Английская Википедия:Coombs' method
Шаблон:Short description Шаблон:Electoral systems
Coombs' method or the Coombs rule[1] is a ranked voting system which uses a ballot counting method for ranked voting created by Clyde Coombs. Coombs' method can be thought of as a cross between instant-runoff voting and anti-plurality voting.
Like instant runoff, Coombs' method candidate elimination and redistribution of votes cast for that candidate until one candidate has a majority of votes. However, unlike instant-runoff, each round eliminates the candidate rated last by the most voters (instead of first by the fewest voters).
Procedures
Each voter rank-orders all of the candidates on their ballot. Otherwise, the candidate ranked last by the largest number (plurality) of voters is eliminated, making each individual round resemble anti-plurality voting. Conversely, under instant-runoff voting, the candidate ranked first (among non-eliminated candidates) by the fewest voters is eliminated.
In some sources, the elimination proceeds regardless of whether any candidate is ranked first by a majority of voters, and the last candidate to be eliminated is the winner.[2] This variant of the method can result in a different winner than the former one (unlike in instant-runoff voting, where checking to see if any candidate is ranked first by a majority of voters is only a shortcut that does not affect the outcome).
An example
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), and 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 any candidate has 51% or more. Thus last-place votes play no role in the final round.
In practice
The voting rounds used in the reality television program Survivor 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
Like anti-plurality voting, Coombs' rule is extremely vulnerable to strategic voting. As a result, it is most often considered as an example of a pathological voting rule rather than in any serious use.[3] Coombs' method is extremely sensitive to incomplete ballots, compromising, push-over, and teaming, and the vast majority of voters' effects on the election come from how they fill out the bottom of their ballots.[3] As a result, voters have a strong incentive to rate the strongest candidates last to defeat them in earlier rounds.
This results in a Keynesian beauty pageant that is extremely sensitive to minor variations in the perceived strengths of candidates.
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.
- ↑ Pacuit, Eric, "Voting Methods", The Stanford Encyclopedia of Philosophy (Fall 2017 Edition), Edward N. Zalta (ed.)
- ↑ 3,0 3,1 "Data on Manipulability"
