CINXE.COM

<!DOCTYPE html> <html class="client-nojs vector-feature-language-in-header-enabled vector-feature-language-in-main-page-header-disabled vector-feature-sticky-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-toc-available" lang="en" dir="ltr"> <head> <meta charset="UTF-8"> <title>Social choice theory - Wikipedia</title> <script>(function(){var className="client-js vector-feature-language-in-header-enabled vector-feature-language-in-main-page-header-disabled vector-feature-sticky-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-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":"7250f56a-58ef-4865-a2c7-b10436d8200a","wgCanonicalNamespace":"","wgCanonicalSpecialPageName":false,"wgNamespaceNumber":0,"wgPageName":"Social_choice_theory","wgTitle":"Social choice theory","wgCurRevisionId":1252573486,"wgRevisionId":1252573486,"wgArticleId":1745670,"wgIsArticle":true,"wgIsRedirect":false,"wgAction":"view","wgUserName":null,"wgUserGroups":["*"],"wgCategories":["Articles with short description","Short description matches Wikidata","Articles to be split from May 2024","All articles to be split","Wikipedia references cleanup from April 2021","All articles needing references cleanup","Articles covered by WikiProject Wikify from April 2021","All articles covered by WikiProject Wikify","Articles with excerpts","All articles with unsourced statements","Articles with unsourced statements from July 2024", "Articles with hatnote templates targeting a nonexistent page","Wikipedia articles needing clarification from March 2024","Articles with unsourced statements from June 2024","Webarchive template wayback links","Social choice theory","Metaethics","Political science","Public economics","Applied mathematics","Collective intelligence","Political philosophy","Mathematical economics","Law and economics","Administrative theory"],"wgPageViewLanguage":"en","wgPageContentLanguage":"en","wgPageContentModel":"wikitext","wgRelevantPageName":"Social_choice_theory","wgRelevantArticleId":1745670,"wgIsProbablyEditable":true,"wgRelevantPageIsProbablyEditable":true,"wgRestrictionEdit":[],"wgRestrictionMove":[],"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,"wgRelatedArticlesCompat":[],"wgCentralAuthMobileDomain":false,"wgEditSubmitButtonLabelPublish":true,"wgULSPosition":"interlanguage","wgULSisCompactLinksEnabled":false,"wgVector2022LanguageInHeader":true,"wgULSisLanguageSelectorEmpty":false,"wgWikibaseItemId":"Q1971461","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","ext.math.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","ext.wikimediaBadges":"ready"};RLPAGEMODULES=["ext.cite.ux-enhancements","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.quicksurveys.init", "ext.growthExperiments.SuggestedEditSession","wikibase.sidebar.tracking"];</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.math.styles%7Cext.uls.interlanguage%7Cext.visualEditor.desktopArticleTarget.noscript%7Cext.wikimediaBadges%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.4"> <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/thumb/8/82/Electoral-systems-gears.svg/1200px-Electoral-systems-gears.svg.png"> <meta property="og:image:width" content="1200"> <meta property="og:image:height" content="1200"> <meta property="og:image" content="https://upload.wikimedia.org/wikipedia/commons/thumb/8/82/Electoral-systems-gears.svg/800px-Electoral-systems-gears.svg.png"> <meta property="og:image:width" content="800"> <meta property="og:image:height" content="800"> <meta property="og:image" content="https://upload.wikimedia.org/wikipedia/commons/thumb/8/82/Electoral-systems-gears.svg/640px-Electoral-systems-gears.svg.png"> <meta property="og:image:width" content="640"> <meta property="og:image:height" content="640"> <meta name="viewport" content="width=1120"> <meta property="og:title" content="Social choice theory - 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/Social_choice_theory"> <link rel="alternate" type="application/x-wiki" title="Edit this page" href="/w/index.php?title=Social_choice_theory&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/Social_choice_theory"> <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-Social_choice_theory rootpage-Social_choice_theory 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" > <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> </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/wiki/Special:FundraiserRedirector?utm_source=donate&utm_medium=sidebar&utm_campaign=C13_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=Social+choice+theory" 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=Social+choice+theory" 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/wiki/Special:FundraiserRedirector?utm_source=donate&utm_medium=sidebar&utm_campaign=C13_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=Social+choice+theory" 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=Social+choice+theory" 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" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#History"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>History</span> </div> </a> <ul id="toc-History-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Key_results" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Key_results"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Key results</span> </div> </a> <button aria-controls="toc-Key_results-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 Key results subsection</span> </button> <ul id="toc-Key_results-sublist" class="vector-toc-list"> <li id="toc-Arrow's_impossibility_theorem" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Arrow's_impossibility_theorem"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>Arrow's impossibility theorem</span> </div> </a> <ul id="toc-Arrow's_impossibility_theorem-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Condorcet_cycles" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Condorcet_cycles"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2</span> <span>Condorcet cycles</span> </div> </a> <ul id="toc-Condorcet_cycles-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Harsanyi's_theorem" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Harsanyi's_theorem"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.3</span> <span>Harsanyi's theorem</span> </div> </a> <ul id="toc-Harsanyi's_theorem-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Manipulation_theorems" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Manipulation_theorems"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.4</span> <span>Manipulation theorems</span> </div> </a> <ul id="toc-Manipulation_theorems-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Median_voter_theorem" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Median_voter_theorem"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.5</span> <span>Median voter theorem</span> </div> </a> <ul id="toc-Median_voter_theorem-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Mechanism_design" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Mechanism_design"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.6</span> <span>Mechanism design</span> </div> </a> <ul id="toc-Mechanism_design-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Others" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Others"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.7</span> <span>Others</span> </div> </a> <ul id="toc-Others-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Interpersonal_utility_comparison" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Interpersonal_utility_comparison"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Interpersonal utility comparison</span> </div> </a> <ul id="toc-Interpersonal_utility_comparison-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Relationship_to_public_choice_theory" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Relationship_to_public_choice_theory"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Relationship to public choice theory</span> </div> </a> <ul id="toc-Relationship_to_public_choice_theory-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Empirical_research" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Empirical_research"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Empirical research</span> </div> </a> <ul id="toc-Empirical_research-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Rules" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Rules"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Rules</span> </div> </a> <ul id="toc-Rules-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Social_choice_functions" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Social_choice_functions"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Social choice functions</span> </div> </a> <ul id="toc-Social_choice_functions-sublist" class="vector-toc-list"> </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">8</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Notes" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Notes"> <div class="vector-toc-text"> <span class="vector-toc-numb">9</span> <span>Notes</span> </div> </a> <ul id="toc-Notes-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">10</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">11</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" > <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">Social choice theory</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 18 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-18" 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">18 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/%D9%86%D8%B8%D8%B1%D9%8A%D8%A9_%D8%A7%D9%84%D8%AE%D9%8A%D8%A7%D8%B1_%D8%A7%D9%84%D8%A7%D8%AC%D8%AA%D9%85%D8%A7%D8%B9%D9%8A" title="نظرية الخيار الاجتماعي – Arabic" lang="ar" hreflang="ar" data-title="نظرية الخيار الاجتماعي" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Sosial_se%C3%A7im_n%C9%99z%C9%99riyy%C9%99si" title="Sosial seçim nəzəriyyəsi – Azerbaijani" lang="az" hreflang="az" data-title="Sosial seçim nəzəriyyəsi" data-language-autonym="Azərbaycanca" data-language-local-name="Azerbaijani" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Sozialwahltheorie" title="Sozialwahltheorie – German" lang="de" hreflang="de" data-title="Sozialwahltheorie" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Teor%C3%ADa_de_la_elecci%C3%B3n_social" title="Teoría de la elección social – Spanish" lang="es" hreflang="es" data-title="Teoría de la elección social" 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%B1%DB%8C%D9%87_%D8%A7%D9%86%D8%AA%D8%AE%D8%A7%D8%A8_%D8%A7%D8%AC%D8%AA%D9%85%D8%A7%D8%B9%DB%8C" title="نظریه انتخاب اجتماعی – Persian" lang="fa" hreflang="fa" data-title="نظریه انتخاب اجتماعی" 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/Th%C3%A9orie_du_choix_social" title="Théorie du choix social – French" lang="fr" hreflang="fr" data-title="Théorie du choix social" 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%82%AC%ED%9A%8C_%EC%84%A0%ED%83%9D_%EC%9D%B4%EB%A1%A0" title="사회 선택 이론 – Korean" lang="ko" hreflang="ko" data-title="사회 선택 이론" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Teori_pemilihan_sosial" title="Teori pemilihan sosial – Indonesian" lang="id" hreflang="id" data-title="Teori pemilihan sosial" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesian" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Teoria_della_scelta_sociale" title="Teoria della scelta sociale – Italian" lang="it" hreflang="it" data-title="Teoria della scelta sociale" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%91%D7%97%D7%99%D7%A8%D7%94_%D7%97%D7%91%D7%A8%D7%AA%D7%99%D7%AA" title="בחירה חברתית – Hebrew" lang="he" hreflang="he" data-title="בחירה חברתית" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Socialekeuzetheorie" title="Socialekeuzetheorie – Dutch" lang="nl" hreflang="nl" data-title="Socialekeuzetheorie" 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/%E7%A4%BE%E4%BC%9A%E9%81%B8%E6%8A%9E%E7%90%86%E8%AB%96" title="社会選択理論 – Japanese" lang="ja" hreflang="ja" data-title="社会選択理論" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Teoria_wyboru_spo%C5%82ecznego" title="Teoria wyboru społecznego – Polish" lang="pl" hreflang="pl" data-title="Teoria wyboru społecznego" 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/Teoria_da_escolha_social" title="Teoria da escolha social – Portuguese" lang="pt" hreflang="pt" data-title="Teoria da escolha social" 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/Teoria_alegerii_sociale" title="Teoria alegerii sociale – Romanian" lang="ro" hreflang="ro" data-title="Teoria alegerii sociale" data-language-autonym="Română" data-language-local-name="Romanian" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Social_choice_theory" title="Social choice theory – Simple English" lang="en-simple" hreflang="en-simple" data-title="Social choice theory" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E7%A4%BE%E6%9C%83%E9%81%B8%E6%93%87%E7%90%86%E8%AB%96" title="社會選擇理論 – Cantonese" lang="yue" hreflang="yue" data-title="社會選擇理論" 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/%E7%A4%BE%E6%9C%83%E9%81%B8%E6%93%87%E7%90%86%E8%AB%96" title="社會選擇理論 – Chinese" lang="zh" hreflang="zh" data-title="社會選擇理論" 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/Q1971461#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/Social_choice_theory" 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:Social_choice_theory" 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/Social_choice_theory"><span>Read</span></a></li><li id="ca-edit" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Social_choice_theory&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=Social_choice_theory&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/Social_choice_theory"><span>Read</span></a></li><li id="ca-more-edit" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Social_choice_theory&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=Social_choice_theory&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/Social_choice_theory" 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/Social_choice_theory" 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="/wiki/Wikipedia:File_Upload_Wizard" title="Upload files [u]" accesskey="u"><span>Upload file</span></a></li><li id="t-specialpages" class="mw-list-item"><a href="/wiki/Special:SpecialPages" title="A list of all special pages [q]" accesskey="q"><span>Special pages</span></a></li><li id="t-permalink" class="mw-list-item"><a href="/w/index.php?title=Social_choice_theory&oldid=1252573486" 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=Social_choice_theory&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=Social_choice_theory&id=1252573486&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%2FSocial_choice_theory"><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%2FSocial_choice_theory"><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=Social_choice_theory&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=Social_choice_theory&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:Social_choice_theory" hreflang="en"><span>Wikimedia Commons</span></a></li><li class="wb-otherproject-link wb-otherproject-wikiquote mw-list-item"><a href="https://en.wikiquote.org/wiki/Social_choice_theory" hreflang="en"><span>Wikiquote</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/Q1971461" 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"></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">Academic discipline</div><style data-mw-deduplicate="TemplateStyles:r1251242444">.mw-parser-output .ambox{border:1px solid #a2a9b1;border-left:10px solid #36c;background-color:#fbfbfb;box-sizing:border-box}.mw-parser-output .ambox+link+.ambox,.mw-parser-output .ambox+link+style+.ambox,.mw-parser-output .ambox+link+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+style+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+link+.ambox{margin-top:-1px}html body.mediawiki .mw-parser-output .ambox.mbox-small-left{margin:4px 1em 4px 0;overflow:hidden;width:238px;border-collapse:collapse;font-size:88%;line-height:1.25em}.mw-parser-output .ambox-speedy{border-left:10px solid #b32424;background-color:#fee7e6}.mw-parser-output .ambox-delete{border-left:10px solid #b32424}.mw-parser-output .ambox-content{border-left:10px solid #f28500}.mw-parser-output .ambox-style{border-left:10px solid #fc3}.mw-parser-output .ambox-move{border-left:10px solid #9932cc}.mw-parser-output .ambox-protection{border-left:10px solid #a2a9b1}.mw-parser-output .ambox .mbox-text{border:none;padding:0.25em 0.5em;width:100%}.mw-parser-output .ambox .mbox-image{border:none;padding:2px 0 2px 0.5em;text-align:center}.mw-parser-output .ambox .mbox-imageright{border:none;padding:2px 0.5em 2px 0;text-align:center}.mw-parser-output .ambox .mbox-empty-cell{border:none;padding:0;width:1px}.mw-parser-output .ambox .mbox-image-div{width:52px}@media(min-width:720px){.mw-parser-output .ambox{margin:0 10%}}@media print{body.ns-0 .mw-parser-output .ambox{display:none!important}}</style><table class="box-Split plainlinks metadata ambox ambox-move" role="presentation"><tbody><tr><td class="mbox-image"><div class="mbox-image-div"><span typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a7/Split-arrows.svg/50px-Split-arrows.svg.png" decoding="async" width="50" height="17" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a7/Split-arrows.svg/75px-Split-arrows.