# Coombs' method

Coombs' method (or the Coombs rule)[1] is a voting system created by Clyde Coombs used for single-winner elections in which each voter ranks the candidates in order of preference. It is very similar to instant-runoff voting (also known as the alternative vote), a more common ranked voting system.

## 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 run-off voting, the candidate ranked first (among non-eliminated candidates) by the fewest voters is eliminated.

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## An example

Imagine that Tennessee is having an election on the location of its capital. The population of Tennessee is concentrated around its four major cities, which are spread throughout the state. For this example, suppose that the entire electorate lives in these four cities and that everyone wants to live as near to the capital as possible.

The candidates for the capital are:

• Memphis, the state's largest city, with 42% of the voters, but located far from the other cities
• Nashville, with 26% of the voters, near the center of the state
• Knoxville, with 17% of the voters
• Chattanooga, with 15% of the voters

The preferences of the voters would be divided like this:

42% of voters
(close to Memphis)
26% of voters
(close to Nashville)
15% of voters
(close to Chattanooga)
17% of voters
(close to Knoxville)
1. Memphis
2. Nashville
3. Chattanooga
4. Knoxville
1. Nashville
2. Chattanooga
3. Knoxville
4. Memphis
1. Chattanooga
2. Knoxville
3. Nashville
4. Memphis
1. Knoxville
2. Chattanooga
3. Nashville
4. Memphis

Assuming all of the voters vote sincerely (strategic voting is discussed below), the results would be as follows, by percentage:

Coombs' method election results
City Round 1 Round 2
First Last First Last
Memphis 42 58 42 0
Nashville 26 0 26 68
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 disregarded in the final round.
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## 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.

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## Potential for strategic voting

The Coombs' method is vulnerable to three tactical voting strategies:[citation needed] compromising, push-over, and teaming.

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