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<span id="openzim-page-title" class="mw-page-title-main"><span class="mw-page-title-main">Sequential elimination method</span></span>
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</style><table class="sidebar sidebar-collapse nomobile nowraplinks"><tbody><tr><td class="sidebar-pretitle">A joint <a href="Portal%3APolitics" title="Portal:Politics">Politics</a> and <a href="Portal%3AEconomics" 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="Social_choice_theory" title="Social choice theory">Social choice</a> and <a href="Electoral_system" title="Electoral system">electoral systems</a></th></tr><tr><td class="sidebar-image"></td></tr><tr><td class="sidebar-above">
<div class="hlist"><ul><li><a href="Social_choice_theory" title="Social choice theory">Social choice</a></li><li><a href="Mechanism_design" title="Mechanism design">Mechanism design</a></li><li><a href="Comparative_politics" title="Comparative politics">Comparative politics</a></li><li><a href="Comparison_of_voting_rules" title="Comparison of voting rules">Comparison</a></li><li><a href="List_of_electoral_systems" title="List of electoral systems">List</a><span class="nowrap"> </span>(<a href="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="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="Plurality_voting" title="Plurality voting">plurality</a> methods</b>
<ul><li><a href="First-past-the-post_voting" title="First-past-the-post voting">First preference plurality (FPP)</a></li>
<li><a href="Two-round_system" title="Two-round system">Two-round</a> (<abbr style="font-size:85%" title=""><a href="American_English" title="American English">US</a>:</abbr> <a href="Nonpartisan_primary" title="Nonpartisan primary">Jungle primary</a>)
<ul><li><a href="Partisan_primary" class="mw-redirect" title="Partisan primary">Partisan primary</a></li></ul></li>
<li><a href="Instant-runoff_voting" title="Instant-runoff voting">Instant-runoff</a>
<ul><li><abbr style="font-size:85%" title=""><a href="British_English" title="British English">UK</a>:</abbr> Alternative vote (AV)</li>
<li><abbr style="font-size:85%" title=""><a href="American_English" title="American English">US</a>:</abbr> Ranked-choice (RCV)</li></ul></li>
<li><a href="Party_block_voting" class="mw-redirect" title="Party block voting">Party block voting</a></li>
<li><a href="Plurality_block_voting" title="Plurality block voting">Plurality block voting</a></li></ul>
<hr>
<p><b><a href="Condorcet_method" title="Condorcet method">Condorcet methods</a></b>
</p>
<ul><li><a href="Tideman_alternative_method" title="Tideman alternative method">Condorcet-IRV</a></li>
<li><a href="Round-robin_voting" title="Round-robin voting">Round-robin voting</a>
<ul><li><a href="Minimax_Condorcet_method" title="Minimax Condorcet method">Minimax</a></li>
<li><a href="Kemeny_method" title="Kemeny method">Kemeny</a></li>
<li><a href="Schulze_method" title="Schulze method">Schulze</a></li>
<li><a href="Ranked_pairs" title="Ranked pairs">Ranked pairs</a></li>
<li><a href="Maximal_lottery" class="mw-redirect" title="Maximal lottery">Maximal lottery</a></li></ul></li></ul>
<hr>
<p><b><a href="Positional_voting" title="Positional voting">Positional voting</a></b>
</p>
<ul><li><a href="First-preference_plurality" class="mw-redirect" title="First-preference plurality">Plurality</a> (<abbr style="font-size:85%" title=""></abbr> <a href="Instant-runoff_voting" title="Instant-runoff voting">IRV</a>)</li>
<li><a href="Borda_count" title="Borda count">Borda count</a> (<abbr style="font-size:85%" title=""></abbr> <a href="Baldwin's_method" class="mw-redirect" title="Baldwin's method">Baldwin</a>, <abbr style="font-size:85%" title=""><a href="Highest_median_voting_rules" title="Highest median voting rules">Mdn.</a></abbr> <a href="Bucklin_voting" title="Bucklin voting">Bucklin</a>)</li>
<li><a href="Anti-plurality_voting" title="Anti-plurality voting">Antiplurality</a> (<abbr style="font-size:85%" title=""></abbr> <a href="Coombs_method" class="mw-redirect" title="Coombs method">Coombs</a>)</li></ul>
