Coombs' method

Coombs' method (or the Coombs rule)^[1] is a ranked voting system created by Clyde Coombs used for single-winner elections. 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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Coombs' method

Example

Coombs' method frequently selects the Condorcet winner. However, this does not always happen. For example:

7:a>c>d>b
6:a>d>b>c
3:b>a>c>d
7:b>c>a>d
9:b>c>d>a
4:c>a>d>b
6:d>a>b>c
3:a>c>b>d

This example, placed in Rob LeGrand's voting calculator, shows that Coombs arrives at a different result than Condorcet. The example is pulled from a Felsenthal and Tideman paper.^[2]

Links

1996
- http://lists.electorama.com/pipermail/election-methods-electorama.com/1996-March/thread.html#65497 - "'Spokane' method"
2005
- https://web.archive.org/web/20050909092356/http://condorcet.org/emr/methods.shtml#Coombs - 2005 archive of Condorcet.org glossary of terminology
2019
- https://imgur.com/gallery/SLTHgCO - Diagram of Coombs' and center squeeze
2020
- https://www.reddit.com/r/EndFPTP/comments/js1qlt/wouldnt_a_rcv_method_where_you_eliminated_the/

Footnotes

↑ Grofman, Bernard, and Scott L. Feld (2004) "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.
↑ Felsenthal, Dan; Tideman, Nicolaus (2013). "Varieties of failure of monotonicity and participation under five voting methods" (PDF). Theory and Decision. 75 (1): 59–77.

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[1] Grofman, Bernard, and Scott L. Feld (2004) "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.

[2] Felsenthal, Dan; Tideman, Nicolaus (2013). "Varieties of failure of monotonicity and participation under five voting methods" (PDF). Theory and Decision. 75 (1): 59–77.

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