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<li id="toc-Notes" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Notes"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>Notes</span> </div> </a> <ul id="toc-Notes-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> <span class="vector-toc-numb">9</span> <span>External links</span> </div> </a> <ul id="toc-External_links-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" 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href="https://fa.wikipedia.org/wiki/%D8%B1%D8%A3%DB%8C%E2%80%8C%DA%AF%DB%8C%D8%B1%DB%8C_%D9%85%DA%A9%D8%B1%D8%B1" title="رأی‌گیری مکرر – Persian" lang="fa" hreflang="fa" data-title="رأی‌گیری مکرر" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Egyenk%C3%A9nti_kies%C3%A9ses_szavaz%C3%A1s" title="Egyenkénti kieséses szavazás – Hungarian" lang="hu" hreflang="hu" data-title="Egyenkénti kieséses szavazás" data-language-autonym="Magyar" data-language-local-name="Hungarian" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Eliminationsmetoden" title="Eliminationsmetoden – Swedish" lang="sv" hreflang="sv" data-title="Eliminationsmetoden" data-language-autonym="Svenska" data-language-local-name="Swedish" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%A3%E0%B8%B0%E0%B8%9A%E0%B8%9A%E0%B8%9A%E0%B8%B1%E0%B8%95%E0%B8%A3%E0%B8%A5%E0%B8%87%E0%B8%84%E0%B8%B0%E0%B9%81%E0%B8%99%E0%B8%99%E0%B8%AB%E0%B8%A5%E0%B8%B2%E0%B8%A2%E0%B8%A3%E0%B8%AD%E0%B8%9A" title="ระบบบัตรลงคะแนนหลายรอบ – Thai" lang="th" hreflang="th" data-title="ระบบบัตรลงคะแนนหลายรอบ" data-language-autonym="ไทย" data-language-local-name="Thai" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E5%A4%9A%E8%BC%AA%E7%B5%95%E5%B0%8D%E5%A4%9A%E6%95%B8%E5%88%B6" title="多輪絕對多數制 – Chinese" lang="zh" hreflang="zh" data-title="多輪絕對多數制" data-language-autonym="中文" data-language-local-name="Chinese" class="interlanguage-link-target"><span>中文</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span 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class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Voting method</div> <style data-mw-deduplicate="TemplateStyles:r1236090951">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">For other types of run-off voting systems, see <a href="/wiki/Run-off_voting_(disambiguation)" class="mw-redirect mw-disambig" title="Run-off voting (disambiguation)">Run-off voting (disambiguation)</a>.</div> <style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output 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a{color:var(--color-progressive)!important}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .sidebar:not(.notheme) .sidebar-list-title,html.skin-theme-clientpref-os .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle{background:transparent!important}html.skin-theme-clientpref-os .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle a{color:var(--color-progressive)!important}}@media print{body.ns-0 .mw-parser-output .sidebar{display:none!important}}</style><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><table class="sidebar sidebar-collapse nomobile nowraplinks"><tbody><tr><td class="sidebar-pretitle">A joint <a href="/wiki/Portal:Politics" title="Portal:Politics">Politics</a> and <a href="/wiki/Portal:Economics" title="Portal:Economics">Economics</a> series</td></tr><tr><th class="sidebar-title-with-pretitle" style="border-top:1px #fafafa solid; border-bottom:1px #fafafa solid; background:#efefef; background: var(--background-color-interactive, #efefef); color: var(--color-base, #000); padding:0.2em;"><a href="/wiki/Social_choice_theory" title="Social choice theory">Social choice</a> and <a href="/wiki/Electoral_system" title="Electoral system">electoral systems</a></th></tr><tr><td class="sidebar-image"><figure class="mw-halign-center" typeof="mw:File"><a href="/wiki/File:Electoral-systems-gears.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/82/Electoral-systems-gears.svg/128px-Electoral-systems-gears.svg.png" decoding="async" width="128" height="128" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/82/Electoral-systems-gears.svg/192px-Electoral-systems-gears.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/82/Electoral-systems-gears.svg/256px-Electoral-systems-gears.svg.png 2x" data-file-width="1024" data-file-height="1024" /></a><figcaption></figcaption></figure></td></tr><tr><td class="sidebar-above"> <div class="hlist"><ul><li><a href="/wiki/Social_choice_theory" title="Social choice theory">Social choice</a></li><li><a href="/wiki/Mechanism_design" title="Mechanism design">Mechanism design</a></li><li><a href="/wiki/Comparative_politics" title="Comparative politics">Comparative politics</a></li><li><a href="/wiki/Comparison_of_voting_rules" title="Comparison of voting rules">Comparison</a></li><li><a href="/wiki/List_of_electoral_systems" title="List of electoral systems">List</a> (<a href="/wiki/List_of_electoral_systems_by_country" title="List of electoral systems by country">By country</a>)</li></ul></div></td></tr><tr><td class="sidebar-content" style="text-align:left;"> <div class="sidebar-list mw-collapsible"><div class="sidebar-list-title" style="background:#efefef; border-top:1px solid;background: var(--background-color-interactive, #efefef); color: var(--color-base, #000);;color: var(--color-base)"><a href="/wiki/Single-member_district" title="Single-member district">Single-winner methods</a></div><div class="sidebar-list-content mw-collapsible-content"><b>Single vote - <a href="/wiki/Plurality_voting" title="Plurality voting">plurality</a> methods</b> <ul><li><a href="/wiki/First-past-the-post_voting" title="First-past-the-post voting">First preference plurality (FPP)</a></li> <li><a href="/wiki/Two-round_system" title="Two-round system">Two-round</a> (<abbr style="font-size:85%" title=""><a href="/wiki/American_English" title="American English">US</a>:</abbr> <a href="/wiki/Nonpartisan_blanket_primary" title="Nonpartisan blanket primary">Jungle primary</a>) <ul><li><a href="/wiki/Partisan_primary" class="mw-redirect" title="Partisan primary">Partisan primary</a></li></ul></li> <li><a href="/wiki/Instant-runoff_voting" title="Instant-runoff voting">Instant-runoff</a> <ul><li><abbr style="font-size:85%" title=""><a href="/wiki/British_English" title="British English">UK</a>:</abbr> Alternative vote (AV)</li> <li><abbr style="font-size:85%" title=""><a href="/wiki/American_English" title="American English">US</a>:</abbr> Ranked-choice (RCV)</li></ul></li></ul> <hr /> <p><b><a href="/wiki/Condorcet_method" title="Condorcet method">Condorcet methods</a></b> </p> <ul><li><a href="/wiki/Tideman_alternative_method" title="Tideman alternative method">Condorcet-IRV</a></li> <li><a href="/wiki/Round-robin_voting" title="Round-robin voting">Round-robin voting</a> <ul><li><a href="/wiki/Minimax_Condorcet_method" title="Minimax Condorcet method">Minimax</a></li> <li><a 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 mw-collapsed"><div