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).
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, 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.)
An example
Suppose that Tennessee is holding an election on the ___location of its capital. The population is concentrated around four major cities. All voters want the capital to be as close to them as possible. The options are:
- Memphis, the largest city, but far from the others (42% of voters)
- Nashville, near the center of the state (26% of voters)
- Chattanooga, somewhat east (15% of voters)
- Knoxville, far to the northeast (17% of voters)
The preferences of each region's voters are:
| 42% of voters Far-West |
26% of voters Center |
15% of voters Center-East |
17% of voters Far-East |
|---|---|---|---|
|
|
|
|
Assuming all of the voters vote sincerely (strategic voting is discussed below), the results would be as follows, by percentage:
| City | Round 1 | Round 2 | ||
|---|---|---|---|---|
| First | Last | First | Last | |
| Memphis | 42 | 58 | ||
| Nashville | 26 | 0 | ||
| 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.
Potential for tactical voting and strategic nomination
The Coombs' method is vulnerable to three strategies: compromising, push-over and teaming.