<hr>
<p><b><a href="Rated_voting" title="Rated voting">Cardinal voting</a></b>
</p>
<ul><li><a href="Score_voting" title="Score voting">Score voting</a></li>
<li><a href="Approval_voting" title="Approval voting">Approval voting</a></li>
<li><a href="Highest_median_voting_rules" title="Highest median voting rules">Majority judgment</a></li>
<li><a href="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="Proportional_representation" title="Proportional representation">Proportional representation</a></div><div class="sidebar-list-content mw-collapsible-content"><b><a href="Party-list_proportional_representation" title="Party-list proportional representation">Party-list</a></b>
<ul><li><a href="Apportionment_(politics)" title="Apportionment (politics)">Apportionment</a>
<ul><li><a href="Highest_averages_method" title="Highest averages method">Highest averages</a></li>
<li><a href="Largest_remainder_method" class="mw-redirect" title="Largest remainder method">Largest remainders</a></li>
<li><a href="National_remnant" title="National remnant">National remnant</a></li>
<li><a href="Biproportional_apportionment" title="Biproportional apportionment">Biproportional</a></li></ul></li>
<li><a href="Electoral_list" title="Electoral list">List type</a>
<ul><li><a href="Closed_list" title="Closed list">Closed list</a></li>
<li><a href="Open_list" title="Open list">Open list</a></li>
<li><a href="Panachage" title="Panachage">Panachage</a></li>
<li><a href="Justified_representation" title="Justified representation">List-free PR</a></li>
<li><a href="Localized_list" title="Localized list">Localized list</a></li></ul></li></ul>
<hr>
<p><b><a href="Electoral_quota" title="Electoral quota">Quota-remainder methods</a></b>
</p>
<ul><li><a href="Single_transferable_vote" title="Single transferable vote">Hare STV</a></li>
<li><a href="Schulze_STV" title="Schulze STV">Schulze STV</a></li>
<li><a href="CPO-STV" title="CPO-STV">CPO-STV</a></li>
<li><a href="Quota_Borda_system" title="Quota Borda system">Quota Borda</a></li></ul>
<hr>
<p><b><a href="Approval-based_committee" class="mw-redirect" title="Approval-based committee">Approval-based committees</a></b>
</p>
<ul><li><a href="Proportional_approval_voting" title="Proportional approval voting">Thiele's method</a></li>
<li><a href="Phragmen's_voting_rules" title="Phragmen's voting rules">Phragmen's method</a></li>
<li><a href="Expanding_approvals_rule" title="Expanding approvals rule">Expanding approvals rule</a></li>
<li><a href="Method_of_equal_shares" title="Method of equal shares">Method of equal shares</a></li></ul>
<hr>
<p><b><a href="Fractional_social_choice" title="Fractional social choice">Fractional social choice</a></b>
</p>
<ul><li><a href="Direct_representation" title="Direct representation">Direct representation</a>
<ul><li><a href="Interactive_representation" title="Interactive representation">Interactive representation</a></li>
<li><a href="Liquid_democracy" title="Liquid democracy">Liquid democracy</a></li></ul></li>
<li><a href="Fractional_approval_voting" title="Fractional approval voting">Fractional approval voting</a></li>
<li><a href="Maximal_lottery" class="mw-redirect" title="Maximal lottery">Maximal lottery</a></li>
<li><a href="Random_ballot" title="Random ballot">Random ballot</a></li></ul>
<hr>
<p><b><a href="Semi-proportional_representation" title="Semi-proportional representation">Semi-proportional representation</a></b>
</p>
<ul><li><a href="Cumulative_voting" title="Cumulative voting">Cumulative</a>
<ul><li><a href="Single_non-transferable_vote" title="Single non-transferable vote">SNTV</a></li></ul></li>
<li><a href="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="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="Mixed-member_majoritarian_representation" title="Mixed-member majoritarian representation">Mixed-member majoritarian</a></li>
<li><a href="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="Compensation_(electoral_systems)" title="Compensation (electoral systems)">compensatory</a></b>