class="sidebar-list-title" style="background:#efefef; border-top:1px solid;background: var(--background-color-interactive, #efefef); color: var(--color-base, #000);;color: var(--color-base)"><a href="/wiki/Social_choice_theory" title="Social choice theory">Social and collective choice</a></div><div class="sidebar-list-content mw-collapsible-content"><b><a href="/wiki/Proof_of_impossibility" title="Proof of impossibility">Impossibility theorems</a></b> <ul><li><a href="/wiki/Arrow%27s_impossibility_theorem" title="Arrow's impossibility theorem">Arrow's theorem</a></li> <li><a href="/wiki/Condorcet_paradox" title="Condorcet paradox">Majority impossibility</a></li> <li><a href="/wiki/Moulin%27s_impossibility_theorem" class="mw-redirect" title="Moulin's impossibility theorem">Moulin's impossibility theorem</a></li> <li><a href="/wiki/McKelvey%E2%80%93Schofield_chaos_theorem" title="McKelvey–Schofield chaos theorem">McKelvey–Schofield chaos theorem</a></li> <li><a href="/wiki/Gibbard%27s_theorem" title="Gibbard's theorem">Gibbard's theorem</a></li></ul> <hr /> <p><b>Positive results</b> </p> <ul><li><a href="/wiki/Median_voter_theorem" title="Median voter theorem">Median voter theorem</a></li> <li><a href="/wiki/Condorcet%27s_jury_theorem" title="Condorcet's jury theorem">Condorcet's jury theorem</a></li> <li><a href="/wiki/May%27s_theorem" title="May's theorem">May's theorem</a></li> <li><a href="/wiki/Arrow%27s_theorem#Minimizing" class="mw-redirect" title="Arrow's theorem">Condorcet dominance theorems</a></li> <li><a href="/w/index.php?title=Harsanyi%27s_utilitarian_theorem&action=edit&redlink=1" class="new" title="Harsanyi's utilitarian theorem (page does not exist)">Harsanyi's utilitarian theorem</a></li></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, 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href="/wiki/File:Nuvola_apps_edu_mathematics_blue-p.svg" class="mw-file-description"><img alt="icon" src="//upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Nuvola_apps_edu_mathematics_blue-p.svg/16px-Nuvola_apps_edu_mathematics_blue-p.svg.png" decoding="async" width="16" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Nuvola_apps_edu_mathematics_blue-p.svg/24px-Nuvola_apps_edu_mathematics_blue-p.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Nuvola_apps_edu_mathematics_blue-p.svg/32px-Nuvola_apps_edu_mathematics_blue-p.svg.png 2x" data-file-width="128" data-file-height="128" /></a></span> </span><a href="/wiki/Portal:Mathematics" title="Portal:Mathematics">Mathematics portal</a></td></tr><tr><td class="sidebar-navbar"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><style data-mw-deduplicate="TemplateStyles:r1239400231">.mw-parser-output .navbar{display:inline;font-size:88%;font-weight:normal}.mw-parser-output .navbar-collapse{float:left;text-align:left}.mw-parser-output .navbar-boxtext{word-spacing:0}.mw-parser-output .navbar ul{display:inline-block;white-space:nowrap;line-height:inherit}.mw-parser-output .navbar-brackets::before{margin-right:-0.125em;content:"[ "}.mw-parser-output .navbar-brackets::after{margin-left:-0.125em;content:" ]"}.mw-parser-output .navbar li{word-spacing:-0.125em}.mw-parser-output .navbar a>span,.mw-parser-output .navbar a>abbr{text-decoration:inherit}.mw-parser-output .navbar-mini abbr{font-variant:small-caps;border-bottom:none;text-decoration:none;cursor:inherit}.mw-parser-output .navbar-ct-full{font-size:114%;margin:0 7em}.mw-parser-output .navbar-ct-mini{font-size:114%;margin:0 4em}html.skin-theme-clientpref-night .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}@media(prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}}@media print{.mw-parser-output .navbar{display:none!important}}</style><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Electoral_systems_sidebar" title="Template:Electoral systems sidebar"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Electoral_systems_sidebar" title="Template talk:Electoral systems sidebar"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Electoral_systems_sidebar" title="Special:EditPage/Template:Electoral systems sidebar"><abbr title="Edit this template">e</abbr></a></li></ul></div></td></tr></tbody></table> <p>The <b>exhaustive ballot</b> is a <a href="/wiki/Voting_system" class="mw-redirect" title="Voting system">voting system</a> used to elect a single winner. Under the exhaustive ballot the elector casts a single vote for his or her chosen candidate. However, if no candidate is supported by an overall majority of votes then the candidate with the fewest votes is eliminated and a further round of voting occurs. This process is repeated for as many rounds as necessary until one candidate has a majority. </p><p>The exhaustive ballot is similar to the <a href="/wiki/Two-round_system" title="Two-round system">two-round system</a> but with key differences. Under the two round system if no candidate wins a majority on the first round, only the top two recipients of votes advance to the second (and final) round of voting, and a majority winner is determined in the second round. By contrast, on the exhaustive ballot only one candidate is eliminated per round; thus, several rounds of voting may be required until a candidate reaches a majority. (In some circumstances, the two or more lowest candidates can be eliminated simultaneously if together they have fewer votes than the lowest candidate above them. In other words, this "bulk exclusion" cannot change the order of elimination, unlike a two-round system.) </p><p>Because voters may have to cast votes several times, the exhaustive ballot is not used in large-scale public elections. Instead it is usually used in elections involving, at most, a few hundred voters, such as the election of a prime minister or the presiding officer of an assembly. The exhaustive ballot is currently used, in different forms, to elect the members of the <a href="/wiki/Swiss_Federal_Council" class="mw-redirect" title="Swiss Federal Council">Swiss Federal Council</a>, the <a href="/wiki/First_Minister_of_Scotland" title="First Minister of Scotland">First Minister of Scotland</a>, the <a href="/wiki/President_of_the_European_Parliament" title="President of the European Parliament">President of the European Parliament</a>, and the <a href="/wiki/Speaker_(politics)" title="Speaker (politics)">speakers</a> of the <a href="/wiki/House_of_Commons_of_Canada" title="House of Commons of Canada">House of Commons of Canada</a>, the <a href="/wiki/House_of_Commons_of_the_United_Kingdom" title="House of Commons of the United Kingdom">British House of Commons</a> and the <a href="/wiki/Scottish_Parliament" title="Scottish Parliament">Scottish Parliament</a>, the host city of the <a href="/wiki/Olympic_Games" title="Olympic Games">Olympic Games</a> and the host of the <a href="/wiki/FIFA_World_Cup" title="FIFA World Cup">FIFA World Cup</a>, and, formerly, to elect the <a href="/wiki/President_of_Israel" title="President of Israel">President</a> and the <a href="/wiki/State_Comptroller_of_Israel" title="State Comptroller of Israel">State Comptroller of Israel</a>, which are now elected—though still indirectly by the <a href="/wiki/Knesset" title="Knesset">Knesset</a>—using a <a href="/wiki/Two-round_system" title="Two-round system">two-round system</a>. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Voting_and_counting">Voting and counting</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Exhaustive_ballot&action=edit&section=1" title="Edit section: Voting and counting"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size mw-halign-left" typeof="mw:File/Thumb"><a href="/wiki/File:Plurality_ballot.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/2f/Plurality_ballot.svg/220px-Plurality_ballot.svg.png" decoding="async" width="220" height="285" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/2f/Plurality_ballot.svg/330px-Plurality_ballot.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/2f/Plurality_ballot.svg/440px-Plurality_ballot.svg.png 2x" data-file-width="765" data-file-height="990" /></a><figcaption>An example of a ballot paper</figcaption></figure> <p>In each round of an exhaustive ballot the voter simply marks an 'x' beside his or her favourite candidate. If no candidate has an absolute majority of votes (i.e., more than half) in the first round, then the candidate with the fewest votes is eliminated while all other candidates advance to a second round. If there is still no candidate with a majority then the candidate with the fewest votes is again eliminated and there is a third round. The process repeats itself for as many rounds as are necessary for one candidate to achieve a majority. If necessary, the election will continue until only two candidates remain. When this occurs one of the two <i>must</i> achieve an absolute majority provided there are an odd number of valid votes cast. </p><p>Between rounds, the voter is entirely free to change their preferred candidate for whatever reason, even if their preferred candidate has not yet been eliminated from voting. </p> <div class="mw-heading mw-heading3"><h3 id="Variations">Variations</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Exhaustive_ballot&action=edit&section=2" title="Edit section: Variations"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>It is possible to impose a larger number of votes to win, such as a two thirds vote, on either all rounds or on the beginning rounds. For example, on the first several rounds of the election of the President of Italy, a supermajority is required to win, dropping to a majority on the fourth and subsequent ballots.</li> <li>Under some variants of the exhaustive ballot there is no formal rule for eliminating candidates from one round to another; rather, candidates are expected to withdraw voluntarily.</li> <li>Some variations slowly raise an elimination threshold in to encourage compromise. For example, the <a href="/wiki/Minnesota_Democratic-Farmer-Labor_Party" class="mw-redirect" title="Minnesota Democratic-Farmer-Labor Party">Minnesota Democratic-Farmer-Labor Party</a> for U.S. Senate endorsement 2008 used an exhaustive ballot with a dropoff rule starting at 5% and increasing to 25% after round 5, after which one candidate with the lowest votes was eliminated per round until no more than two remained.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup></li> <li>There are also variants which exclude more than one candidate at a time. For example, in elections for the speakers of the Canadian and British Houses of Commons any candidate with fewer than 5% of all votes in the first round is immediately eliminated.</li></ul> <div class="mw-heading mw-heading2"><h2 id="Example">Example</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Exhaustive_ballot&action=edit&section=3" title="Edit section: Example"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><span class="anchor" id="Tennessee"></span> </p> <div style="float: left;"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Tenn_voting_example" title="Template:Tenn voting example"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Tenn_voting_example" title="Template talk:Tenn voting example"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Tenn_voting_example" title="Special:EditPage/Template:Tenn voting example"><abbr title="Edit this template">e</abbr></a></li></ul></div></div> <p><span typeof="mw:File"><a href="/wiki/File:Tennessee_map_for_voting_example.svg" class="mw-file-description"><img alt="Tennessee and its four major cities: Memphis in the far west; Nashville in the center; Chattanooga in the east; and Knoxville in the far northeast" src="//upload.wikimedia.org/wikipedia/commons/thumb/8/88/Tennessee_map_for_voting_example.svg/500px-Tennessee_map_for_voting_example.svg.png" decoding="async" width="500" height="122" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/88/Tennessee_map_for_voting_example.svg/750px-Tennessee_map_for_voting_example.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/88/Tennessee_map_for_voting_example.svg/1000px-Tennessee_map_for_voting_example.svg.png 2x" data-file-width="780" data-file-height="190" /></a></span> </p><p>Suppose that <a href="/wiki/Tennessee" title="Tennessee">Tennessee</a> is holding an election on the location of its <a href="/wiki/Capital_(political)" class="mw-redirect" title="Capital (political)">capital</a>. The population is concentrated around four major cities. <a href="/wiki/Spatial_model_of_voting" class="mw-redirect" title="Spatial model of voting">All voters want the capital to be as close to them as possible.</a> The options are: </p> <ul><li><a href="/wiki/Memphis,_Tennessee" title="Memphis, Tennessee">Memphis</a>, the largest city, but far from the others (42% of voters)</li> <li><a href="/wiki/Nashville,_Tennessee" title="Nashville, Tennessee">Nashville</a>, near the center of the state (26% of voters)</li> <li><a href="/wiki/Chattanooga,_Tennessee" title="Chattanooga, Tennessee">Chattanooga</a>, somewhat east (15% of voters)</li> <li><a href="/wiki/Knoxville,_Tennessee" title="Knoxville, Tennessee">Knoxville</a>, far to the northeast (17% of voters)</li></ul> <p>The preferences of each region's voters are: </p> <table class="wikitable"> <tbody><tr> <th width="25%" style="background-color: #ffdddd">42% of voters<br /><small>Far-West</small> </th> <th width="25%" style="background-color: #ccffcc">26% of voters<br /><small>Center</small> </th> <th width="25%" style="background-color: #ddddff">15% of voters<br /><small>Center-East</small> </th> <th width="25%" style="background-color: #ffeedd">17% of voters<br /><small>Far-East</small> </th></tr> <tr> <td> <ol style="margin-left: 1.5em;"> <li> <b>Memphis</b> </li><li> Nashville </li><li> Chattanooga </li><li> Knoxville </li></ol> </td> <td> <ol style="margin-left: 1.5em;"> <li> <b>Nashville</b> </li><li> Chattanooga </li><li> Knoxville </li><li> Memphis </li></ol> </td> <td> <ol style="margin-left: 1.5em;"> <li> <b>Chattanooga</b> </li><li> Knoxville </li><li> Nashville </li><li> Memphis </li></ol> </td> <td> <ol style="margin-left: 1.5em;"> <li> <b>Knoxville</b> </li><li> Chattanooga </li><li> Nashville </li><li> Memphis </li></ol> </td></tr></tbody></table> <p><b>Round 1.