Coombs' method or the Coombs rule is a ranked voting system which uses a ballot counting method for ranked voting created by Clyde Coombs. The Coombs' method is the application of Coombs rule to single-winner elections, similarly to instant-runoff voting, it uses candidate elimination and redistribution of votes cast for that candidate until one candidate has a majority of votes.
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, that candidate wins. Otherwise, the candidate ranked last (again among non-eliminated candidates) by the largest number of (or a plurality of) voters is eliminated. Conversely, under instant-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. 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).
Assuming all of the voters vote sincerely (strategic voting is discussed below), the results would be as follows, by percentage:
In the first round, no candidate has an absolute majority of first-place votes (51).
Memphis, having the most last-place votes (26+15+17=58), is therefore eliminated.
In the second round, Memphis is out of the running, and so must be factored out. Memphis was ranked first on Group A's ballots, so the second choice of Group A, Nashville, gets an additional 42 first-place votes, giving it an absolute majority of first-place votes (68 versus 15+17=32), and making it the winner.
Note that the last-place votes are only used to eliminate a candidate in a voting round where no candidate achieves an absolute majority; they are disregarded in a round where any candidate has 51% or more.
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An electoral system satisfies the Condorcet winner criterion (pronkɒndɔrˈseɪ) if it always chooses the Condorcet winner when one exists. The candidate who wins a majority of the vote in every head-to-head election against each of the other candidates - that is, a candidate preferred by more voters than any others - is the Condorcet winner, although Condorcet winners do not exist in all cases. It is sometimes simply referred to as the "Condorcet criterion", though it is very different from the "Condorcet loser criterion".
Instant-runoff voting (IRV) is an electoral system that uses ranked voting. Its purpose is to elect the majority choice in single-member districts in which there are more than two candidates and thus help ensure majority rule. It is a single-winner version of single transferable voting. Formerly the term "instant-runoff voting" was used for what many people now call contingent voting or supplementary vote.
We address the problem of predicting aggregate vote outcomes (e.g., national) from partial outcomes (e.g., regional) that are revealed sequentially. We combine matrix factorization techniques and generalized linear models (GLMs) to obtain a flexible, effic ...