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Concept
Minimax Condorcet method
Summary
In voting systems, the Minimax Condorcet method (often referred to as "the Minimax method") is one of several Condorcet methods used for tabulating votes and determining a winner when using ranked voting in a single-winner election. It is sometimes referred to as the Simpson–Kramer method, and the successive reversal method.
Minimax selects as the winner the candidate whose greatest pairwise defeat is smaller than the greatest pairwise defeat of any other candidate: or, put another way, "the only candidate whose support never drops below [N] percent" in any pairwise contest, with N as high as possible.
The Minimax Condorcet method selects the candidate for whom the greatest pairwise score for another candidate against him or her is the least such score among all candidates.
Formally, let denote the pairwise score for against . Then the candidate, selected by minimax (aka the winner) is given by:
When it is permitted to rank candidates equally, or to not rank all the candidates, three interpretations of the rule are possible. When voters must rank all the candidates, all three variants are equivalent.
Let be the number of voters ranking X over Y. The variants define the score for candidate X against Y as:
The number of voters ranking X above Y, but only when this score exceeds the number of voters ranking Y above X. If not, then the score for X against Y is zero. This variant is sometimes called winning votes.
The number of voters ranking X above Y minus the number of voters ranking Y above X. This variant is called using margins.
The number of voters ranking X above Y, regardless of whether more voters rank X above Y or vice versa. This variant is sometimes called pairwise opposition.
When one of the first two variants is used, the method can be restated as: "Disregard the weakest pairwise defeat until one candidate is unbeaten." An "unbeaten" candidate possesses a maximum score against him which is zero or negative.
Minimax using winning votes or margins satisfies the Condorcet and the majority criterion, but not the Smith criterion, mutual majority criterion, or Condorcet loser criterion.
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