</b> In the first round of voting everybody votes for their own city: </p> <ul><li>Memphis: 42%</li> <li>Nashville: 26%</li> <li>Knoxville: 17%</li> <li>Chattanooga: 15%</li></ul> <p><b>Round 2.</b> No candidate has a majority in the first round, so Chattanooga (with the fewest votes) is eliminated and the remaining three candidates proceed to Round 2. In this round the Chattanooga supporters vote instead for Knoxville, the next-closest city to their own. None of the other voters need to change their votes. The results are therefore: </p> <ul><li>Memphis: 42%</li> <li>Knoxville: 32%</li> <li>Nashville: 26%</li></ul> <p><b>Round 3.</b> Nashville is now eliminated, so that only two candidates remain for the final round. The Nashville supporters change their vote to Knoxville, the next nearest city to their own. The result of the third round is therefore: </p> <ul><li>Knoxville: 58%</li> <li>Memphis: 42%</li></ul> <p><b>Result:</b> After round three Knoxville has an absolute majority so is the winner. </p> <div class="mw-heading mw-heading2"><h2 id="Use_in_practice">Use in practice</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Exhaustive_ballot&action=edit&section=4" title="Edit section: Use in practice"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><b>Scottish government:</b> The First Minister, and the Presiding Officer and Deputy Presiding Officers of the Scottish Parliament are elected by the exhaustive ballot method.<sup id="cite_ref-:0_2-0" class="reference"><a href="#cite_note-:0-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup></li> <li>The <b>host city of the Olympic Games</b> is chosen by an exhaustive ballot of members of the <a href="/wiki/International_Olympic_Committee" title="International Olympic Committee">International Olympic Committee</a>. Members from a country which has a city competing in the election are forbidden from voting unless the city has been eliminated.</li> <li>The <b><a href="/wiki/President_of_the_European_Parliament" title="President of the European Parliament">President of the European Parliament</a></b> is elected by all members of the body to be its "speaker" or chairperson. In the election if no candidate receives an absolute majority in the first round then there are up to three more rounds. In the second and third rounds anyone who wants to is free to stand, but candidates who perform poorly sometimes withdraw to help others be elected. If no-one achieves an absolute majority in the third round then only the two candidates with most votes are allowed to proceed to the fourth and final round of voting.<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></li> <li>The <b><a href="/wiki/Speaker_of_the_House_of_Commons_(United_Kingdom)" title="Speaker of the House of Commons (United Kingdom)">Speaker of the House of Commons</a></b> is elected by <a href="/wiki/Secret_ballot" title="Secret ballot">secret ballot</a> by members of the house. If no candidate achieves an absolute majority in the first round then the candidate with fewest votes and any other candidate who has received less than 5% of all votes is immediately eliminated. Subsequent rounds proceed according to the ordinary rules of the exhaustive ballot.<sup id="cite_ref-:0_2-1" class="reference"><a href="#cite_note-:0-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup></li> <li>The <b><a href="/wiki/Speaker_of_the_House_of_Commons_of_Canada" class="mw-redirect" title="Speaker of the House of Commons of Canada">Speaker of the House of Commons of Canada</a></b> is elected under essentially the same variant of the exhaustive ballot used for the British counterpart, with candidates on less than 5% in the first round immediately excluded.<sup id="cite_ref-:0_2-2" class="reference"><a href="#cite_note-:0-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup></li> <li>The <b>Leader of the <a href="/wiki/New_Democratic_Party" title="New Democratic Party">New Democratic Party</a> of Canada</b> is elected by the party membership under a mixture of <a href="/wiki/Instant_runoff_voting" class="mw-redirect" title="Instant runoff voting">instant runoff voting</a> (IRV), and exhaustive voting, depending on the member's preferences. Those who want to vote only once may cast a single ballot filled out in the IRV format, while other members may cast separate ballots after each round of balloting. The party used this format for the <a href="/wiki/2012_New_Democratic_Party_leadership_election" title="2012 New Democratic Party leadership election">2012</a>, and <a href="/wiki/2017_New_Democratic_Party_leadership_election" title="2017 New Democratic Party leadership election">2017</a> leadership elections.</li> <li>Candidates to lead the <b><a href="/wiki/Conservative_Party_(UK)" title="Conservative Party (UK)">UK Conservative Party</a></b> are shortlisted by an exhaustive ballot of elected MPs until only two candidates remain. The final two candidates then enter a ballot of the party membership to select the leader.</li> <li>The <b>Leader of the <a href="/wiki/New_Zealand_Labour_Party" title="New Zealand Labour Party">Labour Party</a> of New Zealand</b> is elected by an exhaustive ballot of elected MPs; candidate needs two-thirds vote to be elected. If two candidates remain and neither has two-thirds vote, an electoral college made up of MPs, party members and affiliated unions will vote via simple majority.<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup></li> <li>The <b><a href="/wiki/President_of_South_Africa" title="President of South Africa">President of South Africa</a></b> is elected by exhaustive ballot by members of the <a href="/wiki/National_Assembly_of_South_Africa" title="National Assembly of South Africa">National Assembly</a>.