<ul><li><a href="Parallel_voting" title="Parallel voting">Parallel (superposition)</a></li>
<li><a href="Coexistence_(electoral_systems)" title="Coexistence (electoral systems)">Coexistence</a></li>
<li>Conditional</li>
<li><a href="Majority_bonus_system" title="Majority bonus system">Fusion (majority bonus)</a></li></ul></li>
<li><b><a href="Compensation_(electoral_systems)" title="Compensation (electoral systems)">Compensatory</a></b>
<ul><li>Seat linkage system
<ul><li><abbr style="font-size:85%" title=""><a href="British_English" title="British English">UK</a>:</abbr> <a href="Additional_member_system" class="mw-redirect" title="Additional member system">'AMS'</a></li>
<li><abbr style="font-size:85%" title=""><a href="New_Zealand_English" title="New Zealand English">NZ</a>:</abbr> <a href="Mixed-member_proportional" class="mw-redirect" title="Mixed-member proportional">'MMP'</a></li></ul></li>
<li><a href="Vote_linkage_mixed_system" class="mw-redirect" title="Vote linkage mixed system">Vote linkage system</a>
<ul><li><a href="Scorporo" title="Scorporo">Negative vote transfer</a></li>
<li><a href="Mixed_ballot_transferable_vote" title="Mixed ballot transferable vote">Mixed ballot</a></li></ul></li></ul></li>
<li><a href="Mixed_electoral_system" title="Mixed electoral system">Supermixed systems</a>
<ul><li><a href="Dual-member_proportional_representation" class="mw-redirect" title="Dual-member proportional representation">Dual-member proportional</a></li>
<li><a href="Rural%E2%80%93urban_proportional_representation" title="Rural–urban proportional representation">Rural–urban proportional</a></li>
<li><a href="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="Mixed_single_vote" title="Mixed single vote">Single vote</a>
<ul><li><a href="Double_simultaneous_vote" title="Double simultaneous vote">Double simultaneous vote</a></li></ul></li>
<li><a href="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="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="Spoiler_effect" title="Spoiler effect">Spoiler effect</a></li>
<li><a href="Independence_of_clones" class="mw-redirect" title="Independence of clones">Cloning paradox</a></li>
<li><a href="Condorcet_winner_criterion" title="Condorcet winner criterion">Frustrated majorities paradox</a></li>
<li><a href="Center_squeeze" title="Center squeeze">Center squeeze</a></li></ul>
<hr>
<p><b>Pathological response</b>
</p>
<ul><li><a href="Perverse_response" class="mw-redirect" title="Perverse response">Perverse response</a></li>
<li><a href="Best-is-worst_paradox" class="mw-redirect" title="Best-is-worst paradox">Best-is-worst paradox</a></li>
<li><a href="No-show_paradox" class="mw-redirect" title="No-show paradox">No-show paradox</a></li>
<li><a href="Multiple_districts_paradox" class="mw-redirect" title="Multiple districts paradox">Multiple districts paradox</a></li></ul>
<hr>
<p><b><a href="Strategic_voting" title="Strategic voting">Strategic voting</a></b>
</p>
<ul><li><a href="Sincere_favorite_criterion" title="Sincere favorite criterion">Lesser evil voting</a></li>
<li><a href="Strategic_voting#Exaggeration" title="Strategic voting">Exaggeration</a></li>
<li><a href="Truncation_(voting)" class="mw-redirect" title="Truncation (voting)">Truncation</a></li>
<li><a href="Turkey-raising" class="mw-redirect" title="Turkey-raising">Turkey-raising</a></li>
<li><a href="Wasted_vote" title="Wasted vote">Wasted vote</a></li></ul>
<hr>
<p><b>Paradoxes of <a href="Majority_rule" title="Majority rule">majority rule</a></b>
</p>
<ul><li><a href="Tyranny_of_the_majority" title="Tyranny of the majority">Tyranny of the majority</a></li>
<li><a href="Discursive_dilemma" class="mw-redirect" title="Discursive dilemma">Discursive dilemma</a></li>
<li><a href="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="Social_choice_theory" title="Social choice theory">Social and collective choice</a></div><div class="sidebar-list-content mw-collapsible-content"><b><a href="Proof_of_impossibility" title="Proof of impossibility">Impossibility theorems</a></b>
<ul><li><a href="Arrow's_impossibility_theorem" title="Arrow's impossibility theorem">Arrow's theorem</a></li>
