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Coombs' method is aranked voting system. Likeinstant-runoff (IRV-RCV), Coombs' method is asequential-loser method, where the last-place finisher according to one method is eliminated in each round. However, unlike in instant-runoff, each round has electors voting against their least-favorite candidate; the candidate ranked last by the most voters is eliminated.[1]
The method fails mostvoting system criteria, includingCondorcet's majority criterion,monotonicity,participation, andclone-independence.[2][3] However, it does satisfy Black's single-peakedmedian voter criterion.[1]: prop. 2
The method was popularized byClyde Coombs.[1] It was described byEdward J. Nanson as the "Venetian method"[4] (which should not be confused with theRepublic of Venice's use ofscore voting in elections forDoge).
Each voter rank-orders all of the candidates on their ballot. Otherwise, the candidate ranked last by the largest number (plurality) of voters is eliminated, making each individual round equivalent toanti-plurality voting. Conversely, underinstant-runoff voting, the candidate ranked first (among non-eliminated candidates) by the fewest voters is eliminated.
In some sources, the elimination proceeds regardless of whether any candidate is ranked first by a majority of voters, and the last candidate to be eliminated is the winner.[5] This variant of the method can result in a different winner than the former one (unlike in instant-runoff voting, where checking to see if any candidate is ranked first by a majority of voters is only a shortcut that does not affect the outcome).
Suppose thatTennessee is holding an election on the location of itscapital. The population is concentrated around four major cities.All voters want the capital to be as close to them as possible. The options are:
The preferences of each region's voters are:
| 42% of voters Far-West | 26% of voters Center | 15% of voters Center-East | 17% of voters Far-East |
|---|---|---|---|
|
|
|
|
Assuming all of the voters vote sincerely (strategic voting is discussed below), the results would be as follows, by percentage:
| City | Round 1 | Round 2 | ||
|---|---|---|---|---|
| First | Last | First | Last | |
| Memphis | 42 | 58 | ||
| Nashville | 26 | 0 | ||
| Chattanooga | 15 | 0 | 15 | |
| Knoxville | 17 | 42 | 17 | |
The voting rounds used in thereality television programSurvivor could be considered a variation of Coombs' method but with sequential voting rounds. Everyone votes for one candidate they support for elimination each round, and the candidate with a plurality of that vote is eliminated. A strategy difference is that sequential rounds of voting means the elimination choice is fixed in a ranked ballot Coombs' method until that candidate is eliminated.
Likeanti-plurality voting, Coombs' rule is extremely vulnerable to strategic voting. As a result, it is more often used as an example of apathological voting rule than a serious proposal.[6] The equilibrium position for Coombs' method is extremely sensitive toincomplete ballots andstrategic nomination because the vast majority of voters' effects on the election come from how they fill out the bottom of their ballots.[6] As a result, voters have a strong incentive to rate the strongest candidates last to defeat them in earlier rounds.[7]
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