a href="/wiki/Highest_median_voting_rules" title="Highest median voting rules">Majority judgment</a></li> <li><a href="/wiki/STAR_voting" title="STAR voting">STAR voting</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content" style="text-align:left;"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:#efefef; border-top:1px solid;background: var(--background-color-interactive, #efefef); color: var(--color-base, #000);;color: var(--color-base)"><a href="/wiki/Proportional_representation" title="Proportional representation">Proportional representation</a></div><div class="sidebar-list-content mw-collapsible-content"><b><a href="/wiki/Party-list_proportional_representation" title="Party-list proportional representation">Party-list</a></b> <ul><li><a href="/wiki/Apportionment_(politics)" title="Apportionment (politics)">Apportionment</a> <ul><li><a href="/wiki/Highest_averages_method" title="Highest averages method">Highest averages</a></li> <li><a href="/wiki/Largest_remainder_method" class="mw-redirect" title="Largest remainder method">Largest remainders</a></li> <li><a href="/wiki/National_remnant" title="National remnant">National remnant</a></li> <li><a href="/wiki/Biproportional_apportionment" title="Biproportional apportionment">Biproportional</a></li></ul></li> <li><a href="/wiki/Electoral_list" title="Electoral list">List type</a> <ul><li><a href="/wiki/Closed_list" title="Closed list">Closed list</a></li> <li><a href="/wiki/Open_list" title="Open list">Open list</a></li> <li><a href="/wiki/Panachage" title="Panachage">Panachage</a></li> <li><a href="/wiki/Justified_representation" title="Justified representation">List-free PR</a></li> <li><a href="/wiki/Localized_list" title="Localized list">Localized list</a></li></ul></li></ul> <hr /> <p><b><a href="/wiki/Electoral_quota" title="Electoral quota">Quota-remainder methods</a></b> </p> <ul><li><a href="/wiki/Single_transferable_vote" title="Single transferable vote">Hare STV</a></li> <li><a href="/wiki/Schulze_STV" title="Schulze STV">Schulze STV</a></li> <li><a href="/wiki/CPO-STV" title="CPO-STV">CPO-STV</a></li> <li><a href="/wiki/Quota_Borda_system" title="Quota Borda system">Quota Borda</a></li></ul> <hr /> <p><b><a href="/wiki/Approval-based_committee" class="mw-redirect" title="Approval-based committee">Approval-based committees</a></b> </p> <ul><li><a href="/wiki/Proportional_approval_voting" title="Proportional approval voting">Thiele's method</a></li> <li><a href="/wiki/Phragmen%27s_voting_rules" title="Phragmen's voting rules">Phragmen's method</a></li> <li><a href="/wiki/Expanding_approvals_rule" title="Expanding approvals rule">Expanding approvals rule</a></li> <li><a href="/wiki/Method_of_equal_shares" title="Method of equal shares">Method of equal shares</a></li></ul> <hr /> <p><b><a href="/wiki/Fractional_social_choice" title="Fractional social choice">Fractional social choice</a></b> </p> <ul><li><a href="/wiki/Direct_representation" title="Direct representation">Direct representation</a> <ul><li><a href="/wiki/Interactive_representation" title="Interactive representation">Interactive representation</a></li> <li><a href="/wiki/Liquid_democracy" title="Liquid democracy">Liquid democracy</a></li></ul></li> <li><a href="/wiki/Fractional_approval_voting" title="Fractional approval voting">Fractional approval voting</a></li> <li><a href="/wiki/Maximal_lottery" class="mw-redirect" title="Maximal lottery">Maximal lottery</a></li> <li><a href="/wiki/Random_ballot" title="Random ballot">Random ballot</a></li></ul> <hr /> <p><b><a href="/wiki/Semi-proportional_representation" title="Semi-proportional representation">Semi-proportional representation</a></b> </p> <ul><li><a href="/wiki/Cumulative_voting" title="Cumulative voting">Cumulative</a> <ul><li><a href="/wiki/Single_non-transferable_vote" title="Single non-transferable vote">SNTV</a></li></ul></li> <li><a href="/wiki/Limited_voting" title="Limited voting">Limited voting</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content" style="text-align:left;"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:#efefef; border-top:1px solid;background: var(--background-color-interactive, #efefef); color: var(--color-base, #000);;color: var(--color-base)"><a href="/wiki/Mixed_electoral_system" title="Mixed electoral system">Mixed systems</a></div><div class="sidebar-list-content mw-collapsible-content"><b>By results of combination</b> <ul><li><a href="/wiki/Mixed-member_majoritarian_representation" title="Mixed-member majoritarian representation">Mixed-member majoritarian</a></li> <li><a href="/wiki/Mixed-member_proportional_representation" title="Mixed-member proportional representation">Mixed-member proportional</a></li></ul> <hr /><b>By mechanism of combination</b> <ul><li><b>Non-<a href="/wiki/Compensation_(electoral_systems)" title="Compensation (electoral systems)">compensatory</a></b> <ul><li><a href="/wiki/Parallel_voting" title="Parallel voting">Parallel (superposition)</a></li> <li><a href="/wiki/Coexistence_(electoral_systems)" title="Coexistence (electoral systems)">Coexistence</a></li> <li><a href="/w/index.php?title=Conditional_electoral_system&action=edit&redlink=1" class="new" title="Conditional electoral system (page does not exist)">Conditional</a></li> <li><a href="/wiki/Majority_bonus_system" title="Majority bonus system">Fusion (majority bonus)</a></li></ul></li> <li><b><a href="/wiki/Compensation_(electoral_systems)" title="Compensation (electoral systems)">Compensatory</a></b> <ul><li><a href="/w/index.php?title=Seat_linkage_mixed_system&action=edit&redlink=1" class="new" title="Seat linkage mixed system (page does not exist)">Seat linkage system</a> <ul><li><abbr style="font-size:85%" title=""><a href="/wiki/British_English" title="British English">UK</a>:</abbr> <a href="/wiki/Additional_member_system" class="mw-redirect" title="Additional member system">'AMS'</a></li> <li><abbr style="font-size:85%" title=""><a href="/wiki/New_Zealand_English" title="New Zealand English">NZ</a>:</abbr> <a href="/wiki/Mixed-member_proportional" class="mw-redirect" title="Mixed-member proportional">'MMP'</a></li></ul></li> <li><a href="/wiki/Vote_linkage_mixed_system" class="mw-redirect" title="Vote linkage mixed system">Vote linkage system</a> <ul><li><a href="/wiki/Scorporo" title="Scorporo">Negative vote transfer</a></li> <li><a href="/wiki/Mixed_ballot_transferable_vote" title="Mixed ballot transferable vote">Mixed ballot</a></li></ul></li></ul></li> <li><a href="/wiki/Mixed_electoral_system" title="Mixed electoral system">Supermixed systems</a> <ul><li><a href="/wiki/Dual-member_proportional_representation" class="mw-redirect" title="Dual-member proportional representation">Dual-member proportional</a></li> <li><a href="/wiki/Rural%E2%80%93urban_proportional_representation" title="Rural–urban proportional representation">Rural–urban proportional</a></li> <li><a href="/wiki/Majority_jackpot_system" title="Majority jackpot system">Majority jackpot</a></li></ul></li></ul> <hr /> <p><b>By ballot type</b> </p> <ul><li><a href="/wiki/Mixed_single_vote" title="Mixed single vote">Single vote</a> <ul><li><a href="/wiki/Double_simultaneous_vote" title="Double simultaneous vote">Double simultaneous vote</a></li></ul></li> <li><a href="/wiki/Mixed_electoral_systems" class="mw-redirect" title="Mixed electoral systems">Dual-vote</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content" style="text-align:left;"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:#efefef; border-top:1px solid;background: var(--background-color-interactive, #efefef); color: var(--color-base, #000);;color: var(--color-base)"><a href="/wiki/Pathological_(mathematics)#Voting" title="Pathological (mathematics)">Paradoxes and pathologies</a></div><div class="sidebar-list-content mw-collapsible-content"><b>Spoiler effects</b> <ul><li><a href="/wiki/Spoiler_effect" title="Spoiler effect">Spoiler effect</a></li> <li><a href="/wiki/Independence_of_clones" class="mw-redirect" title="Independence of clones">Cloning paradox</a></li> <li><a href="/wiki/Condorcet_winner_criterion" title="Condorcet winner criterion">Frustrated majorities paradox</a></li> <li><a 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> <li><a href="/wiki/Wasted_vote" title="Wasted vote">Wasted vote</a></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 href="/wiki/File:Emblem-money.svg" class="mw-file-description"><img alt="icon" src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f3/Emblem-money.svg/16px-Emblem-money.svg.png" decoding="async" width="16" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f3/Emblem-money.svg/24px-Emblem-money.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f3/Emblem-money.svg/32px-Emblem-money.svg.png 2x" data-file-width="48" data-file-height="48" /></a></span> </span><a href="/wiki/Portal:Economics" title="Portal:Economics">Economics portal</a></li></ul></div><span class="nowrap"><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Nuvola_apps_edu_mathematics_blue-p.svg" class="mw-file-description"><img alt="icon" src="//upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Nuvola_apps_edu_mathematics_blue-p.svg/16px-Nuvola_apps_edu_mathematics_blue-p.svg.png" decoding="async" width="16" height="16" class="mw-file-element" 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><b>Ranked voting</b> is any <a href="/wiki/Voting_system" class="mw-redirect" title="Voting system">voting system</a> that uses voters' <a href="/wiki/Ordinal_utility" title="Ordinal utility">rankings</a> of candidates to choose a single winner or multiple winners. More formally, a ranked system is one that depends only on which of two candidates is preferred by a voter, and as such does not incorporate any information about <a href="/wiki/Rated_voting" title="Rated voting">intensity of preferences</a>. Ranked voting systems vary dramatically in how preferences are tabulated and counted, which gives them <a href="/wiki/Comparison_of_voting_rules" title="Comparison of voting rules">very different properties</a>. In <a href="/wiki/Instant-runoff_voting" title="Instant-runoff voting">instant-runoff voting</a> (IRV) and the <a href="/wiki/Single_transferable_vote" title="Single transferable vote">single transferable vote</a> system (STV), lower preferences are used as contingencies (back-up preferences) and are only applied when all higher-ranked preferences on a ballot have been eliminated or when the vote has been cast for a candidate who has been elected and surplus votes need to be transferred. </p><p>Some ranked vote systems use ranks as weights; this type of system is called <a href="/wiki/Positional_voting" title="Positional voting">positional voting</a>. In the <a href="/wiki/Borda_count" title="Borda count">Borda method</a>, the 1st, 2nd, 3rd... candidates on each ballot receive <span class="texhtml">1, 2, 3...