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a7/Split-arrows.svg/100px-Split-arrows.svg.png 2x" data-file-width="60" data-file-height="20" /></span></span></div></td><td class="mbox-text"><div class="mbox-text-span">It has been suggested that some portions of this article be <b><a href="/wiki/Wikipedia:Splitting" title="Wikipedia:Splitting">split</a></b> into a new article titled <i><a href="/w/index.php?title=Interpersonal_comparison_of_utility&action=edit&redlink=1" class="new" title="Interpersonal comparison of utility (page does not exist)">interpersonal comparison of utility</a></i>. (<a href="/wiki/Talk:Social_choice_theory" title="Talk:Social choice theory">discuss</a>) <span class="date-container"><i>(<span class="date">May 2024</span>)</i></span></div></td></tr></tbody></table><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1251242444"><table class="box-Citation_style plainlinks metadata ambox ambox-style ambox-citation_style" role="presentation"><tbody><tr><td class="mbox-image"><div class="mbox-image-div"><span typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/f/f2/Edit-clear.svg/40px-Edit-clear.svg.png" decoding="async" width="40" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/f/f2/Edit-clear.svg/60px-Edit-clear.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/f/f2/Edit-clear.svg/80px-Edit-clear.svg.png 2x" data-file-width="48" data-file-height="48" /></span></span></div></td><td class="mbox-text"><div class="mbox-text-span">This article <b>has an unclear <a href="/wiki/Wikipedia:Citing_sources#Citation_style" title="Wikipedia:Citing sources">citation style</a></b>.<span class="hide-when-compact"> The references used may be made clearer with a different or consistent style of <a href="/wiki/Wikipedia:Citing_sources" title="Wikipedia:Citing sources">citation</a> and <a href="/wiki/Help:Footnotes" title="Help:Footnotes">footnoting</a>.</span> <span class="date-container"><i>(<span class="date">April 2021</span>)</i></span><span class="hide-when-compact"><i> (<small><a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove this message</a></small>)</i></span></div></td></tr></tbody></table> <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 class="mw-selflink selflink">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 class="mw-selflink selflink">Social choice</a></li><li><a href="/wiki/Mechanism_design" title="Mechanism design">Mechanism design</a></li><li><a href="/wiki/Comparative_politics" title="Comparative politics">Comparative politics</a></li><li><a href="/wiki/Comparison_of_voting_rules" title="Comparison of voting rules">Comparison</a></li><li><a href="/wiki/List_of_electoral_systems" title="List of electoral systems">List</a> (<a href="/wiki/List_of_electoral_systems_by_country" title="List of electoral systems by country">By country</a>)</li></ul></div></td></tr><tr><td class="sidebar-content" style="text-align:left;"> <div class="sidebar-list mw-collapsible 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_blanket_primary" title="Nonpartisan blanket primary">Jungle primary</a>) <ul><li><a href="/wiki/Partisan_primary" class="mw-redirect" title="Partisan primary">Partisan primary</a></li></ul></li> <li><a href="/wiki/Instant-runoff_voting" title="Instant-runoff voting">Instant-runoff</a> <ul><li><abbr style="font-size:85%" title=""><a href="/wiki/British_English" title="British English">UK</a>:</abbr> Alternative vote (AV)</li> <li><abbr style="font-size:85%" title=""><a href="/wiki/American_English" title="American English">US</a>:</abbr> Ranked-choice (RCV)</li></ul></li></ul> <hr /> <p><b><a href="/wiki/Condorcet_method" title="Condorcet method">Condorcet methods</a></b> </p> <ul><li><a href="/wiki/Tideman_alternative_method" title="Tideman alternative method">Condorcet-IRV</a></li> <li><a href="/wiki/Round-robin_voting" title="Round-robin voting">Round-robin voting</a> <ul><li><a href="/wiki/Minimax_Condorcet_method" title="Minimax Condorcet method">Minimax</a></li> <li><a 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></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"><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 class="mw-selflink selflink">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></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><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1246091330"><style data-mw-deduplicate="TemplateStyles:r1066933788">.mw-parser-output .excerpt-hat .mw-editsection-like{font-style:normal}</style><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1066933788"><table class="sidebar sidebar-collapse nomobile nowraplinks hlist"><tbody><tr><td class="sidebar-pretitle">Part of <a href="/wiki/Category:Economics" title="Category:Economics">a series</a> on</td></tr><tr><th class="sidebar-title-with-pretitle" style="border-top:1px #fafafa solid; border-bottom:1px #fafafa solid; background:#efefef;padding:0.2em;font-size:200%;"><a href="/wiki/Economics" title="Economics">Economics</a></th></tr><tr><td class="sidebar-image"><span typeof="mw:File"><a href="/wiki/File:Supply-demand-equilibrium.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/8c/Supply-demand-equilibrium.svg/120px-Supply-demand-equilibrium.svg.png" decoding="async" width="120" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/8c/Supply-demand-equilibrium.svg/180px-Supply-demand-equilibrium.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/8c/Supply-demand-equilibrium.svg/240px-Supply-demand-equilibrium.svg.png 2x" data-file-width="217" data-file-height="217" /></a></span></td></tr><tr><td class="sidebar-above"> <ul><li><a href="/wiki/History_of_economic_thought" title="History of economic thought">History</a></li> <li><a href="/wiki/Outline_of_economics" title="Outline of economics">Outline</a></li> <li><a href="/wiki/Index_of_economics_articles" title="Index of economics articles">Index</a></li></ul></td></tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:#efefef;;color: var(--color-base)">Branches and <a href="/wiki/JEL_classification_codes" title="JEL classification codes">classifications</a></div><div class="sidebar-list-content mw-collapsible-content"> <ul><li><a href="/wiki/Applied_economics" title="Applied economics">Applied</a></li> <li><a href="/wiki/Econometrics" title="Econometrics">Econometrics</a></li> <li><a href="/wiki/Heterodox_economics" title="Heterodox economics">Heterodox</a></li> <li><a href="/wiki/International_economics" title="International economics">International</a></li> <li><a href="/wiki/Microeconomics" title="Microeconomics">Micro</a> / <a href="/wiki/Macroeconomics" title="Macroeconomics">Macro</a></li> <li><a href="/wiki/Mainstream_economics" title="Mainstream economics">Mainstream</a></li> <li><a href="/wiki/Mathematical_economics" title="Mathematical economics">Mathematical</a></li> <li><a href="/wiki/Economic_methodology" title="Economic methodology">Methodology</a></li> <li><a href="/wiki/Political_economy" title="Political economy">Political</a></li> <li><a href="/wiki/JEL_classification_codes" title="JEL classification codes">JEL classification codes</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:#efefef;;color: var(--color-base)">Concepts, theory and techniques</div><div class="sidebar-list-content mw-collapsible-content"> <ul><li><a href="/wiki/Economic_system" title="Economic system">Economic systems</a></li> <li><a href="/wiki/Economic_growth" title="Economic growth">Economic growth</a></li> <li><a href="/wiki/Market_(economics)" title="Market (economics)">Market</a></li> <li><a href="/wiki/National_accounts" title="National accounts">National accounting</a></li> <li><a href="/wiki/Experimental_economics" title="Experimental economics">Experimental economics</a></li> <li><a href="/wiki/Computational_economics" title="Computational economics">Computational economics</a></li> <li><a href="/wiki/Game_theory" title="Game theory">Game theory</a></li> <li><a href="/wiki/Operations_research" title="Operations research">Operations research</a></li> <li><a href="/wiki/Middle_income_trap" title="Middle income trap">Middle income trap</a></li> <li><a href="/wiki/Industrial_complex" title="Industrial complex">Industrial complex</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:#efefef;;color: var(--color-base)">By application</div><div class="sidebar-list-content mw-collapsible-content"> <ul><li><a href="/wiki/Agricultural_economics" title="Agricultural economics">Agricultural</a></li> <li><a href="/wiki/Behavioral_economics" title="Behavioral economics">Behavioral</a></li> <li><a href="/wiki/Business_economics" title="Business economics">Business</a></li> <li><a href="/wiki/Cultural_economics" title="Cultural economics">Cultural</a></li> <li><a href="/wiki/Democracy_and_economic_growth" title="Democracy and economic growth">Democracy</a></li> <li><a href="/wiki/Demographic_economics" title="Demographic economics">Demographic</a></li> <li><a href="/wiki/Development_economics" title="Development economics">Development</a></li> <li><a href="/wiki/Economics_of_digitization" title="Economics of digitization">Digitization</a></li> <li><a href="/wiki/Ecological_economics" title="Ecological economics">Ecological</a></li> <li><a href="/wiki/Education_economics" title="Education economics">Education</a></li> <li><a href="/wiki/Engineering_economics" title="Engineering economics">Engineering</a></li> <li><a href="/wiki/Environmental_economics" title="Environmental economics">Environmental</a></li> <li><a href="/wiki/Evolutionary_economics" title="Evolutionary economics">Evolutionary</a></li> <li><a href="/wiki/Expeditionary_economics" title="Expeditionary economics">Expeditionary</a></li> <li><a href="/wiki/Feminist_economics" title="Feminist economics">Feminist</a></li> <li><a href="/wiki/Financial_economics" title="Financial economics">Financial</a></li> <li><a href="/wiki/Economic_geography" title="Economic geography">Geographical</a></li> <li><a href="/wiki/Happiness_economics" title="Happiness economics">Happiness</a></li> <li><a href="/wiki/Health_economics" title="Health economics">Health</a></li> <li><a href="/wiki/Economic_history" title="Economic history">Historical</a></li> <li><a href="/wiki/Humanistic_economics" title="Humanistic economics">Humanistic</a></li> <li><a href="/wiki/Industrial_organization" title="Industrial organization">Industrial organization</a></li> <li><a href="/wiki/Information_economics" title="Information economics">Information</a></li> <li><a href="/wiki/Institutional_economics" title="Institutional economics">Institutional</a></li> <li><a href="/wiki/Knowledge_economy" title="Knowledge economy">Knowledge</a></li> <li><a href="/wiki/Labour_economics" title="Labour economics">Labour</a></li> <li><a href="/wiki/Law_and_economics" title="Law and economics">Law</a></li> <li><a href="/wiki/Managerial_economics" title="Managerial economics">Managerial</a></li> <li><a href="/wiki/Monetary_economics" title="Monetary economics">Monetary</a></li> <li><a href="/wiki/Natural_resource_economics" title="Natural resource economics">Natural resource</a></li> <li><a href="/wiki/Organizational_economics" title="Organizational economics">Organizational</a></li> <li><a href="/wiki/Economics_of_participation" title="Economics of participation">Participation</a></li> <li><a href="/wiki/Personnel_economics" title="Personnel economics">Personnel</a></li> <li><a href="/wiki/Economic_planning" title="Economic planning">Planning</a></li> <li><a href="/wiki/Economic_policy" title="Economic policy">Policy</a></li> <li><a href="/wiki/Public_economics" title="Public economics">Public</a></li> <li><a href="/wiki/Public_choice" title="Public choice">Public choice</a> / <a class="mw-selflink selflink">Social choice theory</a></li> <li><a href="/wiki/Regional_economics" title="Regional economics">Regional</a></li> <li><a href="/wiki/Rural_economics" title="Rural economics">Rural</a></li> <li><a href="/wiki/Service_economy" title="Service economy">Service</a></li> <li><a href="/wiki/Socioeconomics" class="mw-redirect" title="Socioeconomics">Socio</a></li> <li><a href="/wiki/Economic_sociology" title="Economic sociology">Sociological</a></li> <li><a href="/wiki/Solidarity_economy" title="Solidarity economy">Solidarity</a></li> <li><a href="/wiki/Economic_statistics" title="Economic statistics">Statistics</a></li> <li><a href="/wiki/Urban_economics" title="Urban economics">Urban</a></li> <li><a href="/wiki/Welfare_economics" title="Welfare economics">Welfare</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:#efefef;;color: var(--color-base)">Notable <a href="/wiki/Economist" title="Economist">economists</a></div><div class="sidebar-list-content mw-collapsible-content"> <div class="excerpt-block"><div class="excerpt"> <ul><li><a href="/wiki/Bernard_de_Mandeville" class="mw-redirect" title="Bernard de Mandeville">de Mandeville</a></li> <li><a href="/wiki/Fran%C3%A7ois_Quesnay" title="François Quesnay">Quesnay</a></li> <li><a href="/wiki/Adam_Smith" title="Adam Smith">Smith</a></li> <li><a href="/wiki/Thomas_Robert_Malthus" title="Thomas Robert Malthus">Malthus</a></li> <li><a href="/wiki/Jean-Baptiste_Say" title="Jean-Baptiste Say">Say</a></li> <li><a href="/wiki/David_Ricardo" title="David Ricardo">Ricardo</a></li> <li><a href="/wiki/Johann_Heinrich_von_Th%C3%BCnen" title="Johann Heinrich von Thünen">von Thünen</a></li> <li><a href="/wiki/Friedrich_List" title="Friedrich List">List</a></li> <li><a