The Coombs' method, also called the Coombs rule is a voting system created by Clyde Coombs 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).
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.)
Assuming all of the voters vote sincerely (strategic voting is discussed below), the results would be as follows, by percentage:
Coombs' method election results
|| Round 1
|| Round 2
|| Last |
|| |42 0
|| |26 68
- 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.
Note that although Coomb's method chose the Condorcet winner here, this is not necessarily the case.
Potential for strategic voting
The Coombs' method is vulnerable to three strategies: compromising, push-over