<li><a href="Condorcet_paradox" title="Condorcet paradox">Majority impossibility</a></li>
<li><a href="Moulin's_impossibility_theorem" class="mw-redirect" title="Moulin's impossibility theorem">Moulin's impossibility theorem</a></li>
<li><a href="McKelvey%E2%80%93Schofield_chaos_theorem" title="McKelvey–Schofield chaos theorem">McKelvey–Schofield chaos theorem</a></li>
<li><a href="Gibbard's_theorem" title="Gibbard's theorem">Gibbard's theorem</a></li></ul>
<hr>
<p><b>Positive results</b>
</p>
<ul><li><a href="Median_voter_theorem" title="Median voter theorem">Median voter theorem</a></li>
<li><a href="Condorcet's_jury_theorem" title="Condorcet's jury theorem">Condorcet's jury theorem</a></li>
<li><a href="May's_theorem" title="May's theorem">May's theorem</a></li>
<li><a href="Arrow's_theorem" class="mw-redirect" title="Arrow's theorem">Condorcet dominance theorems</a></li>
<li>Harsanyi's utilitarian theorem</li>
<li><a href="Vickrey-Clarke-Groves_mechanism" class="mw-redirect" title="Vickrey-Clarke-Groves mechanism">VCG mechanism</a></li>
<li><a href="Quadratic_voting" title="Quadratic voting">Quadratic voting</a></li></ul></div></div></td>
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<p>The <b>sequential elimination methods</b> are a class of <a href="Voting_system" class="mw-redirect" title="Voting system">voting systems</a> that repeatedly eliminate the last-place finisher of another voting method until a single candidate remains.<sup id="cite_ref-:0_1-0" class="reference"><a href="#cite_note-:0-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> The method used to determine the loser is called the <i>base method</i>. Common are the <a href="Two-round_system" title="Two-round system">two-round system</a>, <a href="Instant-runoff_voting" title="Instant-runoff voting">instant-runoff voting</a>, and some <a href="Primary_election" title="Primary election">primary systems</a>.
</p><p><a href="Instant-runoff_voting" title="Instant-runoff voting">Instant-runoff voting</a> is a sequential loser method based on <a href="Plurality_voting" title="Plurality voting">plurality voting</a>, while <a href="Baldwin_method" class="mw-redirect" title="Baldwin method">Baldwin's method</a> is a sequential loser method based on the <a href="Borda_count" title="Borda count">Borda count</a>.<sup id="cite_ref-:1_2-0" class="reference"><a href="#cite_note-:1-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup>
</p>
<div class="mw-heading mw-heading2"><h2 id="Properties">Properties</h2></div>
<p>Proofs of criterion compliance for loser-elimination methods often use <a href="Mathematical_induction" title="Mathematical induction">mathematical induction</a>, and so can be easier than proving such compliance for other method types. For instance, if the base method passes the majority criterion, a sequential loser-elimination method based on it will pass mutual majority. Loser-elimination methods are also not much harder to explain than their base methods.<sup id="cite_ref-:1_2-1" class="reference"><a href="#cite_note-:1-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup>
</p><p>However, loser-elimination methods often fail monotonicity due to <a href="Chaos_theory" title="Chaos theory">chaotic effects</a> (sensitivity to initial conditions): the order in which candidates are eliminated can create erratic behavior.<sup id="cite_ref-:0_1-1" class="reference"><a href="#cite_note-:0-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup>
</p><p>If the base method passes <a href="Local_independence_of_irrelevant_alternatives" class="mw-redirect" title="Local independence of irrelevant alternatives">independence from the weakest alternative</a>, the loser-elimination method is equivalent to the base method.<sup id="cite_ref-:0_1-2" class="reference"><a href="#cite_note-:0-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> In other words, methods that are immune to weak spoilers are already "their own" elimination methods, because eliminating the weakest candidate does not affect the winner.