href="/wiki/Fr%C3%A9d%C3%A9ric_Bastiat" title="Frédéric Bastiat">Bastiat</a></li> <li><a href="/wiki/Antoine_Augustin_Cournot" title="Antoine Augustin Cournot">Cournot</a></li> <li><a href="/wiki/John_Stuart_Mill" title="John Stuart Mill">Mill</a></li> <li><a href="/wiki/Hermann_Heinrich_Gossen" title="Hermann Heinrich Gossen">Gossen</a></li> <li><a href="/wiki/Karl_Marx" title="Karl Marx">Marx</a></li> <li><a href="/wiki/L%C3%A9on_Walras" title="Léon Walras">Walras</a></li> <li><a href="/wiki/William_Stanley_Jevons" title="William Stanley Jevons">Jevons</a></li> <li><a href="/wiki/Henry_George" title="Henry George">George</a></li> <li><a href="/wiki/Carl_Menger" title="Carl Menger">Menger</a></li> <li><a href="/wiki/Alfred_Marshall" title="Alfred Marshall">Marshall</a></li> <li><a href="/wiki/Francis_Ysidro_Edgeworth" title="Francis Ysidro Edgeworth">Edgeworth</a></li> <li><a href="/wiki/John_Bates_Clark" title="John Bates Clark">Clark</a></li> <li><a href="/wiki/Vilfredo_Pareto" title="Vilfredo Pareto">Pareto</a></li> <li><a href="/wiki/Eugen_von_B%C3%B6hm-Bawerk" title="Eugen von Böhm-Bawerk">von Böhm-Bawerk</a></li> <li><a href="/wiki/Friedrich_von_Wieser" title="Friedrich von Wieser">von Wieser</a></li> <li><a href="/wiki/Thorstein_Veblen" title="Thorstein Veblen">Veblen</a></li> <li><a href="/wiki/Irving_Fisher" title="Irving Fisher">Fisher</a></li> <li><a href="/wiki/Arthur_Cecil_Pigou" title="Arthur Cecil Pigou">Pigou</a></li> <li><a href="/wiki/Eli_Heckscher" title="Eli Heckscher">Heckscher</a></li> <li><a href="/wiki/Ludwig_von_Mises" title="Ludwig von Mises">von Mises</a></li> <li><a href="/wiki/Joseph_Schumpeter" title="Joseph Schumpeter">Schumpeter</a></li> <li><a href="/wiki/John_Maynard_Keynes" title="John Maynard Keynes">Keynes</a></li> <li><a href="/wiki/Frank_Knight" title="Frank Knight">Knight</a></li> <li><a href="/wiki/Karl_Polanyi" title="Karl Polanyi">Polanyi</a></li> <li><a href="/wiki/Ragnar_Frisch" title="Ragnar Frisch">Frisch</a></li> <li><a href="/wiki/Piero_Sraffa" title="Piero Sraffa">Sraffa</a></li> <li><a href="/wiki/Gunnar_Myrdal" title="Gunnar Myrdal">Myrdal</a></li> <li><a href="/wiki/Friedrich_Hayek" title="Friedrich Hayek">Hayek</a></li> <li><a href="/wiki/Micha%C5%82_Kalecki" title="Michał Kalecki">Kalecki</a></li> <li><a href="/wiki/Wilhelm_R%C3%B6pke" title="Wilhelm Röpke">Röpke</a></li> <li><a href="/wiki/Simon_Kuznets" title="Simon Kuznets">Kuznets</a></li> <li><a href="/wiki/Jan_Tinbergen" title="Jan Tinbergen">Tinbergen</a></li> <li><a href="/wiki/Joan_Robinson" title="Joan Robinson">Robinson</a></li> <li><a href="/wiki/John_von_Neumann" title="John von Neumann">von Neumann</a></li> <li><a href="/wiki/John_Hicks" title="John Hicks">Hicks</a></li> <li><a href="/wiki/Oskar_R._Lange" title="Oskar R. Lange">Lange</a></li> <li><a href="/wiki/Wassily_Leontief" title="Wassily Leontief">Leontief</a></li> <li><a href="/wiki/John_Kenneth_Galbraith" title="John Kenneth Galbraith">Galbraith</a></li> <li><a href="/wiki/Tjalling_Koopmans" title="Tjalling Koopmans">Koopmans</a></li> <li><a href="/wiki/E._F._Schumacher" title="E. F. Schumacher">Schumacher</a></li> <li><a href="/wiki/Milton_Friedman" title="Milton Friedman">Friedman</a></li> <li><a href="/wiki/Paul_Samuelson" title="Paul Samuelson">Samuelson</a></li> <li><a href="/wiki/Herbert_A._Simon" title="Herbert A. Simon">Simon</a></li> <li><a href="/wiki/James_M._Buchanan" title="James M. Buchanan">Buchanan</a></li> <li><a href="/wiki/Kenneth_Arrow" title="Kenneth Arrow">Arrow</a></li> <li><a href="/wiki/William_Baumol" title="William Baumol">Baumol</a></li> <li><a href="/wiki/Robert_Solow" title="Robert Solow">Solow</a></li> <li><a href="/wiki/Murray_Rothbard" title="Murray Rothbard">Rothbard</a></li> <li><a href="/wiki/Alan_Greenspan" title="Alan Greenspan">Greenspan</a></li> <li><a href="/wiki/Thomas_Sowell" title="Thomas Sowell">Sowell</a></li> <li><a href="/wiki/Gary_Becker" title="Gary Becker">Becker</a></li> <li><a href="/wiki/Elinor_Ostrom" title="Elinor Ostrom">Ostrom</a></li> <li><a href="/wiki/Amartya_Sen" title="Amartya Sen">Sen</a></li> <li><a href="/wiki/Robert_Lucas_Jr." title="Robert Lucas Jr.">Lucas</a></li> <li><a href="/wiki/Joseph_Stiglitz" title="Joseph Stiglitz">Stiglitz</a></li> <li><a href="/wiki/Richard_Thaler" title="Richard Thaler">Thaler</a></li> <li><a href="/wiki/Hans-Hermann_Hoppe" title="Hans-Hermann Hoppe">Hoppe</a></li> <li><a href="/wiki/Paul_Krugman" title="Paul Krugman">Krugman</a></li> <li><a href="/wiki/Thomas_Piketty" title="Thomas Piketty">Piketty</a></li> <li><i><a href="/wiki/Category:Economists" title="Category:Economists">more</a></i></li></ul></div></div> </div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:#efefef;;color: var(--color-base)"><a href="/wiki/Category:Economics_lists" title="Category:Economics lists">Lists</a></div><div class="sidebar-list-content mw-collapsible-content"> <ul><li><a href="/wiki/Glossary_of_economics" title="Glossary of economics">Glossary</a></li> <li><a href="/wiki/List_of_economists" title="List of economists">Economists</a></li> <li><a href="/wiki/List_of_important_publications_in_economics" title="List of important publications in economics">Publications</a> (<a href="/wiki/List_of_economics_journals" title="List of economics journals">journals</a>)</li> <li><a href="/wiki/Schools_of_economic_thought" title="Schools of economic thought">Schools</a></li></ul> </div></div></td> </tr><tr><td class="sidebar-below"> <ul><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:Business" title="Portal:Business">Business portal</a></li> <li><span class="nowrap"><span class="noviewer" typeof="mw:File"><span><img alt="icon" src="//upload.wikimedia.org/wikipedia/commons/thumb/5/55/Bills_and_coins.svg/16px-Bills_and_coins.svg.png" decoding="async" width="16" height="8" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/55/Bills_and_coins.svg/24px-Bills_and_coins.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/55/Bills_and_coins.svg/32px-Bills_and_coins.svg.png 2x" data-file-width="960" data-file-height="465" /></span></span> </span><a href="/wiki/Portal:Money" title="Portal:Money">Money portal</a></li></ul></td></tr><tr><td class="sidebar-navbar"><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:Economics_sidebar" title="Template:Economics sidebar"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Economics_sidebar" title="Template talk:Economics sidebar"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Economics_sidebar" title="Special:EditPage/Template:Economics sidebar"><abbr title="Edit this template">e</abbr></a></li></ul></div></td></tr></tbody></table><p><b>Social choice theory</b> is a branch of <a href="/wiki/Welfare_economics" title="Welfare economics">welfare economics</a> that analyzes methods of combining individual opinions, beliefs, or preferences to reach a collective decision or create measures of <a href="/wiki/Social_welfare_function" title="Social welfare function">social well-being</a>.<sup id="cite_ref-Sen2008_1-0" class="reference"><a href="#cite_note-Sen2008-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> It contrasts with <a href="/wiki/Political_science" title="Political science">political science</a> in that it is a <a href="/wiki/Normative_economics" class="mw-redirect" title="Normative economics">normative</a> field that studies how societies <i>should</i> make decisions, whereas political science is <a href="/wiki/Positive_economics" class="mw-redirect" title="Positive economics">descriptive</a> (observing how societies <i>do</i> make decisions). Social choice incorporates insights from <a href="/wiki/Economics" title="Economics">economics</a>, <a href="/wiki/Mathematics" title="Mathematics">mathematics</a>, <a href="/wiki/Philosophy" title="Philosophy">philosophy</a>, <a href="/wiki/Political_science" title="Political science">political science</a>, and <a href="/wiki/Game_theory" title="Game theory">game theory</a> to find the best ways to combine individual preferences into a coherent whole, called a <a href="/wiki/Social_welfare_function" title="Social welfare function">social welfare function</a>.<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><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><p>Because of its strong connections to <a href="/wiki/Political_philosophy" title="Political philosophy">political philosophy</a> and <a href="/wiki/Voting" title="Voting">voting</a>, social choice is sometimes also called <b>voting theory</b>.<sup id="cite_ref-:1_4-0" class="reference"><a href="#cite_note-:1-4"><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><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> Real-world examples include enacting laws under a <a href="/wiki/Constitution" title="Constitution">constitution</a> or <a href="/wiki/Voting" title="Voting">voting</a>, where individual preferences over candidates are collected to elect a person that best represents the group's preferences.<sup id="cite_ref-:1_4-1" class="reference"><a href="#cite_note-:1-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> The field is closely related to <a href="/wiki/Mechanism_design" title="Mechanism design">mechanism design</a>, which can be thought of as modelling social choice with <a href="/wiki/Homo_economicus" title="Homo economicus">self-interested</a> and potentially <a href="/wiki/Honesty" title="Honesty">dishonest</a> citizens; it thus involves the application of <a href="/wiki/Game_theory" title="Game theory">game theory</a>. </p><p>Social choice differs from <a href="/wiki/Decision_theory" title="Decision theory">decision theory</a> in that the latter is concerned with how <i>individuals</i>, rather than <i>societies</i>, can make rational decisions. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="History">History</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Social_choice_theory&action=edit&section=1" title="Edit section: History"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The earliest work on social choice theory comes from the writings of the <a href="/wiki/Marquis_de_Condorcet" title="Marquis de Condorcet">Marquis de Condorcet</a>, who formulated several key results including his <a href="/wiki/Condorcet%27s_jury_theorem" title="Condorcet's jury theorem">jury theorem</a> and <a href="/wiki/Condorcet_paradox" title="Condorcet paradox">his example</a> showing the impossibility of <a href="/wiki/Majority_rule" title="Majority rule">majority rule</a>. His work was prefigured by <a href="/wiki/Ramon_Llull" title="Ramon Llull">Ramon Llull</a>'s 1299 manuscript <i>Ars Electionis</i> (<i>The Art of Elections</i>), which discussed many of the same concepts, but was lost in the <a href="/wiki/Late_Middle_Ages" title="Late Middle Ages">Late Middle Ages</a> and only rediscovered in the early 21st century.<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><a href="/wiki/Kenneth_Arrow" title="Kenneth Arrow">Kenneth Arrow</a>'s book <i><a href="/wiki/Social_Choice_and_Individual_Values" title="Social Choice and Individual Values">Social Choice and Individual Values</a></i> is often recognized as inaugurating the modern era of social choice theory.<sup id="cite_ref-Sen2008_1-1" class="reference"><a href="#cite_note-Sen2008-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> Later work has also considered approaches to <a href="/wiki/Compensation_principle" title="Compensation principle">legal compensation</a>, <a href="/wiki/Fair_division" title="Fair division">fair division</a>, <a href="/wiki/Population_ethics" title="Population ethics">variable populations</a>,<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (July 2024)">citation needed</span></a></i>]</sup> partial <a href="/wiki/Strategy-proof" class="mw-redirect" title="Strategy-proof">strategy-proofing</a> of social-choice <a href="/wiki/Mechanism_design" title="Mechanism design">mechanisms</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> <a href="/wiki/Natural_resource_economics" title="Natural resource economics">natural resources</a>,<sup id="cite_ref-Sen2008_1-2" class="reference"><a href="#cite_note-Sen2008-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Capabilities_approach" class="mw-redirect" title="Capabilities approach">capabilities and functionings approaches</a>,<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> and <a href="/wiki/Well-being" title="Well-being">measures of welfare</a>.<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><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><sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Key_results">Key results</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Social_choice_theory&action=edit&section=2" title="Edit section: Key results"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Arrow's_impossibility_theorem"><span id="Arrow.27s_impossibility_theorem"></span>Arrow's impossibility theorem</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Social_choice_theory&action=edit&section=3" title="Edit section: Arrow's impossibility theorem"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1236090951">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Arrow%27s_impossibility_theorem" title="Arrow's impossibility theorem">Arrow's impossibility theorem</a></div> <p>Arrow's impossibility theorem is a key result showing that <a href="/wiki/Social_choice_function" class="mw-redirect" title="Social choice function">social choice functions</a> based only on <a href="/wiki/Ordinal_utility" title="Ordinal utility">ordinal comparisons</a>, rather than <a href="/wiki/Cardinal_utility" title="Cardinal utility">cardinal utility</a>, will behave <a href="/wiki/Coherence_(philosophical_gambling_strategy)" class="mw-redirect" title="Coherence (philosophical gambling strategy)">incoherently</a> (unless they are <a href="/wiki/Dictatorship_mechanism" title="Dictatorship mechanism">dictatorial</a>). Such systems violate <a href="/wiki/Independence_of_irrelevant_alternatives" title="Independence of irrelevant alternatives">independence of irrelevant alternatives</a>, i.e. they suffer from <a href="/wiki/Spoiler_effect" title="Spoiler effect">spoiler effects</a> the system can behave erratically in response to changes in the quality or popularity of one of the options. </p> <div class="mw-heading mw-heading3"><h3 id="Condorcet_cycles">Condorcet cycles</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Social_choice_theory&action=edit&section=4" title="Edit section: Condorcet cycles"><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/Condorcet_cycle" class="mw-redirect" title="Condorcet cycle">Condorcet cycle</a></div> <p>Condorcet's example demonstrates that <a href="/wiki/Democracy" title="Democracy">democracy</a> cannot be thought of as being the same as simple <a href="/wiki/Majority_rule" title="Majority rule">majority rule</a> or majoritarianism; otherwise, it will be <a href="/wiki/Paradox" title="Paradox">self-contradictory</a> when three or more options are available. Majority rule can create cycles that violate the <a href="/wiki/Transitive_relation" title="Transitive relation">transitive property</a>: Attempting to use majority rule as a social choice function creates situations where we have A better than B and B better than C, but C is also better than A. </p><p>This contrasts with <a href="/wiki/May%27s_theorem" title="May's theorem">May's theorem</a>, which shows that simple majority is the optimal voting mechanism when there are only two outcomes, and only