Coombs' method: Difference between revisions
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'''Coombs' method''' (or the '''Coombs rule''')<ref>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]] created by [[wikipedia:Clyde Coombs|Clyde Coombs]] used for single-winner [[election]]s. Similarly to [[instant-runoff voting]], it uses candidate elimination and redistribution of votes cast for that candidate until one candidate has a majority of votes. Its difference from [[IRV]] lies in its elimination criterion: instead of eliminating the candidate ranked first by the fewest voters, it eliminates the candidate ranked last by the most. |
'''Coombs' method''' (or the '''Coombs rule''')<ref>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]] created by [[wikipedia:Clyde Coombs|Clyde Coombs]] used for single-winner [[election]]s. Similarly to [[instant-runoff voting]], it uses candidate elimination and redistribution of votes cast for that candidate until one candidate has a majority of votes. Its difference from [[IRV]] lies in its elimination criterion: instead of eliminating the candidate ranked first by the fewest voters, it eliminates the candidate ranked last by the most. |
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==Properties== |
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Coombs' method |
Coombs' method fails the [[Condorcet criterion]], the [[monotonicity criterion]], and the [[participation criterion]]. |
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⚫ | The following examples are due to Felsenthal and Tideman<ref name="FT">{{Cite journal |last=Felsenthal |first=Dan |last2=Tideman |first2=Nicolaus |date=2013 |title=Varieties of failure of monotonicity and participation under five voting methods |url=https://www.researchgate.net/profile/Dan-Felsenthal/publication/257667897_Varieties_of_failure_of_monotonicity_and_participation_under_five_voting_methods/links/54aec0fb0cf21670b35870a6/Varieties-of-failure-of-monotonicity-and-participation-under-five-voting-methods.pdf?origin=publication_detail|journal=Theory and Decision |language=en |volume=75 |issue=1 |pages=59–77}}</ref> unless otherwise noted: |
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=== Condorcet criterion === |
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Even though Coombs' frequently selects the [[Condorcet winner criterion|Condorcet winner]], it sometimes fails to do so. For example: |
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This example, placed in [[Online_poll#Online polling sites|Rob LeGrand's voting calculator]], shows that Coombs arrives at a different result than Condorcet. |
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=== Monotonicity criterion === |
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In the election |
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{{ballots| |
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1: A>B>C |
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10: A>C>B |
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11: B>A>C |
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11: B>C>A |
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10: C>A>B |
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2: C>B>A |
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}} |
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C wins, but if the 11 B>A>C voters raise C and vote B>C>A, then B wins. |
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=== Participation criterion === |
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In the election |
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{{ballots| |
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7: A>C>D>B |
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6: A>D>B>C |
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3: B>A>C>D |
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7: B>C>A>D |
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9: B>C>D>A |
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4: C>A>D>B |
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6: D>A>B>C |
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}} |
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A is the CW and wins. But if three additional voters vote A>C>B>D then B wins. |
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==Links== |
==Links== |