Coombs' method: Difference between revisions

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{{Short description|Single-winner ranked-choice electoralvoting systemrule}}{{Confused|Combs method|text=the [[Combs method]]}}{{Electoral systems sidebar|expanded=Single-winner}}

{{Electoral systems}}

'''Coombs' method''' is a [[ranked voting systems|ranked voting system]]. Like [[Instant-runoff voting|instant-runoff (IRV-RCV)]], Coombs' method is a [[Sequential elimination method|sequential-loser method]], where the last-place finisher according to one method is eliminated in each round. However, unlike in instant-runoff, each round has electors voting against their least-favorite candidate; the candidate ranked last by the most voters is eliminated.<ref name="Grofman">{{Cite journal |last=Grofman |first=Bernard |last2=Feld |first2=Scott L. |date=2004-12-01 |title=If you like the alternative vote (a.k.a. the instant runoff), then you ought to know about the Coombs rule |url=https://www.sciencedirect.com/science/article/abs/pii/S026137940300060X |journal=Electoral Studies |volume=23 |issue=4 |pages=641–659 |doi=10.1016/j.electstud.2003.08.001 |issn=0261-3794|url-access=subscription }}</ref>

'''Coombs' method''' or the '''Coombs rule'''<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> is a [[ranked voting systems|ranked voting system]] which uses a ballot counting method for [[ranked voting]] created by [[Clyde Coombs]]. Coombs' method can be thought of as a cross between [[instant-runoff voting]] and [[anti-plurality voting]].

The method satisfiesfails theseveral [[majorityvoting system 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 |url-access=subscription }}</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 Black's single-peaked [[Median voter property|median voter criterion]].<ref name="Grofman" />{{rp|at=prop. 2}}

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).

== History ==

The method satisfies the [[majority criterion]], the [[pareto criterion]], and the [[Condorcet loser criterion]], but fails to satisfy both [[later-no-harm]] and [[later-no-help criterion|later-no-help]]. The method also fails the [[Condorcet criterion]], the [[monotonicity criterion]], and [[Independence of irrelevant alternatives]].<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>

The method was popularized by [[Clyde Coombs]].<ref name="Grofman" /> It was described by [[Edward J. Nanson]] as the "Venetian method"<ref>{{Cite book |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> (which should not be confused with the [[Republic of Venice]]'s use of [[score voting]] in elections for [[Doge of Venice|Doge]]).

==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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* Memphis, having the most last-place votes (26+15+17=58), is therefore eliminated.

* In the second round, Memphis is out of the running, and so must be factored out. Memphis was ranked first on Group A's ballots, so the second choice of Group A, Nashville, gets an additional 42 first-place votes, giving it an absolute majority of first-place votes (68 versus 15+17=32), and making it the winner.

* Note that the last-place votes are only used to eliminate a candidate in a voting round where no candidate achieves an absolute majority; they are disregarded in a round where any candidate has 51%more orthan more50%. Thus last-place votes play no role in the final round.

== 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 consideredused as an example of a [[Pathological (mathematics)|pathological]] voting rule rather than in anya serious useproposal.<ref name=":0" /> The equilibrium position for 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]], andbecause 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.

==See also==

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{{voting systems}}

[[Category:Single-winner electoral systems]]

[[Category:Non-monotonic electoral systems]]

[[Category:Preferential electoral systems]]