<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></li></ul> <div class="mw-heading mw-heading2"><h2 id="Similar_systems">Similar systems</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Exhaustive_ballot&action=edit&section=5" title="Edit section: Similar systems"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="The_two-round_system">The two-round system</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Exhaustive_ballot&action=edit&section=6" title="Edit section: The two-round system"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>As noted above the exhaustive ballot is similar to the <a href="/wiki/Two-round_system" title="Two-round system">two-round system</a>. However under the two-round system if no candidate achieves an absolute majority in the first round then, rather than just a single candidate being eliminated, all candidates are immediately excluded except the two with the most votes. There is then a second and final round. Because, at most, it requires voters to return to the polls only once, the two-round system is considered more practical for large public elections than the exhaustive ballot, and is used in many countries for the election of presidents and legislative bodies. However the two systems often produce different winners. This is because, under the two-round system, a candidate may be eliminated in the first round who would have gone on to win the contest if they had been permitted to survive to the second round. In the example above, the two round system would have selected Nashville instead of Knoxville. </p> <div class="mw-heading mw-heading3"><h3 id="Primary_two-round_system">Primary two-round system</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Exhaustive_ballot&action=edit&section=7" title="Edit section: Primary two-round system"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>A nonpartisan <a href="/wiki/Partisan_primary" class="mw-redirect" title="Partisan primary">primary election</a> system is a variation of the two-round system which holds a pre-election, and allows the top two candidates to pass to the general election. It generally differs from the two-round system in two ways: (1) the first election is not allowed to pick a winner, and (2) political parties are not allowed to limit their field using a convention or caucus. </p> <div class="mw-heading mw-heading3"><h3 id="Instant-runoff_voting">Instant-runoff voting</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Exhaustive_ballot&action=edit&section=8" title="Edit section: Instant-runoff voting"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In some respects the exhaustive ballot closely resembles <a href="/wiki/Instant-runoff_voting" title="Instant-runoff voting">instant-runoff voting</a> (also known as the "Alternative Vote"). Under both systems if no candidate has an absolute majority in the first round then there are further rounds, with the candidate with the fewest votes being eliminated after each round. However while under the exhaustive ballot each round involves voters returning to cast a new vote, under instant-runoff, voters vote only once. This is possible because, rather than voting for only a single candidate, the voter ranks all of the candidates in order of preference. These preferences are then used to "transfer" the votes of those whose first preference has been eliminated during the course of the count. </p><p>Because the exhaustive ballot involves separate rounds of voting, voters can use the results of one round to inform how they will vote in the next, whereas this is not possible under IRV. Furthermore, because it is necessary to vote only once, instant-runoff voting has been used for large-scale elections in many places. </p> <div class="mw-heading mw-heading2"><h2 id="Tactical_voting">Tactical voting</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Exhaustive_ballot&action=edit&section=9" title="Edit section: Tactical voting"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Like instant-runoff voting, the exhaustive ballot is intended to improve upon the simpler "<a href="/wiki/First-past-the-post" class="mw-redirect" title="First-past-the-post">first-past-the-post</a>" (plurality) system by reducing the potential for <a href="/wiki/Tactical_voting" class="mw-redirect" title="Tactical voting">tactical voting</a> by avoiding "wasted" votes. Under the plurality system, which involves only one round, voters are encouraged to vote tactically by voting for only one of the two leading candidates, because a vote for any other candidate will not affect the result.<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. (December 2011)">citation needed</span></a></i>]</sup> Under the exhaustive ballot this tactic, known as "compromising", is sometimes unnecessary because, even if the voter's first choice is unlikely to be elected, she will still have the opportunity to influence the outcome of the election by voting for more popular candidates once her favourite has been eliminated. However the exhaustive ballot is still vulnerable to tactical voting under some circumstances. Because of the similarity between the two systems it is open to the same forms of tactical voting as instant-runoff voting, as described below. </p><p>Although the exhaustive ballot is designed to avoid "compromising" the tactic is still effective in some elections. Compromising is where a voter votes for a certain candidate, not because they necessarily support them, but as a way of avoiding the election of a candidate whom they dislike even more. The compromising tactic is sometimes effective because the exhaustive ballot eliminates candidates who are unpopular in early rounds, who might have had sufficient support to win the election had they survived a little longer. This can create strong incentives for voters to vote tactically. </p><p>The exhaustive ballot is also vulnerable to the tactic of "push over", where voters vote tactically for an unpopular "push over" candidate in one round as a way of helping their true favourite candidate win in a later round. The purpose of voting for the "push over" is to ensure that it is this weak candidate, rather than a stronger rival, who remains to challenge a voter's preferred candidate in later rounds. By supporting a "push over" candidate it is hoped to eliminate a stronger candidate who might have gone on to win the election.<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. (December 2011)">citation needed</span></a></i>]</sup> The "push over" tactic requires voters to be able to reliably predict how others will vote. It runs the risk of backfiring, because if the tactical voter miscalculates then the candidate intended as a "push over " might end up actually beating the voter's preferred candidate. Instant-runoff voting is less susceptible to this tactic, as voters cannot change their first preference in successive rounds. Once a voter has chosen a push over as their preferred candidate, it will remain so until this candidate is eliminated, increasing the likelihood of the push over getting elected at the expense of the preferred candidate. </p> <div class="mw-heading mw-heading3"><h3 id="Examples">Examples</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Exhaustive_ballot&action=edit&section=10" title="Edit section: Examples"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading4"><h4 id="Compromise">Compromise</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Exhaustive_ballot&action=edit&section=11" title="Edit section: Compromise"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In the example above Knoxville wins, the last choice of both Nashville and Memphis supporters. If Memphis supporters had compromised by voting for Nashville (their second choice) in the first round then Nashville would have been elected immediately, while if Nashville supporters had all compromised