ordinal preferences are allowed. </p> <div class="mw-heading mw-heading3"><h3 id="Harsanyi's_theorem"><span id="Harsanyi.27s_theorem"></span>Harsanyi's theorem</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Social_choice_theory&action=edit&section=5" title="Edit section: Harsanyi's theorem"><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="/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></div> <p><a href="/wiki/John_Harsanyi" title="John Harsanyi">Harsanyi</a>'s utilitarian theorem shows that if individuals have preferences that are <a href="/wiki/Von_Neumann%E2%80%93Morgenstern_axioms" class="mw-redirect" title="Von Neumann–Morgenstern axioms">well-behaved under uncertainty</a> (i.e. <a href="/wiki/Coherence_(philosophical_gambling_strategy)" class="mw-redirect" title="Coherence (philosophical gambling strategy)">coherent</a>), the only <a href="/wiki/Coherence_(philosophical_gambling_strategy)" class="mw-redirect" title="Coherence (philosophical gambling strategy)">coherent</a> and <a href="/wiki/Pareto_efficiency" title="Pareto efficiency">Pareto efficient</a> social choice function is the <a href="/wiki/Utilitarian_rule" title="Utilitarian rule">utilitarian rule</a>. This lends some support to the viewpoint expressed of <a href="/wiki/John_Stuart_Mill" title="John Stuart Mill">John Stuart Mill</a>, who identified democracy with the ideal of maximizing the <a href="/wiki/Common_good" title="Common good">common good</a> (or <a href="/wiki/Utility" title="Utility">utility</a>) of society as a whole, under an <a href="/wiki/Equal_consideration_of_interests" title="Equal consideration of interests">equal consideration of interests</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Manipulation_theorems">Manipulation theorems</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Social_choice_theory&action=edit&section=6" title="Edit section: Manipulation 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/Gibbard%27s_theorem" title="Gibbard's theorem">Gibbard's theorem</a> and <a href="/wiki/Gibbard%E2%80%93Satterthwaite_theorem" title="Gibbard–Satterthwaite theorem">Gibbard–Satterthwaite theorem</a></div> <p>Gibbard's theorem provides limitations on the ability of any voting rule to elicit honest preferences from voters, showing that no voting rule is <a href="/wiki/Strategyproofness" title="Strategyproofness">strategyproof</a> (i.e. does not depend on other voters' preferences) for elections with 3 or more outcomes. </p><p>The Gibbard–Satterthwaite theorem proves a stronger result for <a href="/wiki/Ranked_voting" title="Ranked voting">ranked-choice voting systems</a>, showing that no such voting rule can be sincere (i.e. free of reversed preferences). </p> <div class="mw-heading mw-heading3"><h3 id="Median_voter_theorem">Median voter theorem</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Social_choice_theory&action=edit&section=7" title="Edit section: Median voter theorem"><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> <div class="mw-heading mw-heading3"><h3 id="Mechanism_design">Mechanism design</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Social_choice_theory&action=edit&section=8" title="Edit section: Mechanism design"><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/Mechanism_design" title="Mechanism design">Mechanism design</a></div> <p>The field of <a href="/wiki/Mechanism_design" title="Mechanism design">mechanism design</a>, a subset of social choice theory, deals with the identification of rules that preserve while incentivizing agents to honestly reveal their preferences. One particularly important result is the <a href="/wiki/Revelation_principle" title="Revelation principle">revelation principle</a>, which is almost a reversal of Gibbard's theorem: for any given social choice function, there exists a mechanism that obtains the same results but incentivizes participants to be completely honest. </p><p>Because mechanism design places stronger assumptions on the behavior of voters or , it is sometimes possible to design mechanisms for social choice that accomplish "impossible" tasks. For example, by allowing agents to compensate each other for losses with transfers, the <a href="/wiki/Vickrey%E2%80%93Clarke%E2%80%93Groves_mechanism" title="Vickrey–Clarke–Groves mechanism">Vickrey–Clarke–Groves (VCG) mechanism</a> can achieve the "impossible" according to Gibbard's theorem: the mechanism ensures honest behavior from participants, while still achieving a <a href="/wiki/Pareto_efficiency" title="Pareto efficiency">Pareto efficient</a> outcome. As a result, the VCG mechanism can be considered a "better" way to make decisions than voting (though only so long as monetary transfers are possible). </p> <div class="mw-heading mw-heading3"><h3 id="Others">Others</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Social_choice_theory&action=edit&section=9" title="Edit section: Others"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>If the domain of preferences is restricted to those that include a <a href="/wiki/Condorcet_winner_criterion" title="Condorcet winner criterion">majority-strength Condorcet winner</a>, then selecting that winner is the unique <a href="/wiki/Resolvability_criterion" title="Resolvability criterion">resolvable</a>, <a href="/wiki/Neutrality_(social_choice)" class="mw-redirect" title="Neutrality (social choice)">neutral</a>, <a href="/wiki/Anonymity_(social_choice)" class="mw-redirect" title="Anonymity (social choice)">anonymous</a>, and non-manipulable voting rule.<sup id="cite_ref-:1_4-2" class="reference"><a href="#cite_note-:1-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup><sup class="noprint Inline-Template" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Please_clarify" title="Wikipedia:Please clarify"><span title="More details--what does non-manipulable mean? (March 2024)">further explanation needed</span></a></i>]</sup> </p> <div class="mw-heading mw-heading2"><h2 id="Interpersonal_utility_comparison">Interpersonal utility comparison</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Social_choice_theory&action=edit&section=10" title="Edit section: Interpersonal utility comparison"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Social choice theory is the study of theoretical and practical methods to aggregate or combine individual preferences into a collective social welfare function. The field generally assumes that individuals have <a href="/wiki/Preference" title="Preference">preferences</a>, and it follows that they can be modeled using <a href="/wiki/Utility_function" class="mw-redirect" title="Utility function">utility functions</a>, by the <a href="/wiki/Von_Neumann%E2%80%93Morgenstern_utility_theorem" title="Von Neumann–Morgenstern utility theorem">VNM theorem</a>. But much of the research in the field assumes that those utility functions are internal to humans, lack a meaningful unit of measure and <i>cannot</i> be compared across different individuals.<sup id="cite_ref-Robbins_13-0" class="reference"><a href="#cite_note-Robbins-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> Whether this type of <i>interpersonal utility comparison</i> is possible or not significantly alters the available mathematical structures for social welfare functions and social choice theory.<sup id="cite_ref-Robbins_13-1" class="reference"><a href="#cite_note-Robbins-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> </p><p>In one perspective, following <a href="/wiki/Jeremy_Bentham" title="Jeremy Bentham">Jeremy Bentham</a>, <a href="/wiki/Utilitarianism" title="Utilitarianism">utilitarians</a> have argued that preferences and utility functions of individuals are interpersonally comparable and may therefore be added together to arrive at a measure of aggregate utility. Utilitarian ethics call for maximizing this aggregate. </p><p>In contrast many twentieth century economists, following <a href="/wiki/Lionel_Robbins" title="Lionel Robbins">Lionel Robbins</a>, questioned whether such measures of utility could be measured, or even considered meaningful. Following arguments similar to those espoused by <a href="/wiki/Behaviorism" title="Behaviorism">behaviorists in psychology</a>, Robbins argued concepts of <a href="/wiki/Utility" title="Utility">utility</a> were unscientific and <a href="/wiki/Unfalsifiable" class="mw-redirect" title="Unfalsifiable">unfalsifiable</a>. Consider for instance the <a href="/wiki/Law_of_diminishing_marginal_utility" class="mw-redirect" title="Law of diminishing marginal utility">law of diminishing marginal utility</a>, according to which utility of an added quantity of a good decreases with the amount of the good that is already in possession of the individual. It has been used to defend transfers of wealth from the "rich" to the "poor" on the premise that the former do not derive as much utility as the latter from an extra unit of income. Robbins argued that this notion is beyond <a href="/wiki/Positivism" title="Positivism">positive science</a>; that is, one cannot measure changes in the utility of someone else, nor is it required by positive theory.<sup id="cite_ref-Robbins2_14-0" class="reference"><a href="#cite_note-Robbins2-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> </p><p>Apologists for the interpersonal comparison of utility have argued that Robbins claimed too much. <a href="/wiki/John_Harsanyi" title="John Harsanyi">John Harsanyi</a> agreed that perfect comparisons of mental states are not practically possible, but people can still make <i>some</i> comparisons thanks to their similar backgrounds, cultural experiences, and psychologies. <a href="/wiki/Amartya_Sen" title="Amartya Sen">Amartya Sen</a> argues that even if interpersonal comparisons of utility are imperfect, we can still say that (despite being positive for <a href="/wiki/Nero" title="Nero">Nero</a>) the <a href="/wiki/Great_Fire_of_Rome" title="Great Fire of Rome">Great Fire of Rome</a> had a negative overall value. Harsanyi and Sen thus argue that at least <i>partial</i> comparability of utility is possible, and social choice theory should proceed under that assumption. </p> <div class="mw-heading mw-heading2"><h2 id="Relationship_to_public_choice_theory">Relationship to public choice theory</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Social_choice_theory&action=edit&section=11" title="Edit section: Relationship to public choice theory"><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">See also: <a href="/wiki/Public_choice" title="Public choice">Public choice</a></div> <p>Despite the similar names, "public choice" and "social choice" are two distinct fields that are only weakly related. Public choice deals with the modeling of <a href="/wiki/Political_system" title="Political system">political systems</a> as they actually exist in the real world, and is primarily limited to <a href="/wiki/Positive_economics" class="mw-redirect" title="Positive economics">positive economics</a> (predicting how politicians and other stakeholders will act). It is therefore often thought of as the application of <a href="/wiki/Microeconomics" title="Microeconomics">microeconomic</a> models to <a href="/wiki/Political_science" title="Political science">political science</a>, in order to predict the behavior of <a href="/wiki/Politician" title="Politician">political actors</a>. By contrast, social choice has a much more <a href="/wiki/Normative_economics" class="mw-redirect" title="Normative economics">normative</a> bent, and deals with the abstract study of decision procedures and their properties. </p><p>The <a href="/wiki/JEL_classification_codes" title="JEL classification codes">Journal of Economic Literature classification codes</a> place Social Choice under <a href="/wiki/Microeconomics" title="Microeconomics">Microeconomics</a> at <a href="/wiki/JEL_classification_codes#Microeconomics_JEL:_D_Subcategories" title="JEL classification codes">JEL D71</a> (with Clubs, Committees, and Associations) whereas Public Choice falls under JEL D72 (Economic Models of Political Processes: <a href="/wiki/Rent-seeking" title="Rent-seeking">Rent-Seeking</a>, Elections, Legislatures, and Voting Behavior).<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. (June 2024)">citation needed</span></a></i>]</sup> </p> <div class="mw-heading mw-heading2"><h2 id="Empirical_research">Empirical research</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Social_choice_theory&action=edit&section=12" title="Edit section: Empirical research"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Since Arrow, social choice theory has been characterized by being predominantly <a href="/wiki/Mathematics" title="Mathematics">mathematical</a> and <a href="/wiki/Theoretical" class="mw-redirect" title="Theoretical">theoretical</a>, but some research has aimed at estimating the frequency of various voting paradoxes, such as the <a href="/wiki/Condorcet_paradox" title="Condorcet paradox">Condorcet paradox</a>.<sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-:0_16-0" class="reference"><a href="#cite_note-:0-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> A summary of 37 individual studies, covering a total of 265 real-world elections, large and small, found 25 instances of a Condorcet paradox for a total likelihood of 9.4%.<sup id="cite_ref-:0_16-1" class="reference"><a href="#cite_note-:0-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 325">: 325 </span></sup> While examples of the paradox seem to occur often in small settings like parliaments, very few examples have been found in larger groups (electorates), although some have been identified.