</p><p>If the base method satisfies a criterion for a single candidate (e.g. the <a href="Majority_favorite_criterion" class="mw-redirect" title="Majority favorite criterion">majority criterion</a> or the <a href="Condorcet_criterion" class="mw-redirect" title="Condorcet criterion">Condorcet criterion</a>), then a sequential loser method satisfies the corresponding set criterion (e.g. the <a href="Mutual_majority_criterion" title="Mutual majority criterion">mutual majority criterion</a> or the <a href="Smith_criterion" class="mw-redirect" title="Smith criterion">Smith criterion</a>), so long as eliminating a candidate can't remove another candidate from the set in question. This is because when all but one of the candidates of the set have been eliminated, the single-candidate criterion applies to the remaining candidate.<sup id="cite_ref-:0_1-3" class="reference"><a href="#cite_note-:0-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup>
</p>
<div class="mw-heading mw-heading2"><h2 id="References">References</h2></div>
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<div class="mw-references-wrap"><ol class="references">
<li id="cite_note-:0-1"><span class="mw-cite-backlink">^ <a href="#cite_ref-:0_1-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-:0_1-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-:0_1-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-:0_1-3"><sup><i><b>d</b></i></sup></a></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">
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</style><cite id="CITEREFXiaLangYing2007" class="citation book cs1">Xia, Lirong; Lang, Jérôme; Ying, Mingsheng (2007-06-25). <a rel="nofollow" class="external text" href="https://doi.org/10.1145/1324249.1324286">"Sequential voting rules and multiple elections paradoxes"</a>. <i>Proceedings of the 11th conference on Theoretical aspects of rationality and knowledge - TARK '07</i>. New York, NY, USA: Association for Computing Machinery. pp. <span class="nowrap">279–</span>288. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1145%2F1324249.1324286">10.1145/1324249.1324286</a>. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-1-4503-7841-3</bdi>.</cite></span>
</li>
<li id="cite_note-:1-2"><span class="mw-cite-backlink">^ <a href="#cite_ref-:1_2-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-:1_2-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><cite id="CITEREFBagSabourianWinter" class="citation journal cs1">Bag, PK; Sabourian, H; Winter, E. <a rel="nofollow" class="external text" href="https://www.edge-page.net/jamb2007/papers/Seqelim_ReStud_submission.pdf">"Sequential Elimination vs. Instantaneous Voting"</a> <span class="cs1-format">(PDF)</span>. <i>Mimeo</i>.</cite></span>
</li>
</ol></div></div>
<div class="mw-heading mw-heading2"><h2 id="Further_reading">Further reading</h2></div>
<ul><li><cite id="CITEREFChowdhuryKim2017" class="citation journal cs1">Chowdhury, Subhasish M.; Kim, Sang-Hyun (July 2017). <a rel="nofollow" class="external text" href="https://eprints.whiterose.ac.uk/199698/1/Smallness_GEB.pdf">"'Small, yet Beautiful': Reconsidering the optimal design of multi-winner contests"</a> <span class="cs1-format">(PDF)</span>. <i>Games and Economic Behavior</i>. <b>104</b>: <span class="nowrap">486–</span>493. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2Fj.geb.2017.05.012">10.1016/j.geb.2017.05.012</a>. <a href="S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:43411835">43411835</a>.</cite></li>
<li><cite id="CITEREFKlunover2023" class="citation journal cs1">Klunover, Doron (December 2023). "Bureaucracy and labor market inefficiency: A contest model". <i>European Journal of Political Economy</i>. <b>80</b>: 102472. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2Fj.ejpoleco.2023.102472">10.1016/j.ejpoleco.2023.102472</a>. <a href="S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:262024392">262024392</a>.</cite></li></ul>
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</style></div><div role="navigation" class="navbox" aria-labelledby="Electoral_systems390" style="padding:3px"><table class="nowraplinks mw-collapsible mw-collapsed navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Electoral_systems390" style="font-size:114%;margin:0 4em"><a href="Electoral_system" title="Electoral system">Electoral systems</a></div></th></tr><tr><td class="navbox-abovebelow" colspan="2"><div><i>Part of the <a href="Portal%3APolitics" title="Portal:Politics">politics</a> and <a href="Portal%3AEconomics" title="Portal:Economics">Economics</a> series</i></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="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="Approval_voting" title="Approval voting">Approval voting</a>