</span> points, and the candidate with the fewest points is elected. Thus intensity of preference is assumed to be at ratios of 1 to 2, 2 to 3, etc. Although not typically described as such, the well-known <a href="/wiki/Plurality_voting" title="Plurality voting">plurality rule</a> can be seen as a ranked voting system where a voter gives a single point to the candidate marked as their choice and zero points to all others, and the candidate with the most points is elected. Taking the ranked ballots of instant-runoff voting and the single transferable vote system as indicating one choice at a time (that is, giving one point to the preference in use and zero points to all others), instant-runoff voting can be seen as a non-<a href="/wiki/Degeneracy_(mathematics)" title="Degeneracy (mathematics)">degenerate</a> ranked voting systems. It operates as a staged variant of the plurality system that repeatedly eliminate last-place plurality winners if necessary to determine a majority winner.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p><p>In the United States and Australia, the terms <i>ranked-choice voting</i> and <i>preferential voting</i>, respectively, almost always refer to <a href="/wiki/Instant-runoff_voting" title="Instant-runoff voting">instant-runoff voting</a>; however, because these terms have also been used to mean ranked systems in general, many <a href="/wiki/Social_choice_theorists" class="mw-redirect" title="Social choice theorists">social choice theorists</a> recommend the use of <i>instant-runoff voting</i> in contexts where it could cause confusion. Ranked voting systems, such as Borda count, are usually contrasted with <a href="/wiki/Rated_voting" title="Rated voting">rated voting</a> methods, which allow voters to indicate <i>how strongly</i> they support different candidates (e.g. on a scale from 0 to 10).<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> Ranked vote systems produce more information than X voting systems such as <a href="/wiki/First-past-the-post_voting" title="First-past-the-post voting">first-past-the-post voting</a>. Rated voting systems produce more information than ordinal ballots; as a result, some common results like <a href="/wiki/Arrow%27s_impossibility_theorem" title="Arrow's impossibility theorem">Arrow's theorem</a> do not directly apply to them.<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="History_of_ranked_voting">History of ranked voting</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Ranked_voting&action=edit&section=1" title="Edit section: History of ranked voting"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951" /><div role="note" class="hatnote navigation-not-searchable">Main articles: <a href="/wiki/Electoral_system" title="Electoral system">Electoral system</a> and <a href="/wiki/Social_choice_theory" title="Social choice theory">Social choice theory</a></div> <p>The earliest known proposals for a ranked voting system can be traced to the works of <a href="/wiki/Ramon_Llull" title="Ramon Llull">Ramon Llull</a> in the late 13th century, who developed what would later be known as <a href="/wiki/Copeland%27s_method" title="Copeland's method">Copeland's method</a>, which is similar to <a href="/wiki/Condorcet_method" title="Condorcet method">Condorcet's method</a>. Copeland's method was devised by <a href="/wiki/Ramon_Llull" title="Ramon Llull">Ramon Llull</a> in his 1299 treatise <i>Ars Electionis,</i> which was discussed by <a href="/wiki/Nicholas_of_Cusa" title="Nicholas of Cusa">Nicholas of Cusa</a> in the fifteenth century.<sup id="cite_ref-:0_4-0" class="reference"><a href="#cite_note-:0-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> </p><p>A second wave of analysis began when <a href="/wiki/Jean-Charles_de_Borda" title="Jean-Charles de Borda">Jean-Charles de Borda</a> published a paper in 1781, advocating for the <a href="/wiki/Borda_count" title="Borda count">Borda count</a>, which he called the "order of merit". This methodology drew criticism from the <a href="/wiki/Marquis_de_Condorcet" title="Marquis de Condorcet">Marquis de Condorcet</a>, who developed <a href="/wiki/Condorcet_method" title="Condorcet method">his own methods</a> after arguing Borda's approach did not accurately reflect group preferences, because it was vulnerable to <a href="/wiki/Spoiler_effect" title="Spoiler effect">spoiler effects</a> and did not always elect the <a href="/wiki/Majority-preferred_candidate" class="mw-redirect" title="Majority-preferred candidate">majority-preferred candidate</a>.<sup id="cite_ref-:0_4-1" class="reference"><a href="#cite_note-:0-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p><p>Interest in ranked voting continued throughout the 19th century. <a href="/wiki/Carl_Christoffer_Georg_Andr%C3%A6" title="Carl Christoffer Georg Andræ">Carl Andræ</a> formulated a version of the <a href="/wiki/Single_transferable_vote" title="Single transferable vote">single transferable vote</a> election system, which was adopted by his country, <a href="/wiki/Denmark" title="Denmark">Denmark</a>, in 1855. This used contingent ranked votes but did not include transfers of eliminated candidates.<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><sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> </p><p>Condorcet considered a single-winner version of STV, the <a href="/wiki/Instant-runoff_voting" title="Instant-runoff voting">instant-runoff</a> system, but rejected it as <a href="/wiki/Pathological_(mathematics)#In_voting" title="Pathological (mathematics)">pathological</a>.<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>Professor W.R. Ware held a demonstration STV election in 1871, having 150 M.I.T. students elect four English authors as their favorites. The field of candidates held the names of 35 authors in the first count, and eventually concentrated behind just four. Ware went on to surmise how a casual vacancy might be handled and found that countback would produce a winner. This proved that ranked transferable votes could be used to produce a single winner, despite the qualms of Condorcet and others.<sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> </p><p><a href="/wiki/Single_transferable_voting" class="mw-redirect" title="Single transferable voting">Single transferable voting</a> (contingent ranked transferable vote) later found common use in cities and to elect legislators in North America, Ireland and other parts of the English-speaking world, with single-winner versions, alternative voting (now known as <a href="/wiki/Instant-runoff_voting" title="Instant-runoff voting">instant-runoff voting</a>) and <a href="/wiki/Contingent_vote" title="Contingent vote">contingent voting</a> (also known as supplementary voting), being its companions for single-winner contests of mayors and others.<sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> </p><p>Theoretical exploration of electoral processes was revived by a 1948 paper from <a href="/wiki/Duncan_Black" title="Duncan Black">Duncan Black</a><sup id="cite_ref-black2_12-0" class="reference"><a href="#cite_note-black2-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> and <a href="/wiki/Kenneth_Arrow" title="Kenneth Arrow">Kenneth Arrow</a>'s investigations into <a href="/wiki/Social_choice_theory" title="Social choice theory">social choice theory</a>, a branch of <a href="/wiki/Welfare_economics" title="Welfare economics">welfare economics</a> that extends <a href="/wiki/Decision_theory" title="Decision theory">rational choice</a> to include community decision-making processes.<sup id="cite_ref-Arrow_1963232_13-0" class="reference"><a href="#cite_note-Arrow_1963232-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Adoption">Adoption</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Ranked_voting&action=edit&section=2" title="Edit section: Adoption"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/Plurality_voting" title="Plurality voting">Plurality voting</a> is the most common voting system, and has been in widespread use since the earliest <a href="/wiki/Democracy" title="Democracy">democracies</a>. As <a href="/wiki/Plurality_voting" title="Plurality voting">plurality voting</a> has exhibited weaknesses from its start, especially as soon as a third party joins the race, some individuals turned to transferable votes (facilitated by contingent ranked ballots) to reduce the incidence of wasted votes and unrepresentative election results.<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 2024)">citation needed</span></a></i>]</sup> </p><p>A form of the <a href="/wiki/Single_transferable_vote" title="Single transferable vote">single transferable vote</a> system was invented by <a href="/wiki/Carl_Christoffer_Georg_Andr%C3%A6" title="Carl Christoffer Georg Andræ">Carl Andræ</a> in Denmark, where it was used briefly before being abandoned in favour of <a href="/wiki/Open_list" title="Open list">open list</a> list PR, but still carried on for indirect election of the <a href="/wiki/Landsting_(Denmark)" title="Landsting (Denmark)">upper house</a> until 1953.<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 2024)">citation needed</span></a></i>]</sup> </p><p>At approximately the same time, the single transferable vote system was independently devised by British lawyer <a href="/wiki/Thomas_Hare_(political_reformer)" title="Thomas Hare (political reformer)">Thomas Hare</a>, whose writings soon spread the method throughout the <a href="/wiki/British_Empire" title="British Empire">British Empire</a>. <a href="/wiki/Tasmania" title="Tasmania">Tasmania</a> used STV (called the Hare system) in government elections in the 1890s. STV began permanent and wider adoption throughout Australia beginning in 1907 and the 1910s.<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> The single transferable vote system, using contingent ranked votes, has been adopted in Ireland, South Africa, Malta, and approximately 40 cities <a href="/wiki/Ranked-choice_voting_in_the_United_States" title="Ranked-choice voting in the United States">in the United States</a> and Canada.