<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> However, the frequency of such paradoxes depends heavily on the number of options and other factors. </p> <div class="mw-heading mw-heading2"><h2 id="Rules">Rules</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Social_choice_theory&action=edit&section=13" title="Edit section: Rules"><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/Social_welfare_function" title="Social welfare function">Social welfare function</a></div> <p>Let <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle X}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>X</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle X}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/68baa052181f707c662844a465bfeeb135e82bab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.98ex; height:2.176ex;" alt="{\displaystyle X}"></span> be a set of possible 'states of the world' or 'alternatives'. Society wishes to choose a single state from <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle X}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>X</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle X}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/68baa052181f707c662844a465bfeeb135e82bab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.98ex; height:2.176ex;" alt="{\displaystyle X}"></span>. For example, in a <a href="/wiki/Single-winner_election" class="mw-redirect" title="Single-winner election">single-winner election</a>, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle X}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>X</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle X}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/68baa052181f707c662844a465bfeeb135e82bab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.98ex; height:2.176ex;" alt="{\displaystyle X}"></span> may represent the set of candidates; in a <a href="/wiki/Resource_allocation" title="Resource allocation">resource allocation</a> setting, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle X}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>X</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle X}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/68baa052181f707c662844a465bfeeb135e82bab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.98ex; height:2.176ex;" alt="{\displaystyle X}"></span> may represent all possible allocations. </p><p>Let <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle I}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>I</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle I}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/535ea7fc4134a31cbe2251d9d3511374bc41be9f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.172ex; height:2.176ex;" alt="{\displaystyle I}"></span> be a finite set, representing a collection of individuals. For each <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle i\in I}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>i</mi> <mo>∈</mo> <mi>I</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle i\in I}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2d740fe587228ce31b71c9628e089d1a9b37c6be" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:4.815ex; height:2.176ex;" alt="{\displaystyle i\in I}"></span>, let <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle u_{i}:X\longrightarrow \mathbb {R} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>:</mo> <mi>X</mi> <mo stretchy="false">⟶</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">R</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle u_{i}:X\longrightarrow \mathbb {R} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3a376c84436e1081b4aac2aa1af6297182fa3156" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:12.82ex; height:2.509ex;" alt="{\displaystyle u_{i}:X\longrightarrow \mathbb {R} }"></span> be a <i><a href="/wiki/Utility" title="Utility">utility function</a></i>, describing the amount of happiness an individual <i>i</i> derives from each possible state. </p><p>A <i>social choice rule</i> is a mechanism which uses the data <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (u_{i})_{i\in I}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <msub> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <msub> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mo>∈</mo> <mi>I</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (u_{i})_{i\in I}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0473564e216aa446aabcb13db9ad12022a60780f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.663ex; height:2.843ex;" alt="{\displaystyle (u_{i})_{i\in I}}"></span> to select some element(s) from <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle X}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>X</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle X}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/68baa052181f707c662844a465bfeeb135e82bab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.98ex; height:2.176ex;" alt="{\displaystyle X}"></span> which are 'best' for society. The question of what 'best' means is a common question in social choice theory. The following rules are most common: </p> <ul><li><a href="/wiki/Utilitarian_social_choice_rule" class="mw-redirect" title="Utilitarian social choice rule"><i>Utilitarian rule</i></a> – sometimes called the <i>max-sum rule</i> or <a href="/wiki/Benthamite" class="mw-redirect" title="Benthamite"><i>Benthamite welfare</i></a> – aims to maximize the sum of utilities.</li> <li><a href="/wiki/Egalitarian_social_choice_rule" class="mw-redirect" title="Egalitarian social choice rule"><i>Egalitarian rule</i></a> – sometimes called the <i>max-min rule</i> or <a href="/wiki/Rawlsian" class="mw-redirect" title="Rawlsian"><i>Rawlsian welfare</i></a> – aims to maximize the smallest utility.</li></ul> <div class="mw-heading mw-heading2"><h2 id="Social_choice_functions">Social choice functions</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Social_choice_theory&action=edit&section=14" title="Edit section: Social choice functions"><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/Social_choice_function" class="mw-redirect" title="Social choice function">Social choice function</a></div> <p>A social choice function, sometimes called a <a href="/wiki/Voting_system" class="mw-redirect" title="Voting system">voting system</a> in the context of politics, is a rule that takes an individual's complete and transitive preferences over a set of outcomes and returns a single chosen outcome (or a set of tied outcomes). We can think of this subset as the winners of an election, and compare different social choice functions based on which axioms or mathematical properties they fulfill.<sup id="cite_ref-:1_4-3" class="reference"><a href="#cite_note-:1-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p><p><a href="/wiki/Arrow%27s_impossibility_theorem" title="Arrow's impossibility theorem">Arrow's impossibility theorem</a> is what often comes to mind when one thinks about impossibility theorems in voting. There are several famous theorems concerning social choice functions. The <a href="/wiki/Gibbard%E2%80%93Satterthwaite_theorem" title="Gibbard–Satterthwaite theorem">Gibbard–Satterthwaite theorem</a> implies that the only rule satisfying non-imposition (every alternative can be chosen) and <a href="/wiki/Strategyproofness" title="Strategyproofness">strategyproofness</a> when there are more than two candidates is the <a href="/wiki/Dictatorship_mechanism" title="Dictatorship mechanism">dictatorship mechanism</a>. That is, a voter may be able to cast a ballot that misrepresents their preferences to obtain a result that is more favorable to them under their sincere preferences. <a href="/wiki/May%27s_theorem" title="May's theorem">May's theorem</a> shows that when there are only two candidates and <a href="/wiki/Ordinal_utility" title="Ordinal utility">only rankings of options are available</a>, the <a href="/wiki/Simple_majority_vote" class="mw-redirect" title="Simple majority vote">simple majority vote</a> is the unique <a href="/wiki/Neutrality_(social_choice)" class="mw-redirect" title="Neutrality (social choice)">neutral</a>, <a href="/wiki/Anonymity_(social_choice)" class="mw-redirect" title="Anonymity (social choice)">anonymous</a>, and <a href="/wiki/Positive_response" class="mw-redirect" title="Positive response">positively-responsive</a> voting rule.<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> </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=Social_choice_theory&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" style="column-width: 20em;"> <ul><li><a href="/wiki/Arrow%27s_impossibility_theorem" title="Arrow's impossibility theorem">Arrow's impossibility theorem</a></li> <li><a href="/wiki/Compensation_principle" title="Compensation principle">Compensation principle</a></li> <li><a href="/wiki/Computational_social_choice" title="Computational social choice">Computational social choice</a></li> <li><a href="/wiki/Condorcet_paradox" title="Condorcet paradox">Condorcet paradox</a></li> <li><a href="/wiki/Extended_sympathy" title="Extended sympathy">Extended sympathy</a></li> <li><a href="/wiki/Game_theory" title="Game theory">Game theory</a></li> <li><a href="/wiki/Group_decision-making" title="Group decision-making">Group decision-making</a></li> <li><a href="/wiki/Justice_(economics)" class="mw-redirect" title="Justice (economics)">Justice (economics)</a></li> <li><a href="/wiki/Liberal_paradox" title="Liberal paradox">Liberal paradox</a></li> <li><a href="/wiki/Mechanism_design" title="Mechanism design">Mechanism design</a></li> <li><a href="/wiki/Nakamura_number" title="Nakamura number">Nakamura number</a></li> <li><a href="/wiki/Rational_choice_theory" class="mw-redirect" title="Rational choice theory">Rational choice theory</a></li> <li><a href="/wiki/Rule_according_to_higher_law" title="Rule according to higher law">Rule according to higher law</a></li> <li><a href="/wiki/Voting_system" class="mw-redirect" title="Voting system">Voting system</a></li></ul> </div> <div class="mw-heading mw-heading2"><h2 id="Notes">Notes</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Social_choice_theory&action=edit&section=16" title="Edit section: Notes"><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 reflist-columns references-column-width" style="column-width: 30em;"> <ol class="references"> <li id="cite_note-Sen2008-1"><span class="mw-cite-backlink">^ <a href="#cite_ref-Sen2008_1-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Sen2008_1-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-Sen2008_1-2"><sup><i><b>c</b></i></sup></a></span> <span class="reference-text"><a href="/wiki/Amartya_Sen" title="Amartya Sen">Amartya Sen</a> (2008). "Social Choice,". <i>The New Palgrave Dictionary of Economics</i>, 2nd Edition, <a rel="nofollow" class="external text" href="http://www.dictionaryofeconomics.com/article?id=pde2008_S000164&q=Social%20choice&topicid=&result_number=2">Abstract & TOC.</a></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">For example, in Kenneth J. Arrow (1951). <i>Social Choice and Individual Values</i>, New York: Wiley, ch. <a rel="nofollow" class="external text" href="http://cowles.econ.yale.edu/P/cm/m12-2/m12-2-02.pdf">II</a>, section 2, A Notation for Preferences and Choice, and ch. <a rel="nofollow" class="external text" href="http://cowles.econ.yale.edu/P/cm/m12-2/m12-2-03.pdf">III</a>, "The Social Welfare Function".</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"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFFishburn1974" class="citation journal cs1">Fishburn, Peter C. (1974). <a rel="nofollow" class="external text" href="https://epubs.siam.org/doi/abs/10.1137/1016005">"Social Choice Functions"</a>. <i>SIAM Review</i>. <b>16</b>: 63–90. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1137%2F1016005">10.1137/1016005</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=SIAM+Review&rft.atitle=Social+Choice+Functions&rft.volume=16&rft.pages=63-90&rft.date=1974&rft_id=info%3Adoi%2F10.1137%2F1016005&rft.aulast=Fishburn&rft.aufirst=Peter+C.&rft_id=https%3A%2F%2Fepubs.siam.org%2Fdoi%2Fabs%2F10.1137%2F1016005&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASocial+choice+theory" class="Z3988"></span></span> </li> <li id="cite_note-:1-4"><span class="mw-cite-backlink">^ <a href="#cite_ref-:1_4-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-:1_4-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-:1_4-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-:1_4-3"><sup><i><b>d</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFZwickerMoulin2016" class="citation cs2">Zwicker, William S.; Moulin, Herve (2016), Brandt, Felix; Conitzer, Vincent; Endriss, Ulle; Lang, Jerome (eds.), <a rel="nofollow" class="external text" href="https://www.cambridge.org/core/product/identifier/CBO9781107446984A019/type/book_part">"Introduction to the Theory of Voting"</a>, <i>Handbook of Computational Social Choice</i>, Cambridge: Cambridge University Press, pp. 23–56, <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1017%2Fcbo9781107446984.003">10.1017/cbo9781107446984.003</a>, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-107-44698-4" title="Special:BookSources/978-1-107-44698-4"><bdi>978-1-107-44698-4</bdi></a><span class="reference-accessdate">, retrieved <span class="nowrap">2021-12-24</span></span></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Handbook+of+Computational+Social+Choice&rft.atitle=Introduction+to+the+Theory+of+Voting&rft.pages=23-56&rft.date=2016&rft_id=info%3Adoi%2F10.1017%2Fcbo9781107446984.003&rft.isbn=978-1-107-44698-4&rft.aulast=Zwicker&rft.aufirst=William+S.&rft.au=Moulin%2C+Herve&rft_id=https%3A%2F%2Fwww.cambridge.org%2Fcore%2Fproduct%2Fidentifier%2FCBO9781107446984A019%2Ftype%2Fbook_part&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASocial+choice+theory" class="Z3988"></span></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="CITEREFNurmi2010" class="citation cs2">Nurmi, Hannu (2010), Rios Insua, David; French, Simon (eds.), <a rel="nofollow" class="external text" href="https://doi.org/10.1007/978-90-481-9045-4_7">"Voting Theory"</a>, <i>e-Democracy: A Group Decision and Negotiation Perspective</i>, Advances in Group Decision and Negotiation, vol. 5, Dordrecht: Springer Netherlands, pp. 101–123, <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%2F978-90-481-9045-4_7">10.1007/978-90-481-9045-4_7</a>, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-90-481-9045-4" title="Special:BookSources/978-90-481-9045-4"><bdi>978-90-481-9045-4</bdi></a><span class="reference-accessdate">, retrieved <span class="nowrap">2024-06-20</span></span></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=e-Democracy%3A+A+Group+Decision+and+Negotiation+Perspective&rft.atitle=Voting+Theory&rft.volume=5&rft.pages=101-123&rft.date=2010&rft_id=info%3Adoi%2F10.1007%2F978-90-481-9045-4_7&rft.isbn=978-90-481-9045-4&rft.aulast=Nurmi&rft.aufirst=Hannu&rft_id=https%3A%2F%2Fdoi.org%2F10.1007%2F978-90-481-9045-4_7&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASocial+choice+theory" 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"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFCoughlin1992" class="citation book cs1">Coughlin, Peter J. (1992-10-30). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=dWjV-e4xrXYC"><i>Probabilistic Voting Theory</i></a>. Cambridge University Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-521-36052-4" title="Special:BookSources/978-0-521-36052-4"><bdi>978-0-521-36052-4</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Probabilistic+Voting+Theory&rft.pub=Cambridge+University+Press&rft.date=1992-10-30&rft.isbn=978-0-521-36052-4&rft.aulast=Coughlin&rft.aufirst=Peter+J.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DdWjV-e4xrXYC&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASocial+choice+theory" class="Z3988"></span></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"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFColomer2013" class="citation journal cs1">Colomer, Josep M. (2013-02-01). <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): 317–328. <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+%27Ars+electionis%27+to+social+choice+theory&rft.volume=40&rft.issue=2&rft.pages=317-328&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%3ASocial+choice+theory" class="Z3988"></span></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">Walter Bossert and John A. Weymark (2008). "Social Choice (New Developments)," <i>The New Palgrave Dictionary of Economics</i>, 2nd Edition, <a rel="nofollow" class="external text" href="http://www.dictionaryofeconomics.com/article?id=pde2008_S000503&q=social%20choice&topicid=&result_number=1">Abstract & TOC.</a></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="CITEREFKaushikLòpez-Calva2011" class="citation book cs1">Kaushik, Basu; Lòpez-Calva, Luis F. (2011). <i>Functionings and Capabilities</i>. Handbook of Social Choice and Welfare. Vol. 2. pp. 153–187. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2FS0169-7218%2810%2900016-X">10.1016/S0169-7218(10)00016-X</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9780444508942" title="Special:BookSources/9780444508942"><bdi>9780444508942</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Functionings+and+Capabilities&rft.series=Handbook+of+Social+Choice+and+Welfare&rft.pages=153-187&rft.date=2011&rft_id=info%3Adoi%2F10.1016%2FS0169-7218%2810%2900016-X&rft.isbn=9780444508942&rft.aulast=Kaushik&rft.aufirst=Basu&rft.au=L%C3%B2pez-Calva%2C+Luis+F.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASocial+choice+theory" 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"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFd'AspremontGevers2002" class="citation book cs1">d'Aspremont, Claude; Gevers, Louis (2002). <i>Chapter 10 Social welfare functionals and interpersonal comparability</i>. Handbook of Social Choice and Welfare. Vol. 1. pp. 459–541. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2FS1574-0110%2802%2980014-5">10.1016/S1574-0110(02)80014-5</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9780444829146" title="Special:BookSources/9780444829146"><bdi>9780444829146</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Chapter+10+Social+welfare+functionals+and+interpersonal+comparability&rft.series=Handbook+of+Social+Choice+and+Welfare&rft.pages=459-541&rft.date=2002&rft_id=info%3Adoi%2F10.1016%2FS1574-0110%2802%2980014-5&rft.isbn=9780444829146&rft.aulast=d%27Aspremont&rft.aufirst=Claude&rft.au=Gevers%2C+Louis&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASocial+choice+theory" class="Z3988"></span></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">Amartya Sen ([1987] 2008). "Justice," <i>The New Palgrave Dictionary of Economics,</i> 2nd Edition. <a rel="nofollow" class="external text" href="http://www.dictionaryofeconomics.com/article?id=pde2008_J000033&edition=current&q=justice&topicid=&result_number=1">Abstract & TOC.</a><br />  Bertil Tungodden (2008). "Justice (New Perspectives)," <i>The New Palgrave Dictionary of Economics,</i> 2nd Edition. <a rel="nofollow" class="external text" href="http://www.dictionaryofeconomics.com/article?id=pde2008_J000052&q=justice&topicid=&result_number=2">Abstract.</a><br />  Louis Kaplow (2008). "Pareto Principle and Competing Principles," <i>The New Palgrave Dictionary of Economics</i>, 2nd Edition. <a rel="nofollow" class="external text" href="http://www.dictionaryofeconomics.com/article?id=pde2008_P000315&edition=current&q=">Abstract.</a><br />  Amartya K. Sen (1979 [1984]). <i>Collective Choice and Social Welfare</i>, New York: Elsevier, <a rel="nofollow" class="external text" href="https://www.citeulike.org/user/rlai/article/681900">(description)</a>:<br />    ch. 9, "Equity and Justice," pp. 131-51.<br />    ch. 9*, "Impersonality and Collective Quasi-Orderings," pp. 152-160.<br />  Kenneth J. Arrow (1983). <i>Collected Papers</i>, v. 1, <i>Social Choice and Justice</i>, Cambridge, MA: Belknap Press, <a rel="nofollow" class="external text" href="http://www.hup.harvard.edu/catalog/ARRCO1.html">Description</a>, <a rel="nofollow" class="external text" href="http://www.hup.harvard.edu/catalog/ARRCO1.html?show=contents">contents</a>, and chapter-preview <a rel="nofollow" class="external text" href="https://books.google.com/books?id=iTgmSNjTdjUC&pg=PP11">links.</a><br />  Charles Blackorby, Walter Bossert, and David Donaldson, 2002. "Utilitarianism and the Theory of Justice", in <i>Handbook of Social Choice and Welfare</i>, edited by Kenneth J. Arrow, Amartya K. Sen, and Kotaro Suzumura, v. 1, ch. 11, pp. 543–596. <a rel="nofollow" class="external text" href="http://www.sciencedirect.com/science/article/pii/S1574011002800157">Abstract.</a></span> </li> <li id="cite_note-12"><span class="mw-cite-backlink"><b><a href="#cite_ref-12">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDutta2002" class="citation book cs1">Dutta, Bhaskar (2002). <i>Chapter 12 Inequality, poverty and welfare</i>. Handbook of Social Choice and Welfare. Vol. 1. pp. 597–633. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2FS1574-0110%2802%2980016-9">10.1016/S1574-0110(02)80016-9</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9780444829146" title="Special:BookSources/9780444829146"><bdi>9780444829146</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Chapter+12+Inequality%2C+poverty+and+welfare&rft.series=Handbook+of+Social+Choice+and+Welfare&rft.pages=597-633&rft.date=2002&rft_id=info%3Adoi%2F10.1016%2FS1574-0110%2802%2980016-9&rft.isbn=9780444829146&rft.aulast=Dutta&rft.aufirst=Bhaskar&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASocial+choice+theory" class="Z3988"></span></span> </li> <li id="cite_note-Robbins-13"><span class="mw-cite-backlink">^ <a href="#cite_ref-Robbins_13-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Robbins_13-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text">Lionel Robbins (1932, 1935, 2nd ed.). <i>An Essay on the Nature and Significance of Economic Science</i>, London: Macmillan. Links for <a rel="nofollow" class="external text" href="https://books.google.com/books?id=nySoIkOgWQ4C&pg=PR10">1932 HTML</a> and <a rel="nofollow" class="external text" href="https://www.scribd.com/doc/14242989/An-Essay-on-the-Nature-and-Signicance-of-Economic-Science-Lionel-Robbins-">1935 facsimile</a>.</span> </li> <li id="cite_note-Robbins2-14"><span class="mw-cite-backlink"><b><a href="#cite_ref-Robbins2_14-0">^</a></b></span> <span class="reference-text">Lionel Robbins (1932, 1935, 2nd ed.). <i>An Essay on the Nature and Significance of Economic Science</i>, London: Macmillan. Links for <a rel="nofollow" class="external text" href="https://books.google.com/books?id=nySoIkOgWQ4C&pg=PR10">1932 HTML</a> and <a rel="nofollow" class="external text" href="https://www.scribd.com/doc/14242989/An-Essay-on-the-Nature-and-Signicance-of-Economic-Science-Lionel-Robbins-">1935 facsimile</a>.</span> </li> <li id="cite_note-15"><span class="mw-cite-backlink"><b><a href="#cite_ref-15">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKurrild-Klitgaard2014" class="citation journal cs1">Kurrild-Klitgaard, Peter (2014). "Empirical social choice: An introduction". <i>Public Choice</i>. <b>158</b> (3–4): 297–310. <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%2Fs11127-014-0164-4">10.1007/s11127-014-0164-4</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/0048-5829">0048-5829</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:148982833">148982833</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Public+Choice&rft.atitle=Empirical+social+choice%3A+An+introduction&rft.volume=158&rft.issue=3%E2%80%934&rft.pages=297-310&rft.date=2014&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A148982833%23id-name%3DS2CID&rft.issn=0048-5829&rft_id=info%3Adoi%2F10.1007%2Fs11127-014-0164-4&rft.aulast=Kurrild-Klitgaard&rft.aufirst=Peter&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASocial+choice+theory" class="Z3988"></span></span> </li> <li id="cite_note-:0-16"><span class="mw-cite-backlink">^ <a href="#cite_ref-:0_16-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-:0_16-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFVan_Deemen2014" class="citation journal cs1">Van Deemen, Adrian (2014). "On the empirical relevance of Condorcet's paradox". <i>Public Choice</i>. <b>158</b> (3–4): 311–330. <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%2Fs11127-013-0133-3">10.1007/s11127-013-0133-3</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/0048-5829">0048-5829</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:154862595">154862595</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Public+Choice&rft.atitle=On+the+empirical+relevance+of+Condorcet%27s+paradox&rft.volume=158&rft.issue=3%E2%80%934&rft.pages=311-330&rft.date=2014&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A154862595%23id-name%3DS2CID&rft.issn=0048-5829&rft_id=info%3Adoi%2F10.1007%2Fs11127-013-0133-3&rft.aulast=Van+Deemen&rft.aufirst=Adrian&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASocial+choice+theory" class="Z3988"></span></span> </li> <li id="cite_note-17"><span class="mw-cite-backlink"><b><a href="#cite_ref-17">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKurrild-Klitgaard2014" class="citation journal cs1">Kurrild-Klitgaard, Peter (2014). "An empirical example of the Condorcet paradox of voting in a large electorate". <i>Public Choice</i>. <b>107</b> (1/2): 135–145. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1023%2FA%3A1010304729545">10.1023/A:1010304729545</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/0048-5829">0048-5829</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:152300013">152300013</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Public+Choice&rft.atitle=An+empirical+example+of+the+Condorcet+paradox+of+voting+in+a+large+electorate&rft.volume=107&rft.issue=1%2F2&rft.pages=135-145&rft.date=2014&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A152300013%23id-name%3DS2CID&rft.issn=0048-5829&rft_id=info%3Adoi%2F10.1023%2FA%3A1010304729545&rft.aulast=Kurrild-Klitgaard&rft.aufirst=Peter&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASocial+choice+theory" 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 id="CITEREFMay1952" class="citation journal cs1">May, Kenneth O. (October 1952). <a rel="nofollow" class="external text" href="https://www.jstor.org/stable/1907651">"A Set of Independent Necessary and Sufficient Conditions for Simple Majority Decision"</a>. <i>Econometrica</i>. <b>20</b> (4): 680–684. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.2307%2F1907651">10.2307/1907651</a>. <a href="/wiki/JSTOR_(identifier)" class="mw-redirect" title="JSTOR (identifier)">JSTOR</a> <a rel="nofollow" class="external text" href="https://www.jstor.org/stable/1907651">1907651</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Econometrica&rft.atitle=A+Set+of+Independent+Necessary+and+Sufficient+Conditions+for+Simple+Majority+Decision&rft.volume=20&rft.issue=4&rft.pages=680-684&rft.date=1952-10&rft_id=info%3Adoi%2F10.2307%2F1907651&rft_id=https%3A%2F%2Fwww.jstor.org%2Fstable%2F1907651%23id-name%3DJSTOR&rft.aulast=May&rft.aufirst=Kenneth+O.&rft_id=https%3A%2F%2Fwww.jstor.org%2Fstable%2F1907651&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASocial+choice+theory" class="Z3988"></span></span> </li> </ol></div> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Social_choice_theory&action=edit&section=17" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Kenneth_Arrow" title="Kenneth Arrow">Arrow, Kenneth J.</a> (1951, 2nd ed., 1963). <i><a href="/wiki/Social_Choice_and_Individual_Values" title="Social Choice and Individual Values">Social Choice and Individual Values</a></i>, New York: Wiley. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-300-01364-7" title="Special:BookSources/0-300-01364-7">0-300-01364-7</a></li> <li>_____, (1972). "General Economic Equilibrium: Purpose, Analytic Techniques, Collective Choice", Nobel Prize Lecture, <a rel="nofollow" class="external text" href="http://nobelprize.org/economics/laureates/1972/arrow-lecture.html">Link to text</a>, with Section 8 on the theory and background.</li> <li>_____, (1983). <i>Collected Papers</i>, v. 1, <i>Social Choice and Justice</i>, Oxford: Blackwell <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-674-13760-4" title="Special:BookSources/0-674-13760-4">0-674-13760-4</a></li> <li>Arrow, Kenneth J., Amartya K. Sen, and Kotaro Suzumura, eds. (1997). <i>Social Choice Re-Examined</i>, 2 vol., London: Palgrave Macmillan <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-312-12739-1" title="Special:BookSources/0-312-12739-1">0-312-12739-1</a> & <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-312-12741-3" title="Special:BookSources/0-312-12741-3">0-312-12741-3</a></li> <li>_____, eds. (2002). <i>Handbook of Social Choice and Welfare</i>, v. 1. Chapter-preview <a rel="nofollow" class="external text" href="http://www.sciencedirect.com/science/handbooks/15740110/1">links</a>.</li> <li>_____, ed. (2011). <i>Handbook of Social Choice and Welfare</i>, v. 2, Amsterdam: Elsevier. Chapter-preview <a rel="nofollow" class="external text" href="http://www.sciencedirect.com/science/handbooks/15740110/2">links</a>.</li> <li>Bossert, Walter and John A. Weymark (2008). "Social Choice (New Developments)," <i><a href="/wiki/The_New_Palgrave_Dictionary_of_Economics" title="The New Palgrave Dictionary of Economics">The New Palgrave Dictionary of Economics</a></i>, 2nd Edition, London: Palgrave Macmillan <a rel="nofollow" class="external text" href="http://www.dictionaryofeconomics.com/article?id=pde2008_S000503&q=social%20choice&topicid=&result_number=1">Abstract.</a></li> <li><a href="/wiki/Dryzek,_John_S." class="mw-redirect" title="Dryzek, John S.">Dryzek, John S.</a> and Christian List (2003). "Social Choice Theory and Deliberative Democracy: A Reconciliation," <i>British Journal of Political Science</i>, 33(1), pp. 1–28, <a rel="nofollow" class="external free" href="https://www.jstor.org/discover/10.2307/4092266?uid=3739936&uid=2&uid=4&uid=3739256&sid=21102056001967">https://www.jstor.org/discover/10.2307/4092266?uid=3739936&uid=2&uid=4&uid=3739256&sid=21102056001967</a>, 2002 PDF <a rel="nofollow" class="external text" href="http://personal.lse.ac.uk/LIST/PDF-files/SCTBJPS.pdf">link.</a></li> <li>Feldman, Allan M. and Roberto Serrano (2006). <i>Welfare Economics and Social Choice Theory</i>, 2nd ed., New York: Springer <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-387-29367-1" title="Special:BookSources/0-387-29367-1">0-387-29367-1</a>, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-387-29367-7" title="Special:BookSources/978-0-387-29367-7">978-0-387-29367-7</a> <a rel="nofollow" class="external text" href="https://books.google.com/books?id=7pZV5O5n_WwC&q=%22arrow's+theorem%22">Arrow-searchable chapter previews.</a></li> <li><a href="/wiki/Marc_Fleurbaey" title="Marc Fleurbaey">Fleurbaey, Marc</a> (1996). Théories économiques de la justice, Paris: Economica.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGaertner2006" class="citation book cs1"><a href="/w/index.php?title=Gaertner_Wulf&action=edit&redlink=1" class="new" title="Gaertner Wulf (page does not exist)">Gaertner, Wulf</a> (2006). <i>A primer in social choice theory</i>. Oxford: Oxford University Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-19-929751-1" title="Special:BookSources/978-0-19-929751-1"><bdi>978-0-19-929751-1</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=A+primer+in+social+choice+theory&rft.place=Oxford&rft.pub=Oxford+University+Press&rft.date=2006&rft.isbn=978-0-19-929751-1&rft.aulast=Gaertner&rft.aufirst=Wulf&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASocial+choice+theory" class="Z3988"></span></li> <li><a href="/wiki/John_Harsanyi" title="John Harsanyi">Harsanyi, John C.</a> (1987). "Interpersonal Utility Comparisons," <i>The <a href="/wiki/New_Palgrave:_A_Dictionary_of_Economics" class="mw-redirect" title="New Palgrave: A Dictionary of Economics">New Palgrave: A Dictionary of Economics</a></i>, v. 2, London: Palgrave, pp. 955–58.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMoulin1988" class="citation book cs1"><a href="/wiki/Herve_Moulin" class="mw-redirect" title="Herve Moulin">Moulin, Herve</a> (1988). <i>Axioms of cooperative decision making</i>. Cambridge: Cambridge University Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-521-42458-5" title="Special:BookSources/978-0-521-42458-5"><bdi>978-0-521-42458-5</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Axioms+of+cooperative+decision+making&rft.place=Cambridge&rft.pub=Cambridge+University+Press&rft.date=1988&rft.isbn=978-0-521-42458-5&rft.aulast=Moulin&rft.aufirst=Herve&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASocial+choice+theory" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMyerson2013" class="citation journal cs1"><a href="/wiki/Roger_Myerson" title="Roger Myerson">Myerson, Roger B.