Coombs' method: Difference between revisions

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{{Short description|Single-winner ranked-choice electoral system}}{{Confused|Combs method|text=the [[Combs method]]}}{{Electoral systems}}

'''Coombs' method''' is a [[ranked voting systems|ranked voting system]]. popularizedLike by[[Instant-runoff voting|instant-runoff (IRV-RCV)]], Coombs' method is a [[ClydeSequential Coombselimination 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">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> 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> but should not be confused with the [[Republic of Venice]]'s use of [[score voting]] in elections for [[Doge of Venice|Doge]]. Coombs' method can be thought of as a cross between [[instant-runoff voting]] and [[anti-plurality voting]].

The method fails most [[voting system criteria]], including [[Condorcet winner criterion|Condorcet's majority criterion]], [[Monotonicity criterion|monotonicity]], [[Participation criterion|participation]], and [[Independence of clones criterion|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 theoremproperty|median voter propertycriterion]].

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" />

== History ==

The method fails most [[voting system criteria]], including [[Condorcet winner criterion|Condorcet's majority criterion]], [[Monotonicity criterion|monotonicity]], [[Participation criterion|participation]], and [[Independence of clones criterion|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]].

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> but should not be confused with the [[Republic of Venice]]'s use of [[score voting]] in elections for [[Doge of Venice|Doge]].

==Procedures==