<ul><li><a href="Combined_approval_voting" title="Combined approval voting">Combined approval voting</a></li>
<li><a href="Unified_primary" title="Unified primary">Unified primary</a></li></ul></li>
<li><a href="Borda_count" title="Borda count">Borda count</a></li>
<li><a href="Bucklin_voting" title="Bucklin voting">Bucklin voting</a></li>
<li><a href="Condorcet_methods" class="mw-redirect" title="Condorcet methods">Condorcet methods</a>
<ul><li><a href="Copeland's_method" title="Copeland's method">Copeland's method</a></li>
<li><a href="Dodgson's_method" title="Dodgson's method">Dodgson's method</a></li>
<li><a href="Kemeny_method" title="Kemeny method">Kemeny method</a></li>
<li><a href="Minimax_Condorcet_method" title="Minimax Condorcet method">Minimax Condorcet method</a></li>
<li><a href="Nanson's_method" title="Nanson's method">Nanson's method</a></li>
<li><a href="Ranked_pairs" title="Ranked pairs">Ranked pairs</a></li>
<li><a href="Schulze_method" title="Schulze method">Schulze method</a></li></ul></li>
<li><a href="Exhaustive_ballot" title="Exhaustive ballot">Exhaustive ballot</a></li>
<li><a href="First-past-the-post_voting" title="First-past-the-post voting">First-past-the-post voting</a></li>
<li><a href="Instant-runoff_voting" title="Instant-runoff voting">Instant-runoff voting</a>
<ul><li><a href="Coombs'_method" title="Coombs' method">Coombs' method</a></li>
<li><a href="Contingent_vote" title="Contingent vote">Contingent vote</a></li>
<li><a href="Supplementary_vote" class="mw-redirect" title="Supplementary vote">Supplementary vote</a></li></ul></li>
<li><a href="Majority_rule" title="Majority rule">Simple majoritarianism</a></li>
<li><a href="Plurality_voting_system" class="mw-redirect" title="Plurality voting system">Plurality</a></li>
<li><a href="Positional_voting_system" class="mw-redirect" title="Positional voting system">Positional voting system</a></li>
<li><a href="Score_voting" title="Score voting">Score voting</a></li>
<li><a href="STAR_voting" title="STAR voting">STAR voting</a></li>
<li><a href="Two-round_system" title="Two-round system">Two-round system</a></li>
<li><a href="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="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="Mixed-member_proportional_representation" title="Mixed-member proportional representation">Mixed-member</a></li>
<li><a href="Mixed_single_vote#Proportional_systems" title="Mixed single vote">Mixed single vote</a></li>
<li><a href="Party-list_proportional_representation" title="Party-list proportional representation">Party-list</a></li>
<li><a href="Proportional_approval_voting" title="Proportional approval voting">Proportional approval voting</a></li>
<li><a href="Rural%E2%80%93urban_proportional_representation" title="Rural–urban proportional representation">Rural–urban</a></li>
<li><a href="Sequential_proportional_approval_voting" title="Sequential proportional approval voting">Sequential proportional approval voting</a></li>
<li><a href="Single_transferable_vote" title="Single transferable vote">Single transferable vote</a>
<ul><li><a href="CPO-STV" title="CPO-STV">CPO-STV</a></li>
<li><a href="Hare%E2%80%93Clark_electoral_system" title="Hare–Clark electoral system">Hare–Clark</a></li>
<li><a href="Schulze_STV" title="Schulze STV">Schulze STV</a></li></ul></li>
<li><a href="Spare_vote" title="Spare vote">Spare vote</a></li>
<li><a href="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="Highest_averages_method" title="Highest averages method">Highest averages method</a>
<ul><li><a href="Sainte-Lagu%C3%AB_method" title="Sainte-Laguë method">Webster/Sainte-Laguë</a></li>
<li><a href="D'Hondt_method" title="D'Hondt method">D'Hondt</a></li></ul></li>
<li><a href="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="Droop_quota" title="Droop quota">Droop quota</a></li>
<li><a href="Hagenbach-Bischoff_quota" class="mw-redirect" title="Hagenbach-Bischoff quota">Hagenbach-Bischoff quota</a></li>
<li><a href="Hare_quota" title="Hare quota">Hare quota</a></li>
<li><a href="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="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="Parallel_voting" title="Parallel voting">Parallel voting</a></li>
