The Coombs' method is a voting system used for single-winner elections, in which each voter rank-orders the candidates. If there is a simple majority in people's first choice, the candidate who holds that majority wins. But if there is no simple majority, a series of eliminations occurs. The Coombs' method was invented by Clyde Coombs, hence the name.
Procedures
Each voter rank-orders all of the candidates on their ballot.
The method works as follows. First, if there is a simple majority in people's first choice, that candidate wins. If there isn't a simple majority, the candidate with a majority of last place votes is eliminated. If no such candidate exists, the candidate with the most first place votes is temporarily eliminated from consideration for perminent elimination. Once a perminently eliminated candidate is found, that candidate is factored out of the ballot, and the process is repeated. This is done until a single candidate remains.
An example
Imagine an election for the capital of Tennessee, a state in the United States that is over 500 miles east-to-west, and only 110 miles north-to-south. Let's say the candidates for the capital are Memphis (on the far west end), Nashville (in the center), Chattanooga (129 miles southeast of Nashville), and Knoxville (on the far east side, 114 miles northeast of Chattanooga). Here's the population breakdown by metro area (surrounding county):
- Memphis (Shelby County): 826,330
- Nashville (Davidson County): 510,784
- Chattanooga (Hamilton County): 285,536
- Knoxville (Knox County): 335,749
Let's say that in the vote, the voters vote based on geographic proximity. Assuming that the population distribution of the rest of Tennesee follows from those population centers, one could easily envision an election where the percentages of sincere preferences would be as follows:
|
Group A: 42% of voters (close to Memphis) |
Group B: 26% of voters (close to Nashville) |
Group C: 15% of voters (close to Chattanooga) |
Group D: 17% of voters (close to Knoxville) |
Assuming all of the voters vote sincerely (strategic voting is discussed below), the results would be as follows, by percentage. Note, these are the numbers of last place votes:
| City | Round 1 | Round 2 | Round 3 |
|---|---|---|---|
| Memphis | 58 | n/a | |
| Nashville | 0 | 32 <-winner with least last place votes | |
| Chattanooga | 0 | 0 | |
| Knoxville | 42 |
Starting off, there is no candidate with a simple majority of first place votes. A series of eliminations now occurs:
- In the first round, Memphis, having a majority of last place votes (26+15+17=58), is eliminated.
- In the second round, Memphis is out of the running, and so must be factored out. The lowest ranked candidate on Group B's ballots is Knoxville, and the lowest ranked candidate on Group C and D's ballots is Nashville, so the votes are transferred accordingly. Knoxville now has a majority of last place votes, and is eliminated.
- In the third round, Knoxville is out of the running, and is factored out of the ballots. Now, the lowest ranked candidate on both Group A and Group B's ballots is Chatanooga, so these ballots now count against Chatanooga. Since Chatanooga has a majority against it, it is eliminated, leaving Nashville the winner.
Potential for Tactical voting
The Coombs' method is vulnerable to three strategies: compromising, push-over, and teaming.