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The Coombs' method, created by Clyde Coombs, is a voting system used for single-winner elections in which each voter rank-orders the candidates. It is very similar to Instant Runoff Voting (also known as 'Preferential Voting' or the Alternative Vote).

Contents 1 Procedures 2 An example 3 Potential for tactical voting and strategic nomination 4 See also 5 External links

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, then this is the winner. As long as this is not the case, the candidate which is ranked last (again among non-eliminated candidates) by the most (or a plurality of) voters is eliminated. (Conversely, in Instant Runoff Voting the candidate ranked first (among non-eliminated candidates) by the least amount of voters is eliminated.)

Imagine that the population of Tennessee, a state in the United States, is voting 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 one of these four cities, and that they would like the capital to be established as close to their city 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
• 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)
Memphis Nashville Chattanooga Knoxville	Nashville Chattanooga Knoxville Memphis	Chattanooga Knoxville Nashville Memphis	Knoxville Chattanooga Nashville 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) and making it thus the winner. Note that the last place votes are disregarded in the final round.

Note that although Coomb's method chose the Condorcet winner here, this is not necessarily the case.

The Coombs' method is vulnerable to three strategies: compromising, push-over and teaming.

• List of democracy and elections-related topics

• Condorcet.org EMR: Coombs' method