Coombs Method
The Coombs method is a ranked voting system. Its purpose is to determine a single winner.
Step 1: Each voter assigns a rank to all candidates.
Step 2: The administrator checks if there is an absolute majority of first preferences. If there is a candidate that gains an absolute majority, this candidate wins. If there is no absolute majority, the alternative with the highest number of the lowest preferences gets canceled. The remaining candidates move up.
Step 3: Then, the administrator checks again if there is an absolute majority. The process continues with step 2.
Example
| rank | A | A | B | B | C | C |
| rank | B | C | A | C | A | B |
| rank | C | B | C | A | B | A |
| Number of persons with this preference order | 6 | 0 | 5 | 2 | 5 | 3 |
- A is ranked first by 6 voters.
- B is ranked first by 7 voters.
- C is ranked first by 8 voters.
No candidate gained an absolute majority.
We are eliminating the candidates with the highest number of worst ranks.
- A is ranked worst by 7 voters
- B is ranked worst by 5 voters
- C is ranked worst by 11 voters
Thus, C is eliminated from the election. The remaining candidate set looks as follows:
| rank | A | A | B | B | A | B |
| rank | B | B | A | A | B | A |
| rank | – | |||||
| Number of persons with this preference order | 6 | 0 | 5 | 2 | 5 | 3 |
- A is ranked first by 11 voters
- B is ranked first by 10 voters
Thus, A gained the absolute majority and won the election.
We can see that the result can be surprising. C was preferred by the relative majority of voters but was eliminated first. This means that a candidate can lose if he gets bad ranks by a strong minority.
