Coombs' method (or the Coombs rule) is a ranked voting system created by Clyde Coombs used for single-winner elections. Similarly to instant-runoff voting, it uses candidate elimination and redistribution of votes cast for that candidate until one candidate has a majority of votes.
Contents
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-runoff voting, the candidate ranked first (among non-eliminated candidates) by the fewest voters is eliminated.
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:
The preferences of the voters would be divided like this:
Assuming all of the voters vote sincerely (strategic voting is discussed below), the results would be as follows, by percentage:
Use
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
The Coombs' method is vulnerable to three tactical voting 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.