</a> (June 2013). "Fundamentals of social choice theory". <i><a href="/wiki/Quarterly_Journal_of_Political_Science" title="Quarterly Journal of Political Science">Quarterly Journal of Political Science</a></i>. <b>8</b> (3): 305–337. <a href="/wiki/CiteSeerX_(identifier)" class="mw-redirect" title="CiteSeerX (identifier)">CiteSeerX</a> <span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.297.6781">10.1.1.297.6781</a></span>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1561%2F100.00013006">10.1561/100.00013006</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Quarterly+Journal+of+Political+Science&rft.atitle=Fundamentals+of+social+choice+theory&rft.volume=8&rft.issue=3&rft.pages=305-337&rft.date=2013-06&rft_id=https%3A%2F%2Fciteseerx.ist.psu.edu%2Fviewdoc%2Fsummary%3Fdoi%3D10.1.1.297.6781%23id-name%3DCiteSeerX&rft_id=info%3Adoi%2F10.1561%2F100.00013006&rft.aulast=Myerson&rft.aufirst=Roger+B.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASocial+choice+theory" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFNitzan,_Shmuel2010" class="citation book cs1"><a href="/w/index.php?title=Shmue_Nitzan&action=edit&redlink=1" class="new" title="Shmue Nitzan (page does not exist)">Nitzan, Shmuel</a> (2010). <i>Collective Preference and Choice</i>. Cambridge, UK: Cambridge University Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-521-72213-1" title="Special:BookSources/978-0-521-72213-1"><bdi>978-0-521-72213-1</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Collective+Preference+and+Choice&rft.place=Cambridge%2C+UK&rft.pub=Cambridge+University+Press&rft.date=2010&rft.isbn=978-0-521-72213-1&rft.au=Nitzan%2C+Shmuel&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASocial+choice+theory" class="Z3988"></span></li> <li><a href="/wiki/Lionel_Robbins" title="Lionel Robbins">Robbins, Lionel</a> (1935). <i><a href="/wiki/An_Essay_on_the_Nature_and_Significance_of_Economic_Science" title="An Essay on the Nature and Significance of Economic Science">An Essay on the Nature and Significance of Economic Science</a></i>, 2nd ed., London: Macmillan, ch. VI</li> <li>____, (1938). "Interpersonal Comparisons of Utility: A Comment," <i>Economic Journal</i>, 43(4), 635–41.</li> <li><a href="/wiki/Amartya_Sen" title="Amartya Sen">Sen, Amartya K.</a> (1970 [1984]). <i>Collective Choice and Social Welfare</i>, New York: Elsevier <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-444-85127-5" title="Special:BookSources/0-444-85127-5">0-444-85127-5</a> <a rel="nofollow" class="external text" href="https://www.citeulike.org/user/rlai/article/681900">Description.</a></li> <li>_____, (1998). "The Possibility of Social Choice", Nobel Prize Lecture <a rel="nofollow" class="external autonumber" href="https://www.nobelprize.org/uploads/2018/06/sen-lecture.pdf">[1]</a>.</li> <li>_____, (1987). "Social Choice," <i>The New Palgrave: A Dictionary of Economics</i>, v. 4, London: Palgrave, pp. 382–93.</li> <li>_____, (2008). "Social Choice,". <i>The New Palgrave Dictionary of Economics</i>, 2nd Edition, London: Palgrave <a rel="nofollow" class="external text" href="http://www.dictionaryofeconomics.com/article?id=pde2008_S000164&q=Social%20choice&topicid=&result_number=2">Abstract.</a></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFShohamLeyton-Brown2009" class="citation book cs1">Shoham, Yoav; Leyton-Brown, Kevin (2009). <a rel="nofollow" class="external text" href="http://www.masfoundations.org"><i>Multiagent Systems: Algorithmic, Game-Theoretic, and Logical Foundations</i></a>. New York: <a href="/wiki/Cambridge_University_Press" title="Cambridge University Press">Cambridge University Press</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-521-89943-7" title="Special:BookSources/978-0-521-89943-7"><bdi>978-0-521-89943-7</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Multiagent+Systems%3A+Algorithmic%2C+Game-Theoretic%2C+and+Logical+Foundations&rft.place=New+York&rft.pub=Cambridge+University+Press&rft.date=2009&rft.isbn=978-0-521-89943-7&rft.aulast=Shoham&rft.aufirst=Yoav&rft.au=Leyton-Brown%2C+Kevin&rft_id=http%3A%2F%2Fwww.masfoundations.org&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASocial+choice+theory" class="Z3988"></span>. A comprehensive reference from a computational perspective; see Chapter 9. <a rel="nofollow" class="external text" href="http://www.masfoundations.org/download.html">Downloadable free online</a>.</li> <li><a href="/wiki/Kotaro_Suzumura" title="Kotaro Suzumura">Suzumura, Kotaro</a> (1983). <i>Rational Choice, Collective Decisions, and Social Welfare</i>, Cambridge: Cambridge University Press <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-521-23862-5" title="Special:BookSources/0-521-23862-5">0-521-23862-5</a></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFTaylor2005" class="citation book cs1"><a href="/wiki/Alan_D._Taylor" title="Alan D. Taylor">Taylor, Alan D.</a> (2005). <span class="id-lock-registration" title="Free registration required"><a rel="nofollow" class="external text" href="https://archive.org/details/socialchoicemath0000tayl"><i>Social choice and the mathematics of manipulation</i></a></span>. New York: Cambridge University Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-521-00883-9" title="Special:BookSources/978-0-521-00883-9"><bdi>978-0-521-00883-9</bdi></a>.</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+the+mathematics+of+manipulation&rft.place=New+York&rft.pub=Cambridge+University+Press&rft.date=2005&rft.isbn=978-0-521-00883-9&rft.aulast=Taylor&rft.aufirst=Alan+D.&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fsocialchoicemath0000tayl&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASocial+choice+theory" class="Z3988"></span></li></ul> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Social_choice_theory&action=edit&section=18" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFList" class="citation encyclopaedia cs1">List, Christian. <a rel="nofollow" class="external text" href="https://plato.stanford.edu/entries/social-choice/">"Social Choice Theory"</a>. In <a href="/wiki/Edward_N._Zalta" title="Edward N. Zalta">Zalta, Edward N.</a> (ed.). <i><a href="/wiki/Stanford_Encyclopedia_of_Philosophy" title="Stanford Encyclopedia of Philosophy">Stanford Encyclopedia of Philosophy</a></i>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Social+Choice+Theory&rft.btitle=Stanford+Encyclopedia+of+Philosophy&rft.aulast=List&rft.aufirst=Christian&rft_id=https%3A%2F%2Fplato.stanford.edu%2Fentries%2Fsocial-choice%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASocial+choice+theory" class="Z3988"></span></li> <li><a rel="nofollow" class="external text" href="http://faculty.maxwell.syr.edu/jskelly/biblioho.htm">Social Choice Bibliography by J. S. Kelly</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20171223005623/http://faculty.maxwell.syr.edu/jskelly/biblioho.htm">Archived</a> 2017-12-23 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a></li> <li><a rel="nofollow" class="external text" href="https://electowiki.org/wiki/Main_Page">Electowiki</a>, a <a href="/wiki/Wiki" title="Wiki">wiki</a> covering many subjects of social choice and voting theory</li></ul> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><style data-mw-deduplicate="TemplateStyles:r1236075235">.mw-parser-output .navbox{box-sizing:border-box;border:1px solid #a2a9b1;width:100%;clear:both;font-size:88%;text-align:center;padding:1px;margin:1em auto 0}.mw-parser-output .navbox .navbox{margin-top:0}.mw-parser-output .navbox+.navbox,.mw-parser-output .navbox+.navbox-styles+.navbox{margin-top:-1px}.mw-parser-output .navbox-inner,.mw-parser-output .navbox-subgroup{width:100%}.mw-parser-output .navbox-group,.mw-parser-output .navbox-title,.mw-parser-output .navbox-abovebelow{padding:0.25em 1em;line-height:1.5em;text-align:center}.mw-parser-output .navbox-group{white-space:nowrap;text-align:right}.mw-parser-output .navbox,.mw-parser-output .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="Industrial_and_applied_mathematics" style="padding:3px"><table class="nowraplinks hlist 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:Industrial_and_applied_mathematics" title="Template:Industrial and applied mathematics"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Industrial_and_applied_mathematics" title="Template talk:Industrial and applied mathematics"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Industrial_and_applied_mathematics" title="Special:EditPage/Template:Industrial and applied mathematics"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Industrial_and_applied_mathematics" style="font-size:114%;margin:0 4em"><a href="/wiki/Applied_mathematics" title="Applied mathematics">Industrial and applied mathematics</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Computational_mathematics" title="Computational mathematics">Computational</a></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/Algorithm" title="Algorithm">Algorithms</a> <ul><li><a href="/wiki/Algorithm_design" class="mw-redirect" title="Algorithm design">design</a></li> <li><a href="/wiki/Analysis_of_algorithms" title="Analysis of algorithms">analysis</a></li></ul></li> <li><a href="/wiki/Automata_theory" title="Automata theory">Automata theory</a></li> <li><a href="/wiki/Automated_theorem_proving" title="Automated theorem proving">Automated theorem proving</a></li> <li><a href="/wiki/Coding_theory" title="Coding theory">Coding theory</a></li> <li><a href="/wiki/Computational_geometry" title="Computational geometry">Computational geometry</a></li> <li><a href="/wiki/Constraint_satisfaction_problem" title="Constraint satisfaction problem">Constraint satisfaction</a> <ul><li><a href="/wiki/Constraint_programming" title="Constraint programming">Constraint programming</a></li></ul></li> <li><a href="/wiki/Logic_in_computer_science" title="Logic in computer science">Computational logic</a></li> <li><a href="/wiki/Cryptography" title="Cryptography">Cryptography</a></li> <li><a href="/wiki/Information_theory" title="Information theory">Information theory</a></li> <li><a href="/wiki/Computational_statistics" title="Computational statistics">Statistics</a></li></ul> </div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th id="Mathematical_software" scope="row" class="navbox-group" style="width:1%;font-weight:normal;"><a href="/wiki/Mathematical_software" title="Mathematical software">Mathematical software</a></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/List_of_arbitrary-precision_arithmetic_software" title="List of arbitrary-precision arithmetic software">Arbitrary-precision arithmetic</a></li> <li><a href="/wiki/List_of_finite_element_software_packages" title="List of finite element software packages">Finite element analysis</a></li> <li><a href="/wiki/Tensor_software" title="Tensor software">Tensor software</a></li> <li><a href="/wiki/List_of_interactive_geometry_software" title="List of interactive geometry software">Interactive geometry software</a></li> <li><a href="/wiki/List_of_optimization_software" title="List of optimization software">Optimization software</a></li> <li><a href="/wiki/List_of_statistical_software" title="List of statistical software">Statistical software</a></li> <li><a href="/wiki/List_of_numerical-analysis_software" title="List of numerical-analysis software">Numerical-analysis software</a></li> <li><a href="/wiki/List_of_numerical-analysis_software" title="List of numerical-analysis software">Numerical libraries</a></li> <li><a href="/wiki/Solver" title="Solver">Solvers</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/Discrete_mathematics" title="Discrete mathematics">Discrete</a></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/Computer_algebra" title="Computer algebra">Computer algebra</a></li> <li><a href="/wiki/Computational_number_theory" title="Computational number theory">Computational number theory</a></li> <li><a href="/wiki/Combinatorics" title="Combinatorics">Combinatorics</a></li> <li><a href="/wiki/Graph_theory" title="Graph theory">Graph theory</a></li> <li><a href="/wiki/Discrete_geometry" title="Discrete geometry">Discrete geometry</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Mathematical_analysis" title="Mathematical analysis">Analysis</a></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/Approximation_theory" title="Approximation theory">Approximation theory</a></li> <li><a href="/wiki/Clifford_analysis" title="Clifford analysis">Clifford analysis</a> <ul><li><a href="/wiki/Clifford_algebra" title="Clifford algebra">Clifford algebra</a></li></ul></li> <li><a href="/wiki/Differential_equation" title="Differential equation">Differential equations</a> <ul><li><a href="/wiki/Ordinary_differential_equation" title="Ordinary differential equation">Ordinary differential equations</a></li> <li><a href="/wiki/Partial_differential_equation" title="Partial differential equation">Partial differential equations</a></li> <li><a href="/wiki/Stochastic_differential_equation" title="Stochastic differential equation">Stochastic differential equations</a></li></ul></li> <li><a href="/wiki/Differential_geometry" title="Differential geometry">Differential geometry</a> <ul><li><a href="/wiki/Differential_form" title="Differential form">Differential forms</a></li> <li><a href="/wiki/Gauge_theory_(mathematics)" title="Gauge theory (mathematics)">Gauge theory</a></li> <li><a href="/wiki/Geometric_analysis" title="Geometric analysis">Geometric analysis</a></li></ul></li> <li><a href="/wiki/Dynamical_system" title="Dynamical system">Dynamical systems</a> <ul><li><a href="/wiki/Chaos_theory" title="Chaos theory">Chaos theory</a></li> <li><a href="/wiki/Control_theory" title="Control theory">Control theory</a></li></ul></li> <li><a href="/wiki/Functional_analysis" title="Functional analysis">Functional analysis</a> <ul><li><a href="/wiki/Operator_algebra" title="Operator algebra">Operator algebra</a></li> <li><a href="/wiki/Operator_theory" title="Operator theory">Operator theory</a></li></ul></li> <li><a href="/wiki/Harmonic_analysis_(mathematics)" class="mw-redirect" title="Harmonic analysis (mathematics)">Harmonic analysis</a> <ul><li><a href="/wiki/Fourier_analysis" title="Fourier analysis">Fourier analysis</a></li></ul></li> <li><a href="/wiki/Multilinear_algebra" title="Multilinear algebra">Multilinear algebra</a> <ul><li><a href="/wiki/Exterior_algebra" title="Exterior algebra">Exterior</a></li> <li><a href="/wiki/Geometric_algebra" title="Geometric algebra">Geometric</a></li> <li><a href="/wiki/Tensor" title="Tensor">Tensor</a></li> <li><a href="/wiki/Vector_calculus#Vector_algebra" title="Vector calculus">Vector</a></li></ul></li> <li><a href="/wiki/Multivariable_calculus" title="Multivariable calculus">Multivariable calculus</a> <ul><li><a href="/wiki/Exterior_calculus" class="mw-redirect" title="Exterior calculus">Exterior</a></li> <li><a href="/wiki/Geometric_calculus" title="Geometric calculus">Geometric</a></li> <li><a href="/wiki/Tensor_calculus" class="mw-redirect" title="Tensor calculus">Tensor</a></li> <li><a href="/wiki/Vector_calculus" title="Vector calculus">Vector</a></li></ul></li> <li><a