by voting for their second choice of Chattanooga in the first round, then Chattanooga would have gone on to be elected in the second round. </p> <div class="mw-heading mw-heading4"><h4 id="Push_over">Push over</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Exhaustive_ballot&action=edit&section=12" title="Edit section: Push over"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Imagine an election in which there are 100 voters who vote as follows: </p> <ul><li>Ice Cream: 25 votes</li> <li>Apple Pie: 30 votes</li> <li>Fruit: 45 votes</li></ul> <p>No candidate has an absolute majority of votes so Ice Cream is eliminated in the first round. Ice Cream supporters prefer Apple Pie to Fruit so in the second round they vote for Apple Pie and Apple Pie is the winner. However, if only six Fruit supporters had used the tactic of "push over" then they could have changed this outcome and ensured the election of Fruit. These six voters can do this by voting for Ice Cream in the first round as a "push over". If they do this then the votes cast in the first round will look like this: </p> <ul><li>Ice Cream: 31</li> <li>Apple Pie: 30</li> <li>Fruit: 39</li></ul> <p>This time Apple Pie is eliminated in the first round and Ice Cream and Fruit survive to the second round. This outcome is deliberate. The tactical voters know that Ice Cream will be an easier candidate for Fruit to beat in the second round than Apple Pie—in other words, that Ice Cream will be a "push-over". In the second round the tactical voters vote for their real first preference, Fruit. Therefore, even if only six Apple Pie supporters prefer Fruit to Ice Cream, the result of the second round will be: </p> <ul><li>Ice Cream: 49</li> <li>Fruit: 51</li></ul> <p>Fruit will therefore be elected. The success of this tactic relies on the Fruit supporters being able to predict that Ice Cream can be beaten by Fruit in the second round. If a large majority of Apple Pie supporters had voted for Ice Cream then the "push over" tactic would have backfired, leading to the election of Ice Cream, which Fruit partisans like even less than Apple Pie. </p> <div class="mw-heading mw-heading2"><h2 id="Strategic_nomination">Strategic nomination</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Exhaustive_ballot&action=edit&section=13" title="Edit section: Strategic nomination"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The exhaustive ballot can also be influenced by <a href="/wiki/Strategic_nomination" title="Strategic nomination">strategic nomination</a>; this is where candidates and political factions influence the result of an election by either nominating extra candidates or withdrawing a candidate who would otherwise have stood. The exhaustive ballot is vulnerable to strategic nomination for the same reasons that it is open to the voting tactic of "compromising". This is because a candidate who knows they are unlikely to win can bring about the election of a more desirable compromise candidate by withdrawing from the race, or by never standing in the first place. By the same token a candidate can bring about a less desirable result by unwisely choosing to stand in an election; this is because of the <a href="/wiki/Spoiler_effect" title="Spoiler effect">spoiler effect</a>, by which a new candidate can "split the vote" and cost another similar candidate the election. </p><p>The exhaustive vote's system of multiple rounds makes it less vulnerable to the spoiler effect than the plurality system or the two round system. This is because a potential spoiler candidate often has only minor support; therefore he will be eliminated early and his supporters will have the opportunity to influence the result of the election by voting for more popular candidates in later rounds. Voters can also counteract the effect of vote splitting by using the "compromise" tactic. </p><p>The exhaustive vote is essentially vulnerable to the same forms of strategic nomination as instant-runoff voting, the difference being that under the exhaustive vote candidates can use the results of early rounds to inform whether or not they should strategically withdraw in later rounds. This is impossible under IRV. In IRV the electorate votes only once, so candidates must make the judgement of whether or not to participate in an election before the poll, and before even one round of counting has occurred. </p> <div class="mw-heading mw-heading2"><h2 id="Effect_on_candidates_and_factions">Effect on candidates and factions</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Exhaustive_ballot&action=edit&section=14" title="Edit section: Effect on candidates and factions"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The exhaustive ballot encourages candidates to appeal to a broad cross-section of voters. This is because, in order to eventually receive an <a href="/wiki/Absolute_majority" class="mw-redirect" title="Absolute majority">absolute majority</a> of votes, it is necessary for a candidate to win the support of voters whose favourite candidate has been eliminated. Under the exhaustive ballot, eliminated candidates, and the factions who previously supported them, often issue recommendations to their supporters as to whom they should vote for in the remaining rounds of the contest. This means that eliminated candidates are still able to influence the result of the election. </p> <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=Exhaustive_ballot&action=edit&section=15" 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"> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="http://www.dfl.org/vertical/Sites/%7BC04B0B6A-109E-4F2D-A1B2-C92EC337D546%7D/uploads/%7B10452095-72DC-44D5-8768-91AD4D24B51B%7D.PDF">DFL Call 2008/2009</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20080221010034/http://dfl.org/vertical/Sites/%7BC04B0B6A-109E-4F2D-A1B2-C92EC337D546%7D/uploads/%7B10452095-72DC-44D5-8768-91AD4D24B51B%7D.PDF">Archived</a> 2008-02-21 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a> Page 27: VIII. Endorsement for U.S. Senate: 22. GENERAL ENDORSEMENT RULES: <dl><dd><ul><li><b>Dropoff rule</b>: <i>Candidates receiving less than 5% will be dropped after the first ballot. On subsequent ballots, the dropoff threshold will be raised by 5% each ballot to a maximum of 25%. After the fifth ballot and each subsequent ballot, the lowest remaining candidates will be dropped so that no more than two candidates remain. In the event that application of the dropoff rule would eliminate all but one candidate, then the two candidates who received the highest percent of the vote on the prior ballot shall be the remaining candidates.