Coombs' method

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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.

Properties

Coombs' method fails the Condorcet criterion, the monotonicity criterion, and the participation criterion.

The following examples are due to Felsenthal and Tideman^[2] unless otherwise noted:

Condorcet criterion

Even though Coombs' frequently selects the Condorcet winner, it sometimes fails to do so. 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.

Monotonicity criterion

In the election

 1: A>B>C
10: A>C>B
11: B>A>C
11: B>C>A
10: C>A>B
 2: C>B>A

C wins, but if the 11 B>A>C voters raise C and vote B>C>A, then B wins.

Participation criterion

In the election

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

A is the CW and wins. But if three additional voters vote A>C>B>D then we get the Condorcet failure election where B wins.

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.

[FT-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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