Coombs' method
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| Social choice and electoral systems |
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 Mathematics portal |
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.
Procedures
Each voter rank-orders all of the candidates on their ballot. If at any time one candidate is ranked first (among non-eliminated candidates) by an absolute majority of the voters, that candidate wins. Otherwise, the candidate ranked last (again among non-eliminated candidates) by the largest number of (or a plurality of) voters is eliminated. Conversely, under instant-runoff voting, the candidate ranked first (among non-eliminated candidates) by the fewest voters is eliminated.
An example
Suppose that Tennessee is holding an election on the location of its capital. The population is concentrated around four major cities. All voters want the capital to be as close to them as possible. The options are:
- Memphis, the largest city, but far from the others (42% of voters)
- Nashville, near the center of the state (26% of voters)
- Chattanooga, somewhat east (15% of voters)
- Knoxville, far to the northeast (17% of voters)
The preferences of each region's voters are:
| 42% of voters Far-West |
26% of voters Center |
15% of voters Center-East |
17% of voters Far-East |
|---|---|---|---|
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|
|
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Assuming all of the voters vote sincerely (strategic voting is discussed below), the results would be as follows, by percentage:
| City | Round 1 | Round 2 | ||
|---|---|---|---|---|
| First | Last | First | Last | |
| Memphis | 42 | 58 | ||
| Nashville | 26 | 0 | ||
| Chattanooga | 15 | 0 | 15 | |
| Knoxville | 17 | 42 | 17 | |
- In the first round, no candidate has an absolute majority of first-place votes (51).
- Memphis, having the most last-place votes (26+15+17=58), is therefore eliminated.
- In the second round, Memphis is out of the running, and so must be factored out. Memphis was ranked first on Group A's ballots, so the second choice of Group A, Nashville, gets an additional 42 first-place votes, giving it an absolute majority of first-place votes (68 versus 15+17=32), thus making it the winner. Note that the last-place votes are only used to eliminate a candidate in a voting round where no candidate achieves an absolute majority; they are disregarded in a round where a candidate has 51% or more. Thus last-place votes play no role in the final round.
Use
The voting rounds used in Survivor (TV series) could be considered a variation of Coombs' method, with sequential voting rounds. Everyone votes for one candidate they support for elimination each round, and the candidate with a plurality of that vote is eliminated. A strategy difference is that sequential rounds of voting means the elimination choice is fixed in a ranked ballot Coombs' method until that candidate is eliminated.
Potential for strategic voting
The Coombs' method is vulnerable to three tactical voting strategies:[citation needed] compromising, push-over, and teaming.
See also
Notes
- ^ 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.