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 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. R ...

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 Psycholo ...

. The Coombs' method is the application of Coombs rule to single-winner elections, similarly to

instant-runoff voting Instant-runoff voting (IRV) is a type of ranked preferential voting method. It uses a majority voting rule in single-winner elections where there are more than two candidates. It is commonly referred to as ranked-choice voting (RCV) in the U ...

, 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 Plurality may refer to: Voting * Plurality (voting), or relative majority, when a given candidate receives more votes than any other but still fewer than half of the total ** Plurality voting, system in which each voter votes for one candidate and ...

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

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program ''

Survivor Survivor(s) may refer to: Actual survivors * *Last survivors of historical events Arts, entertainment, and media Fictional entities * Survivors, characters in the 1997 ''KKnD'' video-game series * ''The Survivors'', or the ''New Survivors Found ...

'' 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 Teaming may refer to: * Link aggregation, in computing, known more specifically as NIC teaming or Network teaming * the practice of being a teamster * the formation of a team A team is a group of individuals (human or non-human) working togeth ...

. 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