Coombs election
The Coombs election is an electoral process that determines a single winner. As with instant runoff voting , each voter ranks the candidates according to their preferences. It is named after its inventor, the American psychologist Clyde Hamilton Coombs (1912–1988).
The Coombs election, like the instant runoff voting, follows the principle that candidates are eliminated and their votes are redistributed to the remaining candidates according to the ranking on the ballot papers until one candidate achieves an absolute majority . In contrast to instant run-off voting, in the Coombs election, it is not the candidate with the fewest initial preferences that is eliminated from the remaining candidates, but rather the one who was most frequently elected to last place.
Description of the voting method
If no candidate has achieved an absolute majority among the first preferences, the candidate who was most frequently chosen for the last rank or was not marked with a rank will be removed from the race. The votes allotted to him are distributed to the second preferences. Similarly, the last rank of each voting slip is passed on to the penultimate preference.
If no candidate has obtained an absolute majority after this, the remaining candidate with the most final votes is again removed from the race and the votes allotted to him are distributed to the second preferences; if the second preference has already been eliminated, the third preference is used, etc. This procedure is continued until a candidate has achieved an absolute majority.
example
Consider an election with four candidates A, B, C, and D and the following voter preferences:
| 40% of citizens | 30% of citizens | 19% of citizens | 9% of citizens | 2% of citizens |
|---|---|---|---|---|
| 1. C | 1. A | 1. A | 1. D | 1. B |
| 2. D | 2 B | 2. D | 2. A. | 2. A. |
| 3. B. | 3. C | 3. C | 3. B. | 3. D |
| 4. A. | 4. D | 4. B. | 4. C | 4. C |
The first and last votes of the candidates would be:
| 1 round | ||
|---|---|---|
| candidate | First votes | Final votes |
| A. | 49% | 40% |
| B. | 2% | 19% |
| C. | 40% | 11% |
| D. | 9% | 30% |
Since no candidate has an absolute majority, the candidate with the most final votes, namely candidate A, is eliminated and his votes redistributed:
| 1 round | 2nd round | |||
|---|---|---|---|---|
| candidate | First votes | Final votes | First votes | Final votes |
| A. | 49% | 40% | ||
| B. | 2% | 19% | 32% | 59% |
| C. | 40% | 11% | 40% | 11% |
| D. | 9% | 30% | 28% | 30% |
No candidate still has an absolute majority, so the candidate with the most last places is again deleted, in this case candidate B.
| 1 round | 2nd round | 3rd round | |||
|---|---|---|---|---|---|
| candidate | First votes | Final votes | First votes | Final votes | First votes |
| A. | 49% | 40% | |||
| B. | 2% | 19% | 32% | 59% | |
| C. | 40% | 11% | 40% | 11% | 70% |
| D. | 9% | 30% | 28% | 30% | 30% |
Finally, candidate C has an absolute majority and thus emerges as the winner of the election using the Coombs method.
defects
Like the instant runoff voting, the Coombs election does not meet the Condorcet criterion . You can easily understand that if you look at the above example again:
| 40% of citizens | 30% of citizens | 19% of citizens | 9% of citizens | 2% of citizens |
|---|---|---|---|---|
| 1. C | 1. A | 1. A | 1. D | 1. B |
| 2. D | 2 B | 2. D | 2. A. | 2. A. |
| 3. B. | 3. C | 3. C | 3. B. | 3. D |
| 4. A. | 4. D | 4. B. | 4. C | 4. C |
The Condorcet winner would be A because this candidate is preferred by 58% to candidate B, 60% to candidate C and 51% of the votes to candidate D. Since candidate A with 49% first preferences does not achieve an absolute majority and is most often in last place, candidate A is eliminated first using the Coombs election, although he would be the Condorcet winner.