</i></li></ul></dd></dl> </span></li> <li id="cite_note-:0-2"><span class="mw-cite-backlink">^ <a href="#cite_ref-:0_2-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-:0_2-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-:0_2-2"><sup><i><b>c</b></i></sup></a></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://publications.parliament.uk/pa/cm200001/cmselect/cmproced/40/4005.htm">"House of Commons - Procedure - Second Report"</a>. <i>publications.parliament.uk</i><span class="reference-accessdate">. Retrieved <span class="nowrap">2021-03-08</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=publications.parliament.uk&rft.atitle=House+of+Commons+-+Procedure+-+Second+Report&rft_id=https%3A%2F%2Fpublications.parliament.uk%2Fpa%2Fcm200001%2Fcmselect%2Fcmproced%2F40%2F4005.htm&rfr_id=info%3Asid%2Fen.wikipedia.org%3AExhaustive+ballot" class="Z3988"></span></span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.europarl.europa.eu/news/en/headlines/eu-affairs/20190523STO52405/infographic-how-the-european-parliament-president-gets-elected">"Infographic: how the European Parliament president gets elected | News | European Parliament"</a>. <i>www.europarl.europa.eu</i>. 2019-05-28<span class="reference-accessdate">. Retrieved <span class="nowrap">2021-03-08</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=www.europarl.europa.eu&rft.atitle=Infographic%3A+how+the+European+Parliament+president+gets+elected+%7C+News+%7C+European+Parliament&rft.date=2019-05-28&rft_id=https%3A%2F%2Fwww.europarl.europa.eu%2Fnews%2Fen%2Fheadlines%2Feu-affairs%2F20190523STO52405%2Finfographic-how-the-european-parliament-president-gets-elected&rfr_id=info%3Asid%2Fen.wikipedia.org%3AExhaustive+ballot" class="Z3988"></span></span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation news cs1"><a rel="nofollow" class="external text" href="https://www.rnz.co.nz/news/political/482814/how-the-labour-party-vote-will-work-and-why-we-might-know-the-next-pm-by-saturday">"How the Labour Party vote will work - and why we might know the next PM by Saturday"</a>. <i><a href="/wiki/RNZ" class="mw-redirect" title="RNZ">RNZ</a></i>. 20 January 2023<span class="reference-accessdate">. Retrieved <span class="nowrap">20 January</span> 2023</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=RNZ&rft.atitle=How+the+Labour+Party+vote+will+work+-+and+why+we+might+know+the+next+PM+by+Saturday&rft.date=2023-01-20&rft_id=https%3A%2F%2Fwww.rnz.co.nz%2Fnews%2Fpolitical%2F482814%2Fhow-the-labour-party-vote-will-work-and-why-we-might-know-the-next-pm-by-saturday&rfr_id=info%3Asid%2Fen.wikipedia.org%3AExhaustive+ballot" 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 class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.gov.za/documents/constitution/constitution-republic-south-africa-1996-schedule-3-election-procedures-07">"Constitution of the Republic of South Africa, 1996 - Schedule 3: Election procedures"</a>. Government of South Africa<span class="reference-accessdate">. Retrieved <span class="nowrap">28 May</span> 2024</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Constitution+of+the+Republic+of+South+Africa%2C+1996+-+Schedule+3%3A+Election+procedures&rft.pub=Government+of+South+Africa&rft_id=https%3A%2F%2Fwww.gov.za%2Fdocuments%2Fconstitution%2Fconstitution-republic-south-africa-1996-schedule-3-election-procedures-07&rfr_id=info%3Asid%2Fen.wikipedia.org%3AExhaustive+ballot" class="Z3988"></span></span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Exhaustive_ballot&action=edit&section=16" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20061003121126/http://www.electoral-reform.org.uk/publications/briefings/speaker2.htm">Electoral Reform Society: Briefing on the electoral system for the Speaker of the British House of Commons</a></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 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style="width:1%"><a href="/wiki/Single-winner_voting_system" class="mw-redirect" title="Single-winner voting system">Single-winner</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Approval_voting" title="Approval voting">Approval voting</a> <ul><li><a href="/wiki/Combined_approval_voting" title="Combined approval voting">Combined approval voting</a></li> <li><a href="/wiki/Unified_primary" title="Unified primary">Unified primary</a></li></ul></li> <li><a href="/wiki/Borda_count" title="Borda count">Borda count</a></li> <li><a href="/wiki/Bucklin_voting" title="Bucklin voting">Bucklin voting</a></li> <li><a href="/wiki/Condorcet_methods" class="mw-redirect" title="Condorcet methods">Condorcet methods</a> <ul><li><a href="/wiki/Copeland%27s_method" title="Copeland's method">Copeland's method</a></li> <li><a href="/wiki/Dodgson%27s_method" title="Dodgson's method">Dodgson's method</a></li> <li><a href="/wiki/Kemeny%E2%80%93Young_method" title="Kemeny–Young method">Kemeny–Young method</a></li> <li><a href="/wiki/Minimax_Condorcet_method" title="Minimax Condorcet method">Minimax Condorcet method</a></li> <li><a href="/wiki/Nanson%27s_method" title="Nanson's method">Nanson's method</a></li> <li><a href="/wiki/Ranked_pairs" title="Ranked pairs">Ranked pairs</a></li> <li><a href="/wiki/Schulze_method" title="Schulze method">Schulze method</a></li></ul></li> <li><a class="mw-selflink selflink">Exhaustive ballot</a></li> <li><a href="/wiki/First-past-the-post_voting" title="First-past-the-post voting">First-past-the-post voting</a></li> <li><a href="/wiki/Instant-runoff_voting" title="Instant-runoff voting">Instant-runoff voting</a> <ul><li><a href="/wiki/Coombs%27_method" title="Coombs' method">Coombs' method</a></li> <li><a href="/wiki/Contingent_vote" title="Contingent vote">Contingent vote</a></li> <li><a href="/wiki/Supplementary_vote" class="mw-redirect" title="Supplementary vote">Supplementary vote</a></li></ul></li> <li><a href="/wiki/Majority_rule" title="Majority rule">Simple majoritarianism</a></li> <li><a href="/wiki/Plurality_voting_system" class="mw-redirect" title="Plurality voting system">Plurality</a></li> <li><a href="/wiki/Positional_voting_system" class="mw-redirect" title="Positional voting system">Positional voting system</a></li> <li><a href="/wiki/Score_voting" title="Score voting">Score voting</a></li> <li><a href="/wiki/STAR_voting" title="STAR voting">STAR voting</a></li> <li><a href="/wiki/Two-round_system" title="Two-round system">Two-round system</a></li> <li><a href="/wiki/Graduated_majority_judgment" title="Graduated majority judgment">Graduated majority judgment</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Proportional_representation" title="Proportional representation">Proportional</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%">Systems</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Mixed-member_proportional_representation" title="Mixed-member proportional representation">Mixed-member</a></li> <li><a href="/wiki/Mixed_single_vote#Proportional_systems" title="Mixed single vote">Mixed single vote</a></li> <li><a href="/wiki/Party-list_proportional_representation" title="Party-list proportional representation">Party-list</a></li> <li><a href="/wiki/Proportional_approval_voting" title="Proportional approval voting">Proportional approval voting</a></li> <li><a