Coombs' method (or the Coombs rule) 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[edit | edit source]
The following examples are due to Felsenthal and Tideman unless otherwise noted:
Condorcet criterion[edit | edit source]
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[edit | edit source]
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[edit | edit source]
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[edit | edit source]
- https://web.archive.org/web/20050909092356/http://condorcet.org/emr/methods.shtml#Coombs - 2005 archive of Condorcet.org glossary of terminology
Footnotes[edit | edit source]
- 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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