<sup id="cite_ref-Santucci_15-0" class="reference"><a href="#cite_note-Santucci-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> The single transferable vote system has also been used to elect legislators in Canada, South Africa and India. </p><p>In more recent years, the use of contingent ranked votes has seen a comeback <a href="/wiki/Ranked-choice_voting_in_the_United_States" title="Ranked-choice voting in the United States">in the United States</a>. Single-winner ranked voting (specifically <a href="/wiki/Instant-runoff_voting" title="Instant-runoff voting">instant-runoff voting</a>), is used to elect politicians in Maine<sup id="cite_ref-16" class="reference"><a href="#cite_note-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> and Alaska.<sup id="cite_ref-17" class="reference"><a href="#cite_note-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup> In November 2016, the voters of <a href="/wiki/Maine" title="Maine">Maine</a> narrowly passed Question 5, approving ranked-choice voting (instant-runoff voting) for all elections. This was first put to use in 2018, marking the inaugural use of ranked votes in a statewide election in the United States (when Maine's statewide vote tally was used to determine the two at-large electoral college seats). </p><p>In November 2020, <a href="/wiki/Alaska" title="Alaska">Alaska</a> voters passed Measure 2, bringing ranked choice voting (instant-runoff voting) into effect from 2022.<sup id="cite_ref-18" class="reference"><a href="#cite_note-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-19" class="reference"><a href="#cite_note-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> After a series of <a href="/wiki/Pathological_(mathematics)" title="Pathological (mathematics)">electoral pathologies</a> in Alaska's <a href="/wiki/2022_Alaska%27s_at-large_congressional_district_special_election" title="2022 Alaska's at-large congressional district special election">2022 congressional special election</a>, a poll found 54% of Alaskans supported a repeal of the system. This included a third of the voters who had supported <a href="/wiki/Mary_Peltola" title="Mary Peltola">Peltola</a>, the ultimate winner in the election. However, a referendum on the issue in 2024 saw a narrow majority in favour of retention of IRV.<sup id="cite_ref-z562_20-0" class="reference"><a href="#cite_note-z562-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-North_21-0" class="reference"><a href="#cite_note-North-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup> </p><p>Some <a href="/wiki/Local_elections_in_New_Zealand" title="Local elections in New Zealand">local elections in New Zealand</a> and in the U.S. use the multi-winner <a href="/wiki/Single_transferable_vote" title="Single transferable vote">single transferable vote</a>.<sup id="cite_ref-22" class="reference"><a href="#cite_note-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-h160_23-0" class="reference"><a href="#cite_note-h160-23"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup> STV is also used to elect local authorities in Scotland<sup id="cite_ref-24" class="reference"><a href="#cite_note-24"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup> and Ireland.<sup id="cite_ref-25" class="reference"><a href="#cite_note-25"><span class="cite-bracket">[</span>25<span class="cite-bracket">]</span></a></sup> Nauru uses a rank-weighted <a href="/wiki/Positional_voting" title="Positional voting">positional method</a> called the <a href="/wiki/Dowdall_system" class="mw-redirect" title="Dowdall system">Dowdall system</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Equal-ranked_ballots">Equal-ranked ballots<span class="anchor" id="Equal_ranks"></span><span class="anchor" id="Tied_ranks"></span></h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Ranked_voting&action=edit&section=3" title="Edit section: Equal-ranked ballots"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In <a href="/wiki/Voting" title="Voting">voting</a> with ranked ballots, a <b>tied</b> or <b>equal-rank</b> ballot is one where multiple candidates receive the same rank or rating. In <a href="/wiki/Instant_runoff" class="mw-redirect" title="Instant runoff">instant runoff</a> and <a href="/wiki/First-preference_plurality" class="mw-redirect" title="First-preference plurality">first-preference plurality</a>, such ballots are generally rejected; however, in <a href="/wiki/Social_choice_theory" title="Social choice theory">social choice theory</a> some election systems assume equal-ranked ballots are "split" evenly between all equal-ranked candidates (e.g. in a two-way tie, each candidate receives half a vote). Meanwhile, other election systems, the <a href="/wiki/Borda_count" title="Borda count">Borda count</a> and the <a href="/wiki/Condorcet_method" title="Condorcet method">Condorcet method</a>, can use different rules for handling equal-rank ballots. These rules produce different mathematical properties and behaviors, particularly under <a href="/wiki/Strategic_voting" title="Strategic voting">strategic voting</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Theoretical_foundations_of_ranked_voting">Theoretical foundations of ranked voting</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Ranked_voting&action=edit&section=4" title="Edit section: Theoretical foundations of ranked voting"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Majority-rule">Majority-rule</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Ranked_voting&action=edit&section=5" title="Edit section: Majority-rule"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951" /><div role="note" class="hatnote navigation-not-searchable">Main articles: <a href="/wiki/Condorcet_efficiency" title="Condorcet efficiency">Condorcet efficiency</a> and <a href="/wiki/Condorcet_winner_criterion" title="Condorcet winner criterion">Condorcet winner criterion</a></div> <p>Many concepts formulated by the <a href="/wiki/Marquis_de_Condorcet" title="Marquis de Condorcet">Marquis de Condorcet</a> in the 18th century continue to significantly impact the field. One of these concepts is the <a href="/wiki/Condorcet_winner" class="mw-redirect" title="Condorcet winner">Condorcet winner</a>, a candidate who would win against any other candidate in a two-way race. A voting system that always elects this candidate is called a <a href="/wiki/Condorcet_methods" class="mw-redirect" title="Condorcet methods">Condorcet method</a>; however, it is possible for an election to have no Condorcet winner, a situation called a <a href="/wiki/Condorcet_cycle" class="mw-redirect" title="Condorcet cycle">Condorcet cycle</a>. Suppose an election with 3 candidates <i>A</i>, <i>B</i>, and <i>C</i> has 3 voters. One votes <span class="nowrap"><i>A</i> > <i>C</i> > <i>B</i></span>, one votes <span class="nowrap"><i>B</i> > <i>A</i> > <i>C</i></span>, and one votes <span class="nowrap"><i>C</i> > <i>B</i> > <i>A</i></span>. In this case, no Condorcet winner exists: <i>A</i> cannot be a Condorcet winner as two-thirds of voters prefer <i>B</i> over <i>A</i>. Similarly, <i>B</i> cannot be the winner as two-thirds prefer <i>C</i> over <i>B</i>, and <i>C</i> cannot win as two-thirds prefer <i>A</i> over <i>C</i>. This forms a <a href="/wiki/Rock-paper-scissors" class="mw-redirect" title="Rock-paper-scissors">rock-paper-scissors</a> style cycle with no Condorcet winner. </p> <div class="mw-heading mw-heading3"><h3 id="Social_well-being">Social well-being</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Ranked_voting&action=edit&section=6" title="Edit section: Social well-being"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951" /><div role="note" class="hatnote navigation-not-searchable">Main articles: <a href="/wiki/Social_utility_efficiency" title="Social utility efficiency">Social utility efficiency</a> and <a href="/wiki/Implicit_utilitarian_voting" title="Implicit utilitarian voting">Implicit utilitarian voting</a></div> <p>Voting systems can also be judged on their ability to deliver results that maximize the overall <a href="/wiki/Social_utility_efficiency" title="Social utility efficiency">well-being of society</a>, i.e. to choose the best candidate for society as a whole.<sup id="cite_ref-:1_26-0" class="reference"><a href="#cite_note-:1-26"><span class="cite-bracket">[</span>26<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Spatial_voting_models">Spatial voting models</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Ranked_voting&action=edit&section=7" title="Edit section: Spatial voting models"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951" /><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Median_voter_theorem" title="Median voter theorem">Median voter theorem</a></div> <p>Spatial voting models, initially proposed by <a href="/wiki/Duncan_Black" title="Duncan Black">Duncan Black</a> and further developed by <a href="/wiki/Anthony_Downs" title="Anthony Downs">Anthony Downs</a>, provide a theoretical framework for understanding electoral behavior. In these models, each voter and candidate is positioned within an ideological space that can span multiple dimensions. It is assumed that voters tend to favor candidates who closely align with their ideological position over those more distant. A <a href="/wiki/Political_spectrum" title="Political spectrum">political spectrum</a> is an example of a one-dimensional spatial model. </p> <figure class="mw-halign-left" typeof="mw:File/Thumb"><a href="/wiki/File:IRVCopeland.