Coombs' method: Difference between revisions

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{{Electoral systems}}

'''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]]. The Coombs' method iscan thebe applicationthought of Coombsas rulea tocross between [[Singleinstant-memberrunoff district|single-winner electionvoting]]s, similarly toand [[instantanti-runoffplurality voting]], it(and usesas candidatesuch, eliminationinherits and redistributionmany of votesthe cast[[Pathological for that candidate until one candidate has a majority(mathematics)|pathologies]] of votesboth).

Like instant runoff, Coombs' method cancandidate beelimination thoughtand redistribution of asvotes cast for that candidate until one candidate has a "reversed"majority of votes. However, unlike [[instant-runoff voting]], whereeach individualround rounds eliminateeliminates the candidate who is rated last by the most voters (instead of first by the fewest voters).

==Procedures==

Each voter rank-orders all of the candidates on their ballot. If at any time one candidate is ranked first (among non-eliminated candidates) by an [[absolute majority]] of the voters, that candidate wins. Otherwise, the candidate ranked last (again among non-eliminated candidates) by the largest number of (or a [[plurality (voting)|plurality]]) of) voters is eliminated, making each individual round resemble [[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).

==An example==

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==Potential for strategic voting==

Like [[anti-plurality voting]] and the [[Borda count]], Coombs' rule is extremely vulnerable to strategic voting, and as a result is known more as an example of a [[Pathological (mathematics)|pathological]] social choice function than as a serious voting rule.

The Coombs' method is vulnerable to three [[tactical voting]] strategies:{{Citation needed|date=January 2008}} [[Tactical manipulation of runoff voting#Compromise|compromising]], [[Tactical manipulation of runoff voting#Push over|push-over]], and [[strategic nomination|teaming]]. Coombs is sensitive to [[Instant-runoff voting#Invalid ballots and incomplete ballots|incomplete ballots]], and how voters fill in the bottom of their ballots makes a big difference.<ref>[http://www.accuratedemocracy.com/l_data.htm "Data on Manipulability"]</ref>

Coombs' method is extremely sensitive to [[Instant-runoff voting#Invalid ballots and incomplete ballots|incomplete ballots]], [[Tactical manipulation of runoff voting#Compromise|compromising]], [[Tactical manipulation of runoff voting#Push over|push-over]], and [[strategic nomination|teaming]]; the vast majority of voters' effects on the election comes from how they fill out the bottom of their ballots<ref>[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 early on. This results in a [[Keynesian beauty contest|Keynesian beauty pageant]], where the [[Nash equilibrium]] results in candidates being chosen completely at random. However, naively strategic voters (i.e. [[Bounded rationality|boundedly rational]] voters) will often elect the worst candidate, analogously to the behavior in the "[[Guess 2/3 of the average|2/3 of the average]]" game.

==See also==