Coombs' method

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Coombs’ method is a ranked voting system that eliminates candidates one by one based on voters’ last-place rankings. Each voter ranks all candidates. If a candidate is ranked first by a majority of voters, that candidate wins. If not, the candidate who is last on the most ballots is eliminated, and the process repeats with the remaining candidates. Unlike instant-runoff voting, Coombs’ method focuses on ending the round with the lowest last-place support.

In some explanations, elimination continues even if no candidate has a majority of first-place votes, which can lead to a different winner than the version that stops when someone has a majority. The method was popularized by Clyde Coombs and was described by Edward J. Nanson as the “Venetian method” (not to be confused with Doge-score voting).

Coombs’ method requires each voter to rank all candidates. Although easy to describe, it is very sensitive to how people fill out their ballots, especially the bottom ranks.

The method fails several desirable properties, including Condorcet’s majority criterion, monotonicity, participation, and clone-independence. It does satisfy Black’s single-peaked median voter criterion, meaning it can align with a single-peaked preference order.

Because the outcome depends heavily on voters’ last-place rankings, the method is highly vulnerable to strategic voting: voters may try to rank strong competitors last to push them out early. For this reason, Coombs’ method is often cited as an example of a pathological voting rule rather than a practical one.

Variants and real-world analogies, like the elimination rounds seen in some reality TV formats, illustrate the sequential-elimination idea, but in practice Coombs’ method remains controversial and is rarely used for serious elections.