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/8b/IRVCopeland.png/420px-IRVCopeland.png" decoding="async" width="420" height="220" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/8b/IRVCopeland.png/630px-IRVCopeland.png 1.5x, //upload.wikimedia.org/wikipedia/commons/8/8b/IRVCopeland.png 2x" data-file-width="730" data-file-height="382" /></a><figcaption>A spatial model of voting</figcaption></figure> <p>The accompanying diagram presents a simple one-dimensional spatial model, illustrating the voting methods discussed in subsequent sections of this article. It is assumed that supporters of candidate <i>A</i> cast their votes in the order of <span class="nowrap"><i>A</i> > <i>B</i> > <i>C</i></span>, while candidate <i>C</i><span class="nowrap" style="padding-left:0.1em;">'s</span> supporters vote in the sequence of <span class="nowrap"><i>C</i> > <i>B</i> > <i>A</i></span>. Supporters of candidate <i>B</i> are equally divided between listing <i>A</i> or <i>C</i> as their second preference. From the data in the accompanying table, if there are 100 voters, the distribution of ballots will reflect the positioning of voters and candidates along the ideological spectrum. </p><p>Spatial models offer significant insights because they provide an intuitive visualization of voter preferences. These models give rise to an influential theorem—the median voter theorem—attributed to Duncan Black. This theorem stipulates that within a broad range of spatial models, including all one-dimensional models and all symmetric models across multiple dimensions, a Condorcet winner is guaranteed to exist. Moreover, this winner is the candidate closest to the median of the voter distribution. Empirical research has generally found that spatial voting models give a highly accurate explanation of most voting behavior.<sup id="cite_ref-27" class="reference"><a href="#cite_note-27"><span class="cite-bracket">[</span>27<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Other_theorems">Other theorems</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Ranked_voting&action=edit&section=8" title="Edit section: Other theorems"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951" /><div role="note" class="hatnote navigation-not-searchable">Main articles: <a href="/wiki/Arrow%27s_impossibility_theorem" title="Arrow's impossibility theorem">Arrow's impossibility theorem</a> and <a href="/wiki/Gibbard%27s_theorem" title="Gibbard's theorem">Gibbard's theorem</a></div> <p><a href="/wiki/Arrow%27s_impossibility_theorem" title="Arrow's impossibility theorem">Arrow's impossibility theorem</a> is a generalization of Condorcet's result on the impossibility of majority rule. It demonstrates that every ranked voting algorithm is susceptible to the <a href="/wiki/Spoiler_effect" title="Spoiler effect">spoiler effect</a>. <a href="/wiki/Gibbard%27s_theorem" title="Gibbard's theorem">Gibbard's theorem</a> provides a closely-related corollary, that no voting rule can have a single, always-best strategy that does not depend on other voters' ballots. </p> <div class="mw-heading mw-heading2"><h2 id="Examples">Examples</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Ranked_voting&action=edit&section=9" title="Edit section: Examples"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Borda_count">Borda count</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Ranked_voting&action=edit&section=10" title="Edit section: Borda count"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951" /><div role="note" class="hatnote navigation-not-searchable">Main articles: <a href="/wiki/Borda_count" title="Borda count">Borda count</a> and <a href="/wiki/Positional_voting" title="Positional voting">Positional voting</a></div> <p>The Borda count is a weighted-rank system that assigns scores to each candidate based on their position in each ballot. If <i>m</i> is the total number of candidates, the candidate ranked first on a ballot receives <span class="nowrap"><i>m</i> − 1</span> points, the second receives <span class="nowrap"><i>m</i> − 2</span>, and so on, until the last-ranked candidate who receives zero. In the given example, candidate <i>B</i> emerges as the winner with 130 out of a total 300 points. While the Borda count is simple to administer, it does not meet the Condorcet criterion. Also, it is heavily affected by the entry of candidates who have no real chance of winning. </p> <div class="mw-heading mw-heading4"><h4 id="Other_positional_systems">Other positional systems</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Ranked_voting&action=edit&section=11" title="Edit section: Other positional systems"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Systems that award points in a similar way but possibly with a different formula are called <a href="/wiki/Positional_voting" title="Positional voting">positional systems</a>. The score vector <span class="nowrap">(<i>m</i> − 1, <i>m</i> − 2, ..., 0)</span> is associated with the Borda count, <span class="nowrap">(1, 1/2, 1/3, ..., 1/<i>m</i>)</span> defines the <a href="/wiki/Borda_count#dowdall" title="Borda count">Dowdall system</a> and <span class="nowrap">(1, 0, ..., 0)</span> equates to <a href="/wiki/First-past-the-post" class="mw-redirect" title="First-past-the-post">first-past-the-post</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Instant-runoff_voting">Instant-runoff voting</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Ranked_voting&action=edit&section=12" title="Edit section: Instant-runoff voting"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951" /><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Instant-runoff_voting" title="Instant-runoff voting">Instant-runoff voting</a></div> <p>Instant-runoff voting, often conflated with ranked-choice voting in general, is a contingent ranked-vote voting method that recursively eliminates the <a href="/wiki/Plurality_voting" title="Plurality voting">plurality</a> loser of an election until one candidate has the majority of the remaining votes. In the given example, candidate <i>A</i> is declared winner in the third round, having received a majority of votes through the accumulation of first-choice votes and redistributed votes from candidate <i>B</i>. This system embodies the voters' preferences between the final candidates, stopping when a candidate garners the preference of a majority of voters. Instant-runoff voting does not fulfill the <a href="/wiki/Condorcet_winner_criterion" title="Condorcet winner criterion">Condorcet winner criterion</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Single_transferable_voting">Single transferable voting</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Ranked_voting&action=edit&section=13" title="Edit section: Single transferable voting"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951" /><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Single_transferable_voting" class="mw-redirect" title="Single transferable voting">Single transferable voting</a></div> <p>Single transferable voting is a contingent ranked-vote voting method that elects multiple members. It elects any candidates who achieve quota, and if necessary recursively eliminates the <a href="/wiki/Plurality_voting" title="Plurality voting">plurality</a> loser at each stage of the vote count and transfers surplus votes of winners until enough are elected by quota or by still being in the running when the field of candidates is thinned to the number of remaining open seats. Because elected members are elected with the same or about the same number of votes, each party popular enough for representation receives a number of seats appropriate to the vote tallies of its candidates. The transfers reduce waste to about one quota - which in a five-seat district is about 17 percent of valid votes; in districts with more members than five, the waste is smaller. All but one quota of votes approximately are used to actually elect someone in the district so the percentage of effective votes is dependably about 80 to 90 percent of valid votes.<sup id="cite_ref-28" class="reference"><a href="#cite_note-28"><span class="cite-bracket">[</span>28<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-29" class="reference"><a href="#cite_note-29"><span class="cite-bracket">[</span>29<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Defeat-dropping_Condorcet">Defeat-dropping Condorcet</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Ranked_voting&action=edit&section=14" title="Edit section: Defeat-dropping Condorcet"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951" /><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Round-robin_voting" title="Round-robin voting">Round-robin voting</a></div> <p>The defeat-dropping Condorcet methods all look for a Condorcet winner, i.e. a candidate who is not defeated by any other candidate in a one-on-one majority vote. If there is no Condorcet winner, they repeatedly drop (set the margin to zero) for the one-on-one matchups that are closest to being tied, until there is a Condorcet winner. How "closest to being tied" is defined depends on the specific rule. For the <a href="/wiki/Minimax_Condorcet_method" title="Minimax Condorcet method">Minimax Condorcet method</a>, the elections with the smallest margin of victory are dropped, whereas in <a href="/wiki/Ranked_pairs" title="Ranked pairs">ranked pairs</a> only elections that create a cycle are eligible to be dropped (with defeats being dropped based on the margin of victory). </p> <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=Ranked_voting&action=edit&section=15" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1184024115">.mw-parser-output .div-col{margin-top:0.3em;column-width:30em}.mw-parser-output .div-col-small{font-size:90%}.mw-parser-output .div-col-rules{column-rule:1px solid #aaa}.mw-parser-output .div-col dl,.mw-parser-output .div-col ol,.mw-parser-output .div-col ul{margin-top:0}.mw-parser-output .div-col li,.mw-parser-output .div-col dd{page-break-inside:avoid;break-inside:avoid-column}</style><div class="div-col"> <ul><li><a href="/wiki/Approval_voting" title="Approval voting">Approval voting</a> – Single-winner electoral system</li> <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/Duverger%27s_law" title="Duverger's law">Duverger's law</a> – Winner-takes-all voting systems tend to result in only two viable parties</li> <li><a href="/wiki/Group_voting_ticket" title="Group voting ticket">Group voting ticket</a> – Preference lists submitted by political parties</li> <li><a href="/wiki/History_and_use_of_instant-runoff_voting" title="History and use of instant-runoff voting">History and use of instant-runoff voting</a></li> <li><a href="/wiki/Implicit_utilitarian_voting" title="Implicit utilitarian voting">Implicit utilitarian voting</a> – Use of approximation algorithms in voting</li> <li><a href="/wiki/List_of_electoral_systems_by_country" title="List of electoral systems by country">List of electoral systems by country</a></li> <li><a href="/wiki/Matrix_vote" title="Matrix vote">Matrix vote</a> – Voting procedure</li> <li><a href="/wiki/Preferential_block_voting" class="mw-redirect" title="Preferential block voting">Preferential block voting</a> – majoritarian voting system<span style="display:none" class="category-wikidata-fallback-annotation">Pages displaying wikidata descriptions as a fallback</span></li> <li><a href="/wiki/Voting_methods_in_deliberative_assemblies" title="Voting methods in deliberative assemblies">Voting methods in deliberative assemblies</a></li></ul> </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=Ranked_voting&action=edit&section=16" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap mw-references-columns"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://legislature.vermont.gov/bill/status/2024/H.424">"Bill Status H.424: An act relating to town, city, and village elections for single-seat offices using ranked-choice voting"</a>. <i>legislature.vermont.gov</i><span class="reference-accessdate">. Retrieved <span class="nowrap">March 23,</span> 2024</span>. <q>Condorcet winner. If a candidate is the winning candidate in every paired comparison, the candidate shall be declared the winner of the election.