Coombs' method or the Coombs ruleGrofman, 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. is a

ranked voting system A ranking is a relationship between a set of items such that, for any two items, the first is either "ranked higher than", "ranked lower than" or "ranked equal to" the second. In mathematics, this is known as a weak order or total preorder of ...

which uses a ballot counting method for

ranked voting The term ranked voting (also known as preferential voting or ranked choice voting) refers to any voting system in which voters rank their candidates (or options) in a sequence of first or second (or third, etc.) on their respective ballots. Ra ...

created by

Clyde Coombs Clyde Hamilton Coombs (July 22, 1912 – February 4, 1988) was an American psychologist specializing in the field of mathematical psychology. He devised a voting system, that was hence named Coombs' method. Coombs founded the Mathematical Psychol ...

. The Coombs' method is the application of Coombs rule to

single-winner election A single-member district is an electoral district represented by a single officeholder. It contrasts with a multi-member district, which is represented by multiple officeholders. Single-member districts are also sometimes called single-winner vot ...

s, similarly to

instant-runoff voting Instant-runoff voting (IRV) is a type of Ranked voting, ranked preferential Electoral system, voting method. It uses a Majority rule, majority voting rule in single-winner elections where there are more than two candidates. It is commonly referr ...

, 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 A supermajority, supra-majority, qualified majority, or special majority is a requirement for a proposal to gain a specified level of support which is greater than the threshold of more than one-half used for a simple majority. Supermajority r ...

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

, 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. 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: * 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.

Use

The voting rounds used in the

reality television Reality television is a genre of television programming that documents purportedly unscripted real-life situations, often starring unfamiliar people rather than professional actors. Reality television emerged as a distinct genre in the early 1 ...

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

The Coombs' method is vulnerable to three

tactical voting Strategic voting, also called tactical voting, sophisticated voting or insincere voting, occurs in voting systems when a voter votes for another candidate or party than their ''sincere preference'' to prevent an undesirable outcome. For example, ...

strategies: compromising, push-over, and teaming. Coombs is sensitive to incomplete ballots, and how voters fill in the bottom of their ballots makes a big difference."Data on Manipulability"
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Notes

{{voting systems Single-winner electoral systems Non-monotonic electoral systems Preferential electoral systems

Procedures

An example

Use

Potential for strategic voting

See also

Notes