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Coombs' method

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 sort of works like Instant Runoff Voting in reverse.

Table of contents
1 Procedures
2 An example
3 Potential for Tactical voting
4 External Link


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.

An example

Imagine an election to choose 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):

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)
1. Memphis
2. Nashville
3. Chattanooga
4. Knoxville
Group B: 26% of voters (close to Nashville)
1. Nashville
2. Chattanooga
3. Knoxville
4. Memphis
Group C: 15% of voters (close to Chattanooga)
1. Chattanooga
2. Knoxville
3. Nashville
4. Memphis
Group D: 17% of voters (close to Knoxville)
1. Knoxville
2. Chattanooga
3. Nashville
4. Memphis

Assuming all of the voters vote sincerely (strategic voting is discussed below), the results would be as follows, by percentage:

Coombs' Method Election Results
City Round 1 Round 2
First Last First Last
Memphis 42 58 42 0
Nashville 26 0 26 68
Chattanooga 15 0 15
Knoxville 17 42 17

Note that although Coomb's method chose the Condorcet winner here, this is not necessarily the case.

Potential for Tactical voting

The Coombs' method is vulnerable to three strategies: compromising, push-over and teaming.

External Link