</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=legislature.vermont.gov&rft.atitle=Bill+Status+H.424%3A+An+act+relating+to+town%2C+city%2C+and+village+elections+for+single-seat+offices+using+ranked-choice+voting&rft_id=https%3A%2F%2Flegislature.vermont.gov%2Fbill%2Fstatus%2F2024%2FH.424&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARanked+voting" class="Z3988"></span></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFRiker1982" class="citation book cs1">Riker, William Harrison (1982). <i>Liberalism against populism: a confrontation between the theory of democracy and the theory of social choice</i>. Waveland Pr. pp. <span class="nowrap">29–</span>30. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0881333670" title="Special:BookSources/0881333670"><bdi>0881333670</bdi></a>. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/316034736">316034736</a>. <q><i>Ordinal utility</i> is a measure of preferences in terms of rank orders—that is, first, second, etc. ... <i>Cardinal utility</i> is a measure of preferences on a scale of cardinal numbers, such as the scale from zero to one or the scale from one to ten.</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Liberalism+against+populism%3A+a+confrontation+between+the+theory+of+democracy+and+the+theory+of+social+choice&rft.pages=%3Cspan+class%3D%22nowrap%22%3E29-%3C%2Fspan%3E30&rft.pub=Waveland+Pr&rft.date=1982&rft_id=info%3Aoclcnum%2F316034736&rft.isbn=0881333670&rft.aulast=Riker&rft.aufirst=William+Harrison&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARanked+voting" class="Z3988"></span></span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFHamlin2012" class="citation web cs1">Hamlin, Aaron (October 6, 2012). <a rel="nofollow" class="external text" href="https://web.archive.org/web/20230605225834/https://electionscience.org/commentary-analysis/voting-theory-podcast-2012-10-06-interview-with-nobel-laureate-dr-kenneth-arrow/">"Podcast 2012-10-06: Interview with Nobel Laureate Dr. Kenneth Arrow"</a>. <i>The Center for Election Science</i>. Archived from <a rel="nofollow" class="external text" href="https://www.electionscience.org/commentary-analysis/voting-theory-podcast-2012-10-06-interview-with-nobel-laureate-dr-kenneth-arrow/">the original</a> on June 5, 2023.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=The+Center+for+Election+Science&rft.atitle=Podcast+2012-10-06%3A+Interview+with+Nobel+Laureate+Dr.+Kenneth+Arrow&rft.date=2012-10-06&rft.aulast=Hamlin&rft.aufirst=Aaron&rft_id=https%3A%2F%2Fwww.electionscience.org%2Fcommentary-analysis%2Fvoting-theory-podcast-2012-10-06-interview-with-nobel-laureate-dr-kenneth-arrow%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARanked+voting" class="Z3988"></span> <style data-mw-deduplicate="TemplateStyles:r1162998676">.mw-parser-output div.pbl>div{margin-left:3em;text-indent:-3em}</style><div class="pbl" style="margin:1em auto 1em 5%;"><div><b>CES:</b> Now, you mention that your theorem applies to preferential systems or ranking systems.</div><div><b>Dr. Arrow:</b> Yes.</div><div><b>CES:</b> But the system that you're just referring to, <a href="/wiki/Approval_voting" title="Approval voting">approval voting</a>, falls within a class called <a href="/wiki/Cardinal_voting" class="mw-redirect" title="Cardinal voting">cardinal systems</a>. So not within ranking systems.</div><div><b>Dr. Arrow:</b> And as I said, that in effect implies more information.</div></div></span> </li> <li id="cite_note-:0-4"><span class="mw-cite-backlink">^ <a href="#cite_ref-:0_4-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-:0_4-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text">George G. Szpiro, "Numbers Rule: The Vexing Mathematics of Democracy, from Plato to the Present" (2010).</span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFColomer2013" class="citation journal cs1">Colomer, Josep M. (February 1, 2013). <a rel="nofollow" class="external text" href="https://doi.org/10.1007/s00355-011-0598-2">"Ramon Llull: from 'Ars electionis' to social choice theory"</a>. <i>Social Choice and Welfare</i>. <b>40</b> (2): <span class="nowrap">317–</span>328. <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%2Fs00355-011-0598-2">10.1007/s00355-011-0598-2</a>. <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/1432-217X">1432-217X</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=Ramon+Llull%3A+from+%E2%80%98Ars+electionis%E2%80%99+to+social+choice+theory&rft.volume=40&rft.issue=2&rft.pages=%3Cspan+class%3D%22nowrap%22%3E317-%3C%2Fspan%3E328&rft.date=2013-02-01&rft_id=info%3Adoi%2F10.1007%2Fs00355-011-0598-2&rft.issn=1432-217X&rft.aulast=Colomer&rft.aufirst=Josep+M.&rft_id=https%3A%2F%2Fdoi.org%2F10.1007%2Fs00355-011-0598-2&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARanked+voting" class="Z3988"></span></span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text">Hoag and Hallet, PR (1926), p. 75</span> </li> <li id="cite_note-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-7">^</a></b></span> <span class="reference-text">Droop, On Methods of Electing Representatives, p. 33</span> </li> <li id="cite_note-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-8">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFNanson1882" class="citation journal cs1">Nanson, E. J. (1882). <a rel="nofollow" class="external text" href="https://archive.org/details/transactionsproc1719roya/page/206">"Methods of election: Ware's Method"</a>. <i>Transactions and Proceedings of the Royal Society of Victoria</i>. <b>19</b>: 206. <q>The method was, however, mentioned by Condorcet, but only to be condemned.</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Transactions+and+Proceedings+of+the+Royal+Society+of+Victoria&rft.atitle=Methods+of+election%3A+Ware%27s+Method&rft.volume=19&rft.pages=206&rft.date=1882&rft.aulast=Nanson&rft.aufirst=E.+J.&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Ftransactionsproc1719roya%2Fpage%2F206&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARanked+voting" class="Z3988"></span></span> </li> <li id="cite_note-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-9">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFCondorcet1788" class="citation book cs1 cs1-prop-foreign-lang-source">Condorcet, Jean-Antoine-Nicolas de Caritat (1788). "On the Constitution and the Functions of Provincial Assemblies". <a rel="nofollow" class="external text" href="https://books.google.com/books?id=d0cwAAAAYAAJ&q=Oeuvres+de+Condorcet%2C+Volume+13&pg=PA243"><i>Complete Works of Condorcet</i></a> (in French). Vol. 13 (published 1804). p. 243. <q>En effet, lorsqu'il y a plus de trois concurrents, le véritable vœu de la pluralité peut être pour un candidat qui n'ait eu aucune des voix dans le premier scrutin.</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=On+the+Constitution+and+the+Functions+of+Provincial+Assemblies&rft.btitle=Complete+Works+of+Condorcet&rft.pages=243&rft.date=1788&rft.aulast=Condorcet&rft.aufirst=Jean-Antoine-Nicolas+de+Caritat&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3Dd0cwAAAAYAAJ%26q%3DOeuvres%2Bde%2BCondorcet%252C%2BVolume%2B13%26pg%3DPA243&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARanked+voting" class="Z3988"></span></span> </li> <li id="cite_note-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-10">^</a></b></span> <span class="reference-text">Hare, The Election of Representatives, Parliamentary and Municipal, Appendix M. The Preferential Vote (W.R. Ware), p. 350-355</span> </li> <li id="cite_note-11"><span class="mw-cite-backlink"><b><a href="#cite_ref-11">^</a></b></span> <span class="reference-text">Farrell and McAllister, Australian Electoral System, p. 60-61</span> </li> <li id="cite_note-black2-12"><span class="mw-cite-backlink"><b><a href="#cite_ref-black2_12-0">^</a></b></span> <span class="reference-text">Duncan Black, "On the Rationale of Group Decision-making" (1948).</span> </li> <li id="cite_note-Arrow_1963232-13"><span class="mw-cite-backlink"><b><a href="#cite_ref-Arrow_1963232_13-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFArrow1963" class="citation book cs1">Arrow, Kenneth Joseph Arrow (1963). <a rel="nofollow" class="external text" href="http://cowles.yale.edu/sites/default/files/files/pub/mon/m12-2-all.pdf"><i>Social Choice and Individual Values</i></a> <span class="cs1-format">(PDF)</span>. Yale University Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0300013641" title="Special:BookSources/978-0300013641"><bdi>978-0300013641</bdi></a>. <a rel="nofollow" class="external text" href="https://ghostarchive.org/archive/20221009/http://cowles.yale.edu/sites/default/files/files/pub/mon/m12-2-all.pdf">Archived</a> <span class="cs1-format">(PDF)</span> from the original on October 9, 2022.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Social+Choice+and+Individual+Values&rft.pub=Yale+University+Press&rft.date=1963&rft.isbn=978-0300013641&rft.aulast=Arrow&rft.aufirst=Kenneth+Joseph+Arrow&rft_id=http%3A%2F%2Fcowles.yale.edu%2Fsites%2Fdefault%2Ffiles%2Ffiles%2Fpub%2Fmon%2Fm12-2-all.