Coombs' method: Difference between revisions

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An example: Majority is >50%, not 51%
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{{Electoral systems}}
 
'''Coombs' method''' oris thea '''Coombs[[ranked rule'''voting systems|ranked voting system]] popularized by [[Clyde Coombs]].<ref name="Grofman">Grofman, Bernard, and Scott L. Feld (2004) [https://dx.doi.org/10.1016/j.electstud.2003.08.001 "If you like the alternative vote (a.k.a. the instant runoff), then you ought to know about the Coombs rule,"] ''Electoral Studies'' '''23''':641-59.</ref> isIt awas described by [[rankedEdward votingJ. systems|ranked voting systemNanson]] as the "Venetian method",<ref>{{Cite createdbook by|last=Royal Society of Victoria (Melbourne |first=Vic ) |url=http://archive.org/details/transactionsproc1719roya |title=Transactions and proceedings of the Royal Society of Victoria .. |date=1864 |publisher=Melbourne : The Society |others=American Museum of Natural History Library}}</ref> but should not be confused with the [[ClydeRepublic Coombsof Venice]],'s whichuse usesof a[[score ballotvoting]] countingin methodelections for [[rankedDoge votingof Venice|Doge]]. Coombs' method can be thought of as a cross between [[instant-runoff voting]] and [[anti-plurality voting]].
 
Like instant runoff, Coombs' method candidate elimination and redistribution of votes cast for that candidate until one candidate has a majority of votes. However, unlike instant-runoff, each round eliminates the candidate rated last by the most voters (instead of first by the fewest voters).<ref name="Grofman" />
 
The method satisfiesfails themost [[Majorityvoting favoritesystem criterion|majority criterioncriteria]], theincluding [[paretoCondorcet winner criterion]], and the [[|Condorcet's losermajority criterion]], but fails to satisfy both [[later-no-harm]] and [[later-no-helpMonotonicity criterion|later-no-help]]. The method also fails the [[Condorcet criterionmonotonicity]], the [[monotonicityParticipation criterion|participation]], and [[Independence of irrelevantclones alternativescriterion|clone-independence]].<ref>{{cite journal |last=Nurmi |first=Hannu |title=Voting Procedures: A Summary Analysis |journal=British Journal of Political Science |volume=13 |issue=2 |pages=181-208 |publisher=Cambridge University Press |date=1983-04-01 |language=English |url=https://www.cambridge.org/core/journals/british-journal-of-political-science/article/abs/voting-procedures-a-summary-analysis/67C52E7250EB4B88018B22D59CAA6908 |doi=10.1017/S0007123400003215 |access-date=2024-05-19 }}</ref><ref>{{cite book |last=Nurmi |first=Hannu |title=Comparing Voting systems |publisher=Springer Dordrecht |series= Theory and Decision Library A |volume=3 |edition=Illustrated |date=2012-12-06 |pages=209 |language=English |url= https://link.springer.com/book/10.1007/978-94-009-3985-1?utm_medium=referral&utm_source=google_books&utm_campaign=3_pier05_buy_print&utm_content=en_08082017 |doi= 10.1007/978-94-009-3985-1 |isbn= 9789400939851}}</ref> However, it does satisfy the [[Median voter theorem|median voter property]].
 
==Procedures==
Each voter rank-orders all of the candidates on their ballot. Otherwise, the candidate ranked last by the largest number ([[plurality (voting)|plurality]]) of voters is eliminated, making each individual round resembleequivalent to [[anti-plurality voting]]. Conversely, under [[instant-runoff voting]], the candidate ranked first (among non-eliminated candidates) by the fewest voters is eliminated.
 
In some sources, the elimination proceeds regardless of whether any candidate is ranked first by a majority of voters, and the last candidate to be eliminated is the winner.<ref>Pacuit, Eric, [https://plato.stanford.edu/archives/fall2017/entries/voting-methods/ "Voting Methods"], ''The Stanford Encyclopedia of Philosophy'' (Fall 2017 Edition), Edward N. Zalta (ed.)</ref> This variant of the method can result in a different winner than the former one (unlike in instant-runoff voting, where checking to see if any candidate is ranked first by a majority of voters is only a shortcut that does not affect the outcome).
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== In practice ==
The voting rounds used in the [[reality television]] program ''[[Survivor (TV series)|Survivor]]'' could be considered a variation of Coombs' method, but with sequential voting rounds. Everyone votes for one candidate they support for elimination each round, and the candidate with a plurality of that vote is eliminated. A strategy difference is that sequential rounds of voting means the elimination choice is fixed in a ranked ballot Coombs' method until that candidate is eliminated.
 
=== Potential for strategic voting ===
Like [[anti-plurality voting]], Coombs' rule is extremely vulnerable to strategic voting. As a result, it is mostmore often considered as an example of a [[Pathological (mathematics)|pathological]] voting rule rather than init anyis a serious userule.<ref name=":0" /> Coombs' method is extremely sensitive to [[Instant-runoffExhausted voting#Invalid ballots and incomplete ballotsballot|incomplete ballots]], [[Tactical manipulation of runoff voting#Compromise|compromising]], [[Tactical manipulation of runoff voting#Push over|push-over]], and [[strategic nomination|teaming]], and the vast majority of voters' effects on the election come from how they fill out the bottom of their ballots.<ref name=":0">[http://www.accuratedemocracy.com/l_data.htm "Data on Manipulability"]</ref> As a result, voters have a strong incentive to rate the strongest candidates last to defeat them in earlier rounds.<ref>{{Cite journal |last=Smith |first=Warren D. |date=12 July 2006 |title=Descriptions of single-winner voting systems |url=http://www.9mail.de/m-schulze/votedesc.pdf |journal=Voting Systems}}</ref>
 
This results in a [[Keynesian beauty contest|Keynesian beauty pageant]] that is extremely sensitive to minor variations in the perceived strengths of candidates.