href="/wiki/Rural%E2%80%93urban_proportional_representation" title="Rural–urban proportional representation">Rural–urban</a></li> <li><a href="/wiki/Sequential_proportional_approval_voting" title="Sequential proportional approval voting">Sequential proportional approval voting</a></li> <li><a href="/wiki/Single_transferable_vote" title="Single transferable vote">Single transferable vote</a> <ul><li><a href="/wiki/CPO-STV" title="CPO-STV">CPO-STV</a></li> <li><a href="/wiki/Hare%E2%80%93Clark_electoral_system" title="Hare–Clark electoral system">Hare-Clark</a></li> <li><a href="/wiki/Schulze_STV" title="Schulze STV">Schulze STV</a></li></ul></li> <li><a href="/wiki/Spare_vote" title="Spare vote">Spare vote</a></li> <li><a href="/wiki/Indirect_single_transferable_voting" title="Indirect single transferable voting">Indirect single transferable voting</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Allocation</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Highest_averages_method" title="Highest averages method">Highest averages method</a> <ul><li><a href="/wiki/Sainte-Lagu%C3%AB_method" title="Sainte-Laguë method">Webster/Sainte-Laguë</a></li> <li><a href="/wiki/D%27Hondt_method" title="D'Hondt method">D'Hondt</a></li></ul></li> <li><a href="/wiki/Largest_remainders_method" class="mw-redirect" title="Largest remainders method">Largest remainders method</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Quotas</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Droop_quota" title="Droop quota">Droop quota</a></li> <li><a href="/wiki/Hagenbach-Bischoff_quota" class="mw-redirect" title="Hagenbach-Bischoff quota">Hagenbach-Bischoff quota</a></li> <li><a href="/wiki/Hare_quota" title="Hare quota">Hare quota</a></li> <li><a href="/wiki/Imperiali_quota" title="Imperiali quota">Imperiali quota</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Mixed_electoral_system" title="Mixed electoral system">Mixed</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Parallel_voting" title="Parallel voting">Parallel voting</a></li> <li><a href="/wiki/Mixed-member_proportional_representation" title="Mixed-member proportional representation">MMP</a></li> <li><a href="/wiki/Additional_member_system" class="mw-redirect" title="Additional member system">Additional member system</a></li> <li><a href="/wiki/Alternative_vote_plus" title="Alternative vote plus">Alternative vote plus</a></li> <li><a href="/wiki/Mixed_single_vote" title="Mixed single vote">Mixed single vote</a></li> <li><a href="/wiki/Mixed_ballot_transferable_vote" title="Mixed ballot transferable vote">Mixed ballot transferable vote</a></li> <li><a href="/wiki/Scorporo" title="Scorporo">Scorporo</a></li> <li><a href="/wiki/Vote_linkage_mixed_system" class="mw-redirect" title="Vote linkage mixed system">Vote linkage mixed system</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Semi-proportional_representation" title="Semi-proportional representation">Semi-proportional</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Single_non-transferable_vote" title="Single non-transferable vote">Single non-transferable vote</a></li> <li><a href="/wiki/Limited_voting" title="Limited voting">Limited voting</a></li> <li><a href="/wiki/Cumulative_voting" title="Cumulative voting">Cumulative voting</a></li> <li><a href="/wiki/Satisfaction_approval_voting" title="Satisfaction approval voting">Satisfaction approval voting</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Criteria</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Condorcet_winner_criterion" title="Condorcet winner criterion">Condorcet winner criterion</a></li> <li><a href="/wiki/Condorcet_loser_criterion" title="Condorcet loser criterion">Condorcet loser criterion</a></li> <li><a href="/wiki/Consistency_criterion" class="mw-redirect" title="Consistency criterion">Consistency criterion</a></li> <li><a href="/wiki/Independence_of_clones_criterion" title="Independence of clones criterion">Independence of clones</a></li> <li><a href="/wiki/Independence_of_irrelevant_alternatives" title="Independence of irrelevant alternatives">Independence of irrelevant alternatives</a></li> <li><a href="/wiki/Independence_of_Smith-dominated_alternatives" title="Independence of Smith-dominated alternatives">Independence of Smith-dominated alternatives</a></li> <li><a href="/wiki/Later-no-harm_criterion" title="Later-no-harm criterion">Later-no-harm criterion</a></li> <li><a href="/wiki/Majority_favorite_criterion" class="mw-redirect" title="Majority favorite criterion">Majority criterion</a></li> <li><a href="/wiki/Majority_loser_criterion" title="Majority loser criterion">Majority loser criterion</a></li> <li><a href="/wiki/Monotonicity_criterion" class="mw-redirect" title="Monotonicity criterion">Monotonicity criterion</a></li> <li><a href="/wiki/Mutual_majority_criterion" title="Mutual majority criterion">Mutual majority criterion</a></li> <li><a href="/wiki/Participation_criterion" class="mw-redirect" title="Participation criterion">Participation criterion</a></li> <li><a href="/wiki/Plurality_criterion" title="Plurality criterion">Plurality criterion</a></li> <li><a href="/wiki/Resolvability_criterion" title="Resolvability criterion">Resolvability criterion</a></li> <li><a href="/wiki/Reversal_symmetry" class="mw-redirect" title="Reversal symmetry">Reversal symmetry</a></li> <li><a href="/wiki/Smith_criterion" class="mw-redirect" title="Smith criterion">Smith criterion</a></li> <li><a href="/wiki/Seats-to-votes_ratio" title="Seats-to-votes ratio">Seats-to-votes ratio</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Other</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Ballot" title="Ballot">Ballot</a></li> <li><a href="/wiki/Election_threshold" class="mw-redirect" title="Election threshold">Election threshold</a></li> <li><a href="/wiki/First-preference_votes" title="First-preference votes">First-preference votes</a></li> <li><a href="/wiki/Liquid_democracy" title="Liquid democracy">Liquid democracy</a></li> <li><a href="/wiki/Spoilt_vote" title="Spoilt vote">Spoilt vote</a></li> <li><a href="/wiki/Sortition" title="Sortition">Sortition</a></li> <li><a href="/wiki/Unseating" title="Unseating">Unseating</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Comparison</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Comparison_of_electoral_systems" class="mw-redirect" title="Comparison of electoral systems">Comparison of voting systems</a></li> <li><a href="/wiki/List_of_electoral_systems_by_country" title="List of electoral systems by country">Voting systems by country</a></li></ul> </div></td></tr><tr><td class="navbox-abovebelow" colspan="2"><div><b><a href="/wiki/Portal:Politics" title="Portal:Politics">Portal</a></b> — <b><a href="/wiki/Wikipedia:WikiProject_Politics" title="Wikipedia:WikiProject Politics">Project</a></b></div></td></tr></tbody></table></div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; position: 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