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARanked+voting" class="Z3988"></span></span> </li> <li id="cite_note-14"><span class="mw-cite-backlink"><b><a href="#cite_ref-14">^</a></b></span> <span class="reference-text">Farrell and McAllister, The Australian Electoral System, p. 17</span> </li> <li id="cite_note-Santucci-15"><span class="mw-cite-backlink"><b><a href="#cite_ref-Santucci_15-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFSantucci2017" class="citation thesis cs1">Santucci, Jon M. (2017). <a rel="nofollow" class="external text" href="https://repository.library.georgetown.edu/bitstream/handle/10822/1044631/Santucci_georgetown_0076D_13763.pdf"><i>Three Articles on Proportional Representation in American Cities (with an Introduction)</i></a> <span class="cs1-format">(PDF)</span> (Ph.D thesis). Georgetown University.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Adissertation&rft.title=Three+Articles+on+Proportional+Representation+in+American+Cities+%28with+an+Introduction%29&rft.degree=Ph.D&rft.inst=Georgetown+University&rft.date=2017&rft.aulast=Santucci&rft.aufirst=Jon+M.&rft_id=https%3A%2F%2Frepository.library.georgetown.edu%2Fbitstream%2Fhandle%2F10822%2F1044631%2FSantucci_georgetown_0076D_13763.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARanked+voting" class="Z3988"></span></span> </li> <li id="cite_note-16"><span class="mw-cite-backlink"><b><a href="#cite_ref-16">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://legislature.maine.gov/lawlibrary/ranked-choice-voting-in-maine/9509">"Ranked Choice Voting in Maine"</a>. <i>Maine State Legislature</i><span class="reference-accessdate">. Retrieved <span class="nowrap">October 21,</span> 2021</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Maine+State+Legislature&rft.atitle=Ranked+Choice+Voting+in+Maine&rft_id=https%3A%2F%2Flegislature.maine.gov%2Flawlibrary%2Franked-choice-voting-in-maine%2F9509&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARanked+voting" class="Z3988"></span></span> </li> <li id="cite_note-17"><span class="mw-cite-backlink"><b><a href="#cite_ref-17">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.elections.alaska.gov/Core/RCV.php">"Alaska Better Elections Implementation"</a>. <i>Alaska Division of Elections</i><span class="reference-accessdate">. Retrieved <span class="nowrap">October 21,</span> 2021</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Alaska+Division+of+Elections&rft.atitle=Alaska+Better+Elections+Implementation&rft_id=https%3A%2F%2Fwww.elections.alaska.gov%2FCore%2FRCV.php&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARanked+voting" class="Z3988"></span></span> </li> <li id="cite_note-18"><span class="mw-cite-backlink"><b><a href="#cite_ref-18">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.legislature.maine.gov/lawlibrary/ranked-choice-voting-in-maine/9509">"Ranked Choice Voting in Maine"</a>. <i>legislature.maine.gov</i>. State of Maine. August 23, 2022<span class="reference-accessdate">. Retrieved <span class="nowrap">November 20,</span> 2022</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=legislature.maine.gov&rft.atitle=Ranked+Choice+Voting+in+Maine&rft.date=2022-08-23&rft_id=https%3A%2F%2Fwww.legislature.maine.gov%2Flawlibrary%2Franked-choice-voting-in-maine%2F9509&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARanked+voting" class="Z3988"></span></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"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFPiper2020" class="citation web cs1">Piper, Kelsey (November 19, 2020). <a rel="nofollow" class="external text" href="https://www.vox.com/2020/11/19/21537126/alaska-measure-2-ranked-choice-voting-results">"Alaska voters adopt ranked-choice voting in ballot initiative"</a>. <i>vox.com</i>. Vox Media<span class="reference-accessdate">. Retrieved <span class="nowrap">November 20,</span> 2022</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=vox.com&rft.atitle=Alaska+voters+adopt+ranked-choice+voting+in+ballot+initiative&rft.date=2020-11-19&rft.aulast=Piper&rft.aufirst=Kelsey&rft_id=https%3A%2F%2Fwww.vox.com%2F2020%2F11%2F19%2F21537126%2Falaska-measure-2-ranked-choice-voting-results&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARanked+voting" class="Z3988"></span></span> </li> <li id="cite_note-z562-20"><span class="mw-cite-backlink"><b><a href="#cite_ref-z562_20-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFJett2024" class="citation web cs1">Jett, Jennifer (November 5, 2024). <a rel="nofollow" class="external text" href="https://www.nbcnews.com/politics/2024-elections/alaska-ballot-measures">"Alaska Ballot Measures: Election 2024 Live Results"</a>. <i>NBC News</i><span class="reference-accessdate">. Retrieved <span class="nowrap">January 22,</span> 2025</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=NBC+News&rft.atitle=Alaska+Ballot+Measures%3A+Election+2024+Live+Results&rft.date=2024-11-05&rft.aulast=Jett&rft.aufirst=Jennifer&rft_id=https%3A%2F%2Fwww.nbcnews.com%2Fpolitics%2F2024-elections%2Falaska-ballot-measures&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARanked+voting" class="Z3988"></span></span> </li> <li id="cite_note-North-21"><span class="mw-cite-backlink"><b><a href="#cite_ref-North_21-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://alaskapublic.org/2023/09/19/north-to-the-future-alaskas-ranked-choice-voting-system-is-praised-and-criticized-nationally/">"North to the Future: Alaska's Ranked Choice Voting System is Praised and Criticized Nationally"</a>. Alaska Public Media.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=North+to+the+Future%3A+Alaska%E2%80%99s+Ranked+Choice+Voting+System+is+Praised+and+Criticized+Nationally&rft.pub=Alaska+Public+Media&rft_id=https%3A%2F%2Falaskapublic.org%2F2023%2F09%2F19%2Fnorth-to-the-future-alaskas-ranked-choice-voting-system-is-praised-and-criticized-nationally%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARanked+voting" class="Z3988"></span></span> </li> <li id="cite_note-22"><span class="mw-cite-backlink"><b><a href="#cite_ref-22">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.fairvote.org/new_zealand_cities_voting_to_implement_ranked_choice_voting">"New Zealand Cities Voting to Implement Ranked Choice Voting"</a>. September 19, 2017.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=New+Zealand+Cities+Voting+to+Implement+Ranked+Choice+Voting&rft.date=2017-09-19&rft_id=https%3A%2F%2Fwww.fairvote.org%2Fnew_zealand_cities_voting_to_implement_ranked_choice_voting&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARanked+voting" class="Z3988"></span></span> </li> <li id="cite_note-h160-23"><span class="mw-cite-backlink"><b><a href="#cite_ref-h160_23-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFSmart2022" class="citation web cs1">Smart, Peter (November 11, 2022). <a rel="nofollow" class="external text" href="https://www.electoral-reform.org.uk/a-wave-of-cities-across-the-united-states-switch-to-fair-voting-systems/">"A wave of cities across the United States switch to fair voting systems"</a>. <i>Electoral Reform Society</i><span class="reference-accessdate">. Retrieved <span class="nowrap">January 22,</span> 2025</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Electoral+Reform+Society&rft.atitle=A+wave+of+cities+across+the+United+States+switch+to+fair+voting+systems&rft.date=2022-11-11&rft.aulast=Smart&rft.aufirst=Peter&rft_id=https%3A%2F%2Fwww.electoral-reform.org.uk%2Fa-wave-of-cities-across-the-united-states-switch-to-fair-voting-systems%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARanked+voting" class="Z3988"></span></span> </li> <li id="cite_note-24"><span class="mw-cite-backlink"><b><a href="#cite_ref-24">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external free" href="https://ballotbox.scot/councils/stv-explained/">https://ballotbox.scot/councils/stv-explained/</a></span> </li> <li id="cite_note-25"><span class="mw-cite-backlink"><b><a href="#cite_ref-25">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external free" href="https://lgiu.org/blog-article/how-irelands-local-elections-work/">https://lgiu.org/blog-article/how-irelands-local-elections-work/</a></span> </li> <li id="cite_note-:1-26"><span class="mw-cite-backlink"><b><a href="#cite_ref-:1_26-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFWeber1978" class="citation journal cs1">Weber, Robert J. (September 1978). <a rel="nofollow" class="external text" href="https://cowles.yale.edu/publications/cfdp/cfdp-498">"Comparison of Public Choice Systems"</a>. <i>Cowles Foundation Discussion Papers</i>. Cowles Foundation for Research in Economics: 16, 38, 62. No. 498.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Cowles+Foundation+Discussion+Papers&rft.atitle=Comparison+of+Public+Choice+Systems&rft.pages=16%2C+38%2C+62&rft.date=1978-09&rft.aulast=Weber&rft.aufirst=Robert+J.&rft_id=https%3A%2F%2Fcowles.yale.edu%2Fpublications%2Fcfdp%2Fcfdp-498&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARanked+voting" class="Z3988"></span></span> </li> <li id="cite_note-27"><span class="mw-cite-backlink"><b><a href="#cite_ref-27">^</a></b></span> <span class="reference-text">T. N. Tideman and F. Plassman, "Modeling the Outcomes of Vote-Casting in Actual Elections" (2012).</span> </li> <li id="cite_note-28"><span class="mw-cite-backlink"><b><a href="#cite_ref-28">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFGallagher" class="citation web cs1">Gallagher, Michael. <a rel="nofollow" class="external text" href="https://www.tcd.ie/Political_Science/about/people/michael_gallagher/BJPS1992.pdf">"Comparing P.R. Electoral Systems. Quotas, Thresholds, Paradoxes, Majorities"</a> <span class="cs1-format">(PDF)</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Comparing+P.R.+Electoral+Systems.+Quotas%2C+Thresholds%2C+Paradoxes%2C+Majorities&rft.aulast=Gallagher&rft.aufirst=Michael&rft_id=https%3A%2F%2Fwww.tcd.ie%2FPolitical_Science%2Fabout%2Fpeople%2Fmichael_gallagher%2FBJPS1992.