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, more complicated procedures take place. 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 for tabulating is relatively simple. 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 the least votes is eliminated. Then, for the people whose candidate was elimated, their rank ordering gets shifted up by one. So, for example, if my ordering was 1. A, 2. C, 3. B and A was eliminated, my new ranking would be 1. C, 2. B. Then the process is repeated. This is done until a candidate is chosen by simple majority.
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:
|
42% of voters (close to Memphis) |
26% of voters (close to Nashville) |
15% of voters (close to Chattanooga) |
17% of voters (close to Knoxville) |
Assuming all of the voters vote sincerely (strategic voting is discussed below), the results would be (going by percentage):
| City | Round 1 | Round 2 | Round 3 |
|---|---|---|---|
| Memphis | 42 | 42 | 42 |
| Nashville | 26 | 26 | |
| Chattanooga | 15 | 0 | |
| Knoxville | 17 |
In the first round, Chattanooga, having the smallest vote, is eliminated. All of the votes for Chattanooga have Knoxville have a second choice, so they are transferred to Knoxville. Now, Nashville has the smallest vote, so it is eliminated. The votes for Nashville have Chattanooga as a second choice, but as Chatanooga has been eliminated, they instead transfer to their third choice, Knoxville. Knoxville now has 58% of the vote, which is a simple majority, making it the winner.
Potential for Tactical voting
The Coombs' method is vulnerable to three strategies: compromising, push-over, and teaming.