<li><a href="Mixed-member_proportional_representation" title="Mixed-member proportional representation">MMP</a></li>
<li><a href="Additional_member_system" class="mw-redirect" title="Additional member system">Additional member system</a></li>
<li><a href="Alternative_vote_plus" title="Alternative vote plus">Alternative vote plus</a></li>
<li><a href="Mixed_single_vote" title="Mixed single vote">Mixed single vote</a></li>
<li><a href="Mixed_ballot_transferable_vote" title="Mixed ballot transferable vote">Mixed ballot transferable vote</a></li>
<li><a href="Scorporo" title="Scorporo">Scorporo</a></li>
<li><a href="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="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="Single_non-transferable_vote" title="Single non-transferable vote">Single non-transferable vote</a></li>
<li><a href="Limited_voting" title="Limited voting">Limited voting</a></li>
<li><a href="Cumulative_voting" title="Cumulative voting">Cumulative voting</a></li>
<li><a href="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="Condorcet_winner_criterion" title="Condorcet winner criterion">Condorcet winner criterion</a></li>
<li><a href="Condorcet_loser_criterion" title="Condorcet loser criterion">Condorcet loser criterion</a></li>
<li><a href="Consistency_criterion" title="Consistency criterion">Consistency criterion</a></li>
<li><a href="Independence_of_clones_criterion" title="Independence of clones criterion">Independence of clones</a></li>
<li><a href="Independence_of_irrelevant_alternatives" title="Independence of irrelevant alternatives">Independence of irrelevant alternatives</a></li>
<li><a href="Independence_of_Smith-dominated_alternatives" title="Independence of Smith-dominated alternatives">Independence of Smith-dominated alternatives</a></li>
<li><a href="Later-no-harm_criterion" title="Later-no-harm criterion">Later-no-harm criterion</a></li>
<li><a href="Majority_favorite_criterion" class="mw-redirect" title="Majority favorite criterion">Majority criterion</a></li>
<li><a href="Majority_loser_criterion" title="Majority loser criterion">Majority loser criterion</a></li>
<li><a href="Monotonicity_criterion" class="mw-redirect" title="Monotonicity criterion">Monotonicity criterion</a></li>
<li><a href="Mutual_majority_criterion" title="Mutual majority criterion">Mutual majority criterion</a></li>
<li><a href="Participation_criterion" title="Participation criterion">Participation criterion</a></li>
<li><a href="Plurality_criterion" class="mw-redirect" title="Plurality criterion">Plurality criterion</a></li>
<li><a href="Resolvability_criterion" class="mw-redirect" title="Resolvability criterion">Resolvability criterion</a></li>
<li><a href="Reversal_symmetry" title="Reversal symmetry">Reversal symmetry</a></li>
<li><a href="Smith_criterion" class="mw-redirect" title="Smith criterion">Smith criterion</a></li>
<li><a href="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="Ballot" title="Ballot">Ballot</a></li>
<li><a href="Election_threshold" class="mw-redirect" title="Election threshold">Election threshold</a></li>
<li><a href="First-preference_votes" class="mw-redirect" title="First-preference votes">First-preference votes</a></li>
<li><a href="Liquid_democracy" title="Liquid democracy">Liquid democracy</a></li>
<li><a href="Spoilt_vote" title="Spoilt vote">Spoilt vote</a></li>
<li><a href="Sortition" title="Sortition">Sortition</a></li>
<li><a href="Unseating" title="Unseating">Unseating</a></li>
<li><a href="Wasted_vote" title="Wasted vote">Wasted vote</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Comparison</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="Comparison_of_voting_rules" title="Comparison of voting rules">Comparison of voting systems</a></li>
<li><a href="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="Portal%3APolitics" title="Portal:Politics">Portal</a></b> — <b>Project</b></div></td></tr></tbody></table></div></div><!--htdig_noindex--><div><div class="zim-footer">
This article is issued from <a class="external text" title="Last edited on 2024-10-20" href="https://en.wikipedia.org/wiki/?title=Sequential_elimination_method&oldid=1252225008">Wikipedia</a>. The text is available under <a class="external text" href="https://creativecommons.org/licenses/by-sa/4.0/deed.en">Creative Commons Attribution-Share Alike 4.0</a> unless otherwise noted. Additional terms may apply for the media files.
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