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARanked+voting" class="Z3988"></span></span> </li> <li id="cite_note-29"><span class="mw-cite-backlink"><b><a href="#cite_ref-29">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://lgiu.org/blog-article/how-irelands-local-elections-work/">"How Ireland's local elections work"</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=How+Ireland%27s+local+elections+work&rft_id=https%3A%2F%2Flgiu.org%2Fblog-article%2Fhow-irelands-local-elections-work%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARanked+voting" class="Z3988"></span></span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Ranked_voting&action=edit&section=17" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1236088147">.mw-parser-output .sister-bar{display:flex;justify-content:center;align-items:baseline;font-size:88%;background-color:#fdfdfd;border:1px solid #a2a9b1;clear:both;margin:1em 0 0;padding:0 2em}.mw-parser-output .sister-bar-header{margin:0 1em 0 0.5em;padding:0.2em 0;flex:0 0 auto;min-height:24px;line-height:22px}.mw-parser-output .sister-bar-content{display:flex;flex-flow:row wrap;flex:0 1 auto;align-items:baseline;padding:0.2em 0;column-gap:1em;margin:0;list-style:none}.mw-parser-output .sister-bar-item{display:flex;align-items:baseline;margin:0.15em 0;min-height:24px;text-align:left}.mw-parser-output .sister-bar-logo{width:22px;line-height:22px;margin:0 0.2em;text-align:right}.mw-parser-output .sister-bar-link{margin:0 0.2em;text-align:left}@media screen and (max-width:960px){.mw-parser-output .sister-bar{flex-flow:column wrap;margin:1em auto 0}.mw-parser-output .sister-bar-header{flex:0 1}.mw-parser-output .sister-bar-content{flex:1;border-top:1px solid #a2a9b1;margin:0;list-style:none}.mw-parser-output .sister-bar-item{flex:0 0 20em;min-width:20em}}.mw-parser-output .navbox+link+.sister-bar,.mw-parser-output .navbox+style+.sister-bar,.mw-parser-output .portal-bar+link+.sister-bar,.mw-parser-output .portal-bar+style+.sister-bar,.mw-parser-output .sister-bar+.navbox-styles+.navbox,.mw-parser-output .sister-bar+.navbox-styles+.portal-bar{margin-top:-1px}@media print{body.ns-0 .mw-parser-output .sister-bar{display:none!important}}</style><div class="noprint metadata sister-bar" role="navigation" aria-label="sister-projects"><div class="sister-bar-header"><b>Ranked voting</b> at Wikipedia's <a href="/wiki/Wikipedia:Wikimedia_sister_projects" title="Wikipedia:Wikimedia sister projects"><span id="sister-projects" style="white-space:nowrap;">sister projects</span></a>:</div><ul class="sister-bar-content"><li class="sister-bar-item"><span class="sister-bar-logo"><span typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/14px-Commons-logo.svg.png" decoding="async" width="14" height="19" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/21px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/28px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></span></span></span><span class="sister-bar-link"><b><a href="https://commons.wikimedia.org/wiki/Category:Ranked_voting" class="extiw" title="c:Category:Ranked voting">Media</a></b> from Commons</span></li><li class="sister-bar-item"><span class="sister-bar-logo"><span typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/f/ff/Wikidata-logo.svg/21px-Wikidata-logo.svg.png" decoding="async" width="21" height="12" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/ff/Wikidata-logo.svg/32px-Wikidata-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/ff/Wikidata-logo.svg/42px-Wikidata-logo.svg.png 2x" data-file-width="1050" data-file-height="590" /></span></span></span><span class="sister-bar-link"><b><a href="https://www.wikidata.org/wiki/Q1078003" class="extiw" title="d:Q1078003">Data</a></b> from Wikidata</span></li></ul></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1184024115" /><div class="div-col"> <ul><li><a rel="nofollow" class="external text" href="https://www.youtube.com/watch?v=oHRPMJmzBBw">Explainer video: How does ranked-choice voting work?</a>, Minnesota Public Radio MPR.org</li> <li><a rel="nofollow" class="external text" href="https://ballotpedia.org/Ranked-choice_voting_(RCV)">Ballotpedia: "Ranked Choice Voting"</a></li> <li>Examples from RCV123.org <ul><li><a rel="nofollow" class="external text" href="https://www.rcv123.org/practice-rcv/sample/maine_ballot_2020">US State of Maine, 2020 Ballot</a></li> <li><a rel="nofollow" class="external text" href="https://www.rcv123.org/practice-rcv/sample/alaska_sample_ballot">US State of Alaska, 2021 Ballot</a></li></ul></li> <li><a rel="nofollow" class="external text" href="https://www.fairvote.org/">FairVote.Org</a></li></ul> </div> <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 .navbox-subgroup{background-color:#fdfdfd}.mw-parser-output .navbox-list{line-height:1.5em;border-color:#fdfdfd}.mw-parser-output .navbox-list-with-group{text-align:left;border-left-width:2px;border-left-style:solid}.mw-parser-output tr+tr>.navbox-abovebelow,.mw-parser-output tr+tr>.navbox-group,.mw-parser-output tr+tr>.navbox-image,.mw-parser-output tr+tr>.navbox-list{border-top:2px solid #fdfdfd}.mw-parser-output .navbox-title{background-color:#ccf}.mw-parser-output .navbox-abovebelow,.mw-parser-output .navbox-group,.mw-parser-output .navbox-subgroup .navbox-title{background-color:#ddf}.mw-parser-output .navbox-subgroup .navbox-group,.mw-parser-output .navbox-subgroup .navbox-abovebelow{background-color:#e6e6ff}.mw-parser-output .navbox-even{background-color:#f7f7f7}.mw-parser-output .navbox-odd{background-color:transparent}.mw-parser-output .navbox .hlist td dl,.mw-parser-output .navbox .hlist td ol,.mw-parser-output .navbox .hlist td ul,.mw-parser-output .navbox td.hlist 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 href="/wiki/Borda_count" title="Borda count">Borda count</a></li> <li><a href="/wiki/Bucklin_voting" title="Bucklin voting">Bucklin voting</a></li> <li><a href="/wiki/Condorcet_methods" class="mw-redirect" title="Condorcet methods">Condorcet methods</a> <ul><li><a href="/wiki/Copeland%27s_method" title="Copeland's method">Copeland's method</a></li> <li><a href="/wiki/Dodgson%27s_method" title="Dodgson's method">Dodgson's method</a></li> <li><a href="/wiki/Kemeny%E2%80%93Young_method" title="Kemeny–Young method">Kemeny–Young method</a></li> <li><a href="/wiki/Minimax_Condorcet_method" title="Minimax Condorcet method">Minimax Condorcet method</a></li> <li><a href="/wiki/Nanson%27s_method" title="Nanson's method">Nanson's method</a></li> <li><a href="/wiki/Ranked_pairs" title="Ranked pairs">Ranked pairs</a></li> <li><a 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" class="mw-redirect" 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> <li><a href="/wiki/Wasted_vote" title="Wasted vote">Wasted vote</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 class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374" /><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235" /></div><div role="navigation" class="navbox authority-control" aria-label="Navbox506" style="padding:3px"><table class="nowraplinks hlist navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Help:Authority_control" title="Help:Authority control">Authority control databases</a>: National <span class="mw-valign-text-top noprint" typeof="mw:File/Frameless"><a href="https://www.wikidata.org/wiki/Q1078003#identifiers" title="Edit this at Wikidata"><img alt="Edit this at Wikidata" src="//upload.wikimedia.org/wikipedia/en/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/10px-OOjs_UI_icon_edit-ltr-progressive.svg.png" decoding="async" width="10" height="10" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/15px-OOjs_UI_icon_edit-ltr-progressive.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/20px-OOjs_UI_icon_edit-ltr-progressive.svg.png 2x" data-file-width="20" data-file-height="20" /></a></span></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"><ul><li><span class="uid"><a rel="nofollow" class="external text" href="https://id.loc.gov/authorities/sh85106272">United States</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://www.nli.org.il/en/authorities/987007533941605171">Israel</a></span></li></ul></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: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Retrieved from "<a dir="ltr" href="https://en.wikipedia.org/w/index.php?title=Ranked_voting&oldid=1276976550">https://en.wikipedia.org/w/index.php?title=Ranked_voting&oldid=1276976550</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Help:Category" title="Help:Category">Categories</a>: <ul><li><a href="/wiki/Category:Instant-runoff_voting" title="Category:Instant-runoff voting">Instant-runoff voting</a></li><li><a href="/wiki/Category:Cardinal_electoral_systems" title="Category:Cardinal electoral systems">Cardinal electoral systems</a></li><li><a href="/wiki/Category:Electoral_systems" title="Category:Electoral systems">Electoral systems</a></li><li><a href="/wiki/Category:Preferential_electoral_systems" title="Category:Preferential electoral systems">Preferential electoral systems</a></li><li><a href="/wiki/Category:Proportional_representation_electoral_systems" title="Category:Proportional representation electoral systems">Proportional representation electoral systems</a></li><li><a href="/wiki/Category:Psephology" title="Category:Psephology">Psephology</a></li><li><a href="/wiki/Category:Public_choice_theory" title="Category:Public choice theory">Public choice theory</a></li><li><a href="/wiki/Category:Social_choice_theory" title="Category:Social choice theory">Social choice theory</a></li></ul></div><div id="mw-hidden-catlinks" class="mw-hidden-catlinks mw-hidden-cats-hidden">Hidden categories: <ul><li><a href="/wiki/Category:CS1_French-language_sources_(fr)" title="Category:CS1 French-language sources (fr)">CS1 French-language sources (fr)</a></li><li><a href="/wiki/Category:Articles_with_short_description" title="Category:Articles with short description">Articles with short description</a></li><li><a href="/wiki/Category:Short_description_matches_Wikidata" title="Category:Short description matches Wikidata">Short description matches Wikidata</a></li><li><a href="/wiki/Category:Use_mdy_dates_from_February_2025" title="Category:Use mdy dates from February 2025">Use mdy dates from February 2025</a></li><li><a href="/wiki/Category:All_articles_with_unsourced_statements" title="Category:All articles with unsourced statements">All articles with unsourced statements</a></li><li><a href="/wiki/Category:Articles_with_unsourced_statements_from_July_2024" title="Category:Articles with unsourced statements from July 2024">Articles with unsourced statements from July 2024</a></li><li><a href="/wiki/Category:Pages_displaying_wikidata_descriptions_as_a_fallback_via_Module:Annotated_link" title="Category:Pages displaying wikidata descriptions as a fallback via Module:Annotated link">Pages displaying wikidata descriptions as a fallback via Module:Annotated link</a></li></ul></div></div> </div> </main> </div> <div class="mw-footer-container"> <footer id="footer" class="mw-footer" > <ul id="footer-info"> <li id="footer-info-lastmod"> This page was last edited on 21 February 2025, at 22:13<span class="anonymous-show"> (UTC)</span>.