href="/wiki/Numerical_analysis" title="Numerical analysis">Numerical analysis</a> <ul><li><a href="/wiki/Numerical_linear_algebra" title="Numerical linear algebra">Numerical linear algebra</a></li> <li><a href="/wiki/Numerical_methods_for_ordinary_differential_equations" title="Numerical methods for ordinary differential equations">Numerical methods for ordinary differential equations</a></li> <li><a href="/wiki/Numerical_methods_for_partial_differential_equations" title="Numerical methods for partial differential equations">Numerical methods for partial differential equations</a></li> <li><a href="/wiki/Validated_numerics" title="Validated numerics">Validated numerics</a></li></ul></li> <li><a href="/wiki/Calculus_of_variations" title="Calculus of variations">Variational calculus</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Probability_theory" title="Probability theory">Probability theory</a></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/Probability_distribution" title="Probability distribution">Distributions</a> (<a href="/wiki/Random_variable" title="Random variable">random variables</a>)</li> <li><a href="/wiki/Stochastic_process" title="Stochastic process">Stochastic processes</a> / <a href="/wiki/Stochastic_calculus" title="Stochastic calculus">analysis</a></li> <li><a href="/wiki/Functional_integration" title="Functional integration">Path integral</a></li> <li><a href="/wiki/Malliavin_calculus" title="Malliavin calculus">Stochastic variational calculus</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Mathematical_physics" title="Mathematical physics">Mathematical<br />physics</a></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/Analytical_mechanics" title="Analytical mechanics">Analytical mechanics</a> <ul><li><a href="/wiki/Lagrangian_mechanics" title="Lagrangian mechanics">Lagrangian</a></li> <li><a href="/wiki/Hamiltonian_mechanics" title="Hamiltonian mechanics">Hamiltonian</a></li></ul></li> <li><a href="/wiki/Field_theory_(physics)" class="mw-redirect" title="Field theory (physics)">Field theory</a> <ul><li><a href="/wiki/Classical_field_theory" title="Classical field theory">Classical</a></li> <li><a href="/wiki/Conformal_field_theory" title="Conformal field theory">Conformal</a></li> <li><a href="/wiki/Effective_field_theory" title="Effective field theory">Effective</a></li> <li><a href="/wiki/Gauge_theory" title="Gauge theory">Gauge</a></li> <li><a href="/wiki/Quantum_field_theory" title="Quantum field theory">Quantum</a></li> <li><a href="/wiki/Statistical_field_theory" title="Statistical field theory">Statistical</a></li> <li><a href="/wiki/Topological_field_theory" class="mw-redirect" title="Topological field theory">Topological</a></li></ul></li> <li><a href="/wiki/Perturbation_theory" title="Perturbation theory">Perturbation theory</a> <ul><li><a href="/wiki/Perturbation_theory_(quantum_mechanics)" title="Perturbation theory (quantum mechanics)">in quantum mechanics</a></li></ul></li> <li><a href="/wiki/Potential_theory" title="Potential theory">Potential theory</a></li> <li><a href="/wiki/String_theory" title="String theory">String theory</a> <ul><li><a href="/wiki/Bosonic_string_theory" title="Bosonic string theory">Bosonic</a></li> <li><a href="/wiki/Topological_string_theory" title="Topological string theory">Topological</a></li></ul></li> <li><a href="/wiki/Supersymmetry" title="Supersymmetry">Supersymmetry</a> <ul><li><a href="/wiki/Supersymmetric_quantum_mechanics" title="Supersymmetric quantum mechanics">Supersymmetric quantum mechanics</a></li> <li><a href="/wiki/Supersymmetric_theory_of_stochastic_dynamics" title="Supersymmetric theory of stochastic dynamics">Supersymmetric theory of stochastic dynamics</a></li></ul></li></ul> </div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th id="Algebraic_structures" scope="row" class="navbox-group" style="width:1%;font-weight:normal;"><a href="/wiki/Algebraic_structures" class="mw-redirect" title="Algebraic structures">Algebraic structures</a></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/Algebra_of_physical_space" title="Algebra of physical space">Algebra of physical space</a></li> <li><a href="/wiki/Path_integral_formulation" title="Path integral formulation">Feynman integral</a></li> <li><a href="/wiki/Poisson_algebra" title="Poisson algebra">Poisson algebra</a></li> <li><a href="/wiki/Quantum_group" title="Quantum group">Quantum group</a></li> <li><a href="/wiki/Renormalization_group" title="Renormalization group">Renormalization group</a></li> <li><a href="/wiki/Particle_physics_and_representation_theory" title="Particle physics and representation theory">Representation theory</a></li> <li><a href="/wiki/Spacetime_algebra" title="Spacetime algebra">Spacetime algebra</a></li> <li><a href="/wiki/Superalgebra" title="Superalgebra">Superalgebra</a></li> <li><a href="/wiki/Supersymmetry_algebra" title="Supersymmetry algebra">Supersymmetry algebra</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/Decision_theory" title="Decision theory">Decision sciences</a></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/Game_theory" title="Game theory">Game theory</a></li> <li><a href="/wiki/Operations_research" title="Operations research">Operations research</a></li> <li><a href="/wiki/Mathematical_optimization" title="Mathematical optimization">Optimization</a></li> <li><a class="mw-selflink selflink">Social choice theory</a></li> <li><a href="/wiki/Statistics" title="Statistics">Statistics</a></li> <li><a href="/wiki/Mathematical_economics" title="Mathematical economics">Mathematical economics</a></li> <li><a href="/wiki/Mathematical_finance" title="Mathematical finance">Mathematical finance</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Other applications</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/Mathematical_and_theoretical_biology" title="Mathematical and theoretical biology">Biology</a></li> <li><a href="/wiki/Mathematical_chemistry" title="Mathematical chemistry">Chemistry</a></li> <li><a href="/wiki/Mathematical_psychology" title="Mathematical psychology">Psychology</a></li> <li><a href="/wiki/Mathematical_sociology" title="Mathematical sociology">Sociology</a></li> <li>"<a href="/wiki/The_Unreasonable_Effectiveness_of_Mathematics_in_the_Natural_Sciences" title="The Unreasonable Effectiveness of Mathematics in the Natural Sciences">The Unreasonable Effectiveness of Mathematics in the Natural Sciences</a>"</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Related</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/Mathematics" title="Mathematics">Mathematics</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Organizations</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/Society_for_Industrial_and_Applied_Mathematics" title="Society for Industrial and Applied Mathematics">Society for Industrial and Applied Mathematics</a> <ul><li><a href="/wiki/Japan_Society_for_Industrial_and_Applied_Mathematics" title="Japan Society for Industrial and Applied Mathematics">Japan Society for Industrial and Applied Mathematics</a></li></ul></li> <li><a href="/wiki/Soci%C3%A9t%C3%A9_de_Math%C3%A9matiques_Appliqu%C3%A9es_et_Industrielles" title="Société de Mathématiques Appliquées et Industrielles">Société de Mathématiques Appliquées et Industrielles</a></li> <li><a href="/wiki/International_Council_for_Industrial_and_Applied_Mathematics" title="International Council for Industrial and Applied Mathematics">International Council for Industrial and Applied Mathematics</a></li> <li><a href="/w/index.php?title=European_Community_on_Computational_Methods_in_Applied_Sciences&action=edit&redlink=1" class="new" title="European Community on Computational Methods in Applied Sciences (page does not exist)">European Community on Computational Methods in Applied Sciences</a></li></ul> </div></td></tr><tr><td class="navbox-abovebelow" colspan="2"><div> <ul><li><b><a href="/wiki/Category:Mathematics" title="Category:Mathematics">Category</a></b></li> <li><a href="/wiki/Portal:Mathematics" title="Portal:Mathematics">Mathematics portal</a> / <a href="/wiki/Topic_outline_of_mathematics" class="mw-redirect" title="Topic outline of mathematics">outline</a> / <a href="/wiki/List_of_mathematics_topics" class="mw-redirect" title="List of mathematics topics">topics list</a></li></ul> </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"><style data-mw-deduplicate="TemplateStyles:r1038841319">.mw-parser-output .tooltip-dotted{border-bottom:1px dotted;cursor:help}</style><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1038841319"></div><div role="navigation" class="navbox authority-control" aria-label="Navbox" 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/Q1971461#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/sh85123920">United States</a></span></li><li><span class="uid"><span class="rt-commentedText tooltip tooltip-dotted" title="Choix collectif"><a rel="nofollow" class="external text" href="https://catalogue.bnf.fr/ark:/12148/cb11967857z">France</a></span></span></li><li><span class="uid"><span class="rt-commentedText tooltip tooltip-dotted" title="Choix collectif"><a rel="nofollow" class="external text" href="https://data.bnf.fr/ark:/12148/cb11967857z">BnF data</a></span></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="http://olduli.nli.org.il/F/?func=find-b&local_base=NLX10&find_code=UID&request=987007551161805171">Israel</a></span></li></ul></div></td></tr></tbody></table></div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Retrieved from "<a dir="ltr" href="https://en.wikipedia.org/w/index.php?title=Social_choice_theory&oldid=1252573486">https://en.wikipedia.org/w/index.php?title=Social_choice_theory&oldid=1252573486</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:Social_choice_theory" title="Category:Social choice theory">Social choice theory</a></li><li><a href="/wiki/Category:Metaethics" title="Category:Metaethics">Metaethics</a></li><li><a href="/wiki/Category:Political_science" title="Category:Political science">Political science</a></li><li><a href="/wiki/Category:Public_economics" title="Category:Public economics">Public economics</a></li><li><a href="/wiki/Category:Applied_mathematics" title="Category:Applied mathematics">Applied mathematics</a></li><li><a href="/wiki/Category:Collective_intelligence" title="Category:Collective intelligence">Collective intelligence</a></li><li><a href="/wiki/Category:Political_philosophy" title="Category:Political philosophy">Political philosophy</a></li><li><a href="/wiki/Category:Mathematical_economics" title="Category:Mathematical economics">Mathematical economics</a></li><li><a href="/wiki/Category:Law_and_economics" title="Category:Law and economics">Law and economics</a></li><li><a href="/wiki/Category:Administrative_theory" title="Category:Administrative theory">Administrative 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: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:Articles_to_be_split_from_May_2024" title="Category:Articles to be split from May 2024">Articles to be split from May 2024</a></li><li><a href="/wiki/Category:All_articles_to_be_split" title="Category:All articles to be split">All articles to be split</a></li><li><a href="/wiki/Category:Wikipedia_references_cleanup_from_April_2021" title="Category:Wikipedia references cleanup from April 2021">Wikipedia references cleanup from April 2021</a></li><li><a href="/wiki/Category:All_articles_needing_references_cleanup" title="Category:All articles needing references cleanup">All articles needing references cleanup</a></li><li><a href="/wiki/Category:Articles_covered_by_WikiProject_Wikify_from_April_2021" title="Category:Articles covered by WikiProject Wikify from April 2021">Articles covered by WikiProject Wikify from April 2021</a></li><li><a href="/wiki/Category:All_articles_covered_by_WikiProject_Wikify" title="Category:All articles covered by WikiProject Wikify">All articles covered by WikiProject Wikify</a></li><li><a href="/wiki/Category:Articles_with_excerpts" title="Category:Articles with excerpts">Articles with excerpts</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:Articles_with_hatnote_templates_targeting_a_nonexistent_page" title="Category:Articles with hatnote templates targeting a nonexistent page">Articles with hatnote templates targeting a nonexistent page</a></li><li><a href="/wiki/Category:Wikipedia_articles_needing_clarification_from_March_2024" title="Category:Wikipedia articles needing clarification from March 2024">Wikipedia articles needing clarification from March 2024</a></li><li><a href="/wiki/Category:Articles_with_unsourced_statements_from_June_2024" title="Category:Articles with unsourced statements from June 2024">Articles with unsourced statements from June 2024</a></li><li><a href="/wiki/Category:Webarchive_template_wayback_links" title="Category:Webarchive template wayback links">Webarchive template wayback links</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 October 2024, at 23:33<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=Social_choice_theory&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"><img src="/static/images/footer/wikimedia-button.svg" width="84" height="29" alt="Wikimedia Foundation" loading="lazy"></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"><img src="/w/resources/assets/poweredby_mediawiki.svg" alt="Powered by MediaWiki" width="88" height="31" loading="lazy"></a></li> </ul> </footer> </div> </div> </div> <div class="vector-settings" id="p-dock-bottom"> <ul></ul> </div><script>(RLQ=window.RLQ||[]).push(function(){mw.config.set({"wgHostname":"mw-web.codfw.main-694cf4987f-bfscj","wgBackendResponseTime":186,"wgPageParseReport":{"limitreport":{"cputime":"0.967","walltime":"1.229","ppvisitednodes":{"value":5317,"limit":1000000},"postexpandincludesize":{"value":156289,"limit":2097152},"templateargumentsize":{"value":4376,"limit":2097152},"expansiondepth":{"value":16,"limit":100},"expensivefunctioncount":{"value":23,"limit":500},"unstrip-depth":{"value":1,"limit":20},"unstrip-size":{"value":130550,"limit":5000000},"entityaccesscount":{"value":1,"limit":400},"timingprofile":["100.00% 947.299 1 -total"," 21.30% 201.772 2 Template:Sidebar_with_collapsible_lists"," 21.05% 199.418 1 Template:Reflist"," 14.85% 140.669 1 Template:Electoral_systems_sidebar"," 14.07% 133.255 7 Template:Cite_journal"," 7.73% 73.196 1 Template:Short_description"," 7.32% 69.353 8 Template:ISBN"," 6.92% 65.541 1 Template:Economics_sidebar"," 6.67% 63.176 2 Template:Hlist"," 6.54% 61.921 1 Template:Splitto"]},"scribunto":{"limitreport-timeusage":{"value":"0.560","limit":"10.000"},"limitreport-memusage":{"value":9212372,"limit":52428800},"limitreport-logs":"table#1 {\n [\"size\"] = \"tiny\",\n}\ntable#1 {\n [\"size\"] = \"tiny\",\n}\ntable#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-6bcd787d7f-jxb99","timestamp":"20241126014546","ttl":2592000,"transientcontent":false}}});});</script> <script type="application/ld+json">{"@context":"https:\/\/schema.org","@type":"Article","name":"Social choice theory","url":"https:\/\/en.wikipedia.org\/wiki\/Social_choice_theory","sameAs":"http:\/\/www.wikidata.org\/entity\/Q1971461","mainEntity":"http:\/\/www.wikidata.org\/entity\/Q1971461","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":"2005-04-15T20:09:26Z","dateModified":"2024-10-21T23:33:30Z","image":"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/8\/82\/Electoral-systems-gears.svg","headline":"academic discipline"}</script> </body> </html>