</li> <li id="footer-info-copyright">Text is available under the <a href="/wiki/Wikipedia:Text_of_the_Creative_Commons_Attribution-ShareAlike_4.0_International_License" title="Wikipedia:Text of the Creative Commons Attribution-ShareAlike 4.0 International License">Creative Commons Attribution-ShareAlike 4.0 License</a>; additional terms may apply. By using this site, you agree to the <a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Terms_of_Use" class="extiw" title="foundation:Special:MyLanguage/Policy:Terms of Use">Terms of Use</a> and <a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Privacy_policy" class="extiw" title="foundation:Special:MyLanguage/Policy:Privacy policy">Privacy Policy</a>. Wikipedia® is a registered trademark of the <a rel="nofollow" class="external text" href="https://wikimediafoundation.org/">Wikimedia Foundation, Inc.</a>, a non-profit organization.</li> </ul> <ul id="footer-places"> <li id="footer-places-privacy"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Privacy_policy">Privacy policy</a></li> <li id="footer-places-about"><a href="/wiki/Wikipedia:About">About Wikipedia</a></li> <li id="footer-places-disclaimers"><a href="/wiki/Wikipedia:General_disclaimer">Disclaimers</a></li> <li id="footer-places-contact"><a href="//en.wikipedia.org/wiki/Wikipedia:Contact_us">Contact Wikipedia</a></li> <li id="footer-places-wm-codeofconduct"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Universal_Code_of_Conduct">Code of Conduct</a></li> <li id="footer-places-developers"><a href="https://developer.wikimedia.org">Developers</a></li> <li id="footer-places-statslink"><a href="https://stats.wikimedia.org/#/en.wikipedia.org">Statistics</a></li> <li id="footer-places-cookiestatement"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Cookie_statement">Cookie statement</a></li> <li id="footer-places-mobileview"><a href="//en.m.wikipedia.org/w/index.php?title=Ranked_voting&mobileaction=toggle_view_mobile" class="noprint stopMobileRedirectToggle">Mobile view</a></li> </ul> <ul id="footer-icons" class="noprint"> <li id="footer-copyrightico"><a href="https://wikimediafoundation.org/" class="cdx-button cdx-button--fake-button cdx-button--size-large cdx-button--fake-button--enabled"><picture><source media="(min-width: 500px)" srcset="/static/images/footer/wikimedia-button.svg" width="84" height="29"><img src="/static/images/footer/wikimedia.svg" width="25" height="25" alt="Wikimedia Foundation" lang="en" loading="lazy"></picture></a></li> <li id="footer-poweredbyico"><a href="https://www.mediawiki.org/" class="cdx-button cdx-button--fake-button cdx-button--size-large cdx-button--fake-button--enabled"><picture><source media="(min-width: 500px)" srcset="/w/resources/assets/poweredby_mediawiki.svg" width="88" height="31"><img src="/w/resources/assets/mediawiki_compact.svg" alt="Powered by MediaWiki" lang="en" width="25" height="25" loading="lazy"></picture></a></li> </ul> </footer> </div> </div> </div> <div class="vector-header-container vector-sticky-header-container"> <div id="vector-sticky-header" class="vector-sticky-header"> <div class="vector-sticky-header-start"> <div class="vector-sticky-header-icon-start vector-button-flush-left vector-button-flush-right" aria-hidden="true"> <button class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-sticky-header-search-toggle" tabindex="-1" data-event-name="ui.vector-sticky-search-form.icon"><span class="vector-icon mw-ui-icon-search mw-ui-icon-wikimedia-search"></span> <span>Search</span> </button> </div> <div role="search" class="vector-search-box-vue vector-search-box-show-thumbnail vector-search-box"> <div class="vector-typeahead-search-container"> <div class="cdx-typeahead-search cdx-typeahead-search--show-thumbnail"> <form action="/w/index.php" id="vector-sticky-search-form" class="cdx-search-input cdx-search-input--has-end-button"> <div class="cdx-search-input__input-wrapper" data-search-loc="header-moved"> <div class="cdx-text-input cdx-text-input--has-start-icon"> <input class="cdx-text-input__input" type="search" name="search" placeholder="Search Wikipedia"> <span class="cdx-text-input__icon cdx-text-input__start-icon"></span> </div> <input type="hidden" name="title" value="Special:Search"> </div> <button class="cdx-button cdx-search-input__end-button">Search</button> </form> </div> </div> </div> <div class="vector-sticky-header-context-bar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-sticky-header-toc" class="vector-dropdown mw-portlet mw-portlet-sticky-header-toc vector-sticky-header-toc vector-button-flush-left" > <input type="checkbox" id="vector-sticky-header-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-sticky-header-toc" class="vector-dropdown-checkbox " aria-label="Toggle the table of contents" > <label id="vector-sticky-header-toc-label" for="vector-sticky-header-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Toggle the table of contents</span> </label> <div class="vector-dropdown-content"> <div id="vector-sticky-header-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <div class="vector-sticky-header-context-bar-primary" aria-hidden="true" ><span class="mw-page-title-main">Ranked voting</span></div> </div> </div> <div class="vector-sticky-header-end" aria-hidden="true"> <div class="vector-sticky-header-icons"> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only" id="ca-talk-sticky-header" tabindex="-1" data-event-name="talk-sticky-header"><span class="vector-icon mw-ui-icon-speechBubbles mw-ui-icon-wikimedia-speechBubbles"></span> <span></span> </a> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only" id="ca-subject-sticky-header" tabindex="-1" data-event-name="subject-sticky-header"><span class="vector-icon mw-ui-icon-article mw-ui-icon-wikimedia-article"></span> <span></span> </a> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only" id="ca-history-sticky-header" tabindex="-1" data-event-name="history-sticky-header"><span class="vector-icon mw-ui-icon-wikimedia-history mw-ui-icon-wikimedia-wikimedia-history"></span> <span></span> </a> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only mw-watchlink" id="ca-watchstar-sticky-header" tabindex="-1" data-event-name="watch-sticky-header"><span class="vector-icon mw-ui-icon-wikimedia-star mw-ui-icon-wikimedia-wikimedia-star"></span> <span></span> </a> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only" id="ca-edit-sticky-header" tabindex="-1" data-event-name="wikitext-edit-sticky-header"><span class="vector-icon mw-ui-icon-wikimedia-wikiText mw-ui-icon-wikimedia-wikimedia-wikiText"></span> <span></span> </a> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only" id="ca-ve-edit-sticky-header" tabindex="-1" data-event-name="ve-edit-sticky-header"><span class="vector-icon mw-ui-icon-wikimedia-edit mw-ui-icon-wikimedia-wikimedia-edit"></span> <span></span> </a> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only" id="ca-viewsource-sticky-header" tabindex="-1" data-event-name="ve-edit-protected-sticky-header"><span class="vector-icon mw-ui-icon-wikimedia-editLock mw-ui-icon-wikimedia-wikimedia-editLock"></span> <span></span> </a> </div> <div class="vector-sticky-header-buttons"> <button class="cdx-button cdx-button--weight-quiet mw-interlanguage-selector" id="p-lang-btn-sticky-header" tabindex="-1" data-event-name="ui.dropdown-p-lang-btn-sticky-header"><span class="vector-icon mw-ui-icon-wikimedia-language mw-ui-icon-wikimedia-wikimedia-language"></span> <span>26 languages</span> </button> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive" id="ca-addsection-sticky-header" tabindex="-1" data-event-name="addsection-sticky-header"><span class="vector-icon mw-ui-icon-speechBubbleAdd-progressive mw-ui-icon-wikimedia-speechBubbleAdd-progressive"></span> <span>Add topic</span> </a> </div> <div class="vector-sticky-header-icon-end"> <div class="vector-user-links"> </div> </div> </div> </div> </div> <div class="mw-portlet mw-portlet-dock-bottom emptyPortlet" id="p-dock-bottom"> <ul> </ul> </div> <script>(RLQ=window.RLQ||[]).push(function(){mw.config.set({"wgHostname":"mw-web.codfw.main-64b5bb4b79-wblp7","wgBackendResponseTime":153,"wgPageParseReport":{"limitreport":{"cputime":"0.710","walltime":"0.867","ppvisitednodes":{"value":3530,"limit":1000000},"postexpandincludesize":{"value":107765,"limit":2097152},"templateargumentsize":{"value":3850,"limit":2097152},"expansiondepth":{"value":12,"limit":100},"expensivefunctioncount":{"value":20,"limit":500},"unstrip-depth":{"value":1,"limit":20},"unstrip-size":{"value":106864,"limit":5000000},"entityaccesscount":{"value":1,"limit":400},"timingprofile":["100.00% 765.411 1 -total"," 22.91% 175.371 1 Template:Reflist"," 18.22% 139.453 1 Template:Electoral_systems"," 17.66% 135.169 1 Template:Sidebar_with_collapsible_lists"," 16.19% 123.953 6 Template:Annotated_link"," 14.18% 108.530 12 Template:Cite_web"," 10.66% 81.626 1 Template:Short_description"," 8.35% 63.888 2 Template:Hlist"," 6.44% 49.328 2 Template:Pagetype"," 6.39% 48.874 1 Template:Subject_bar"]},"scribunto":{"limitreport-timeusage":{"value":"0.473","limit":"10.000"},"limitreport-memusage":{"value":22547954,"limit":52428800},"limitreport-logs":"table#1 {\n [\"size\"] = \"tiny\",\n}\ntable#1 {\n [\"size\"] = \"tiny\",\n}\ntable#1 {\n [\"size\"] = \"tiny\",\n}\n"},"cachereport":{"origin":"mw-api-int.codfw.main-67794785f5-cg9fw","timestamp":"20250228165929","ttl":2592000,"transientcontent":false}}});});</script> <script type="application/ld+json">{"@context":"https:\/\/schema.org","@type":"Article","name":"Ranked voting","url":"https:\/\/en.wikipedia.org\/wiki\/Ranked_voting","sameAs":"http:\/\/www.wikidata.org\/entity\/Q1078003","mainEntity":"http:\/\/www.wikidata.org\/entity\/Q1078003","author":{"@type":"Organization","name":"Contributors to Wikimedia projects"},"publisher":{"@type":"Organization","name":"Wikimedia Foundation, Inc.","logo":{"@type":"ImageObject","url":"https:\/\/www.wikimedia.org\/static\/images\/wmf-hor-googpub.png"}},"datePublished":"2003-07-15T17:47:25Z","dateModified":"2025-02-21T22:13:59Z","image":"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/4\/4d\/Rankballotoval.gif","headline":"voting systems that use ranked ballots"}</script> </body> </html>