Minimax is often considered to be the simplest of the Condorcet methods. It is also known as the Simpson-Kramer method, and the successive reversal method. Any election method conforming to the Condorcet criterion is known as a Condorcet method. ...

Minimax selects the candidate for whom the greatest pairwise score for another candidate against him is the least such score among all candidates. Any election method conforming to the Condorcet criterion is known as a Condorcet method. ...

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 rules are equivalent.

The score for candidate x against y can be defined as:

1. 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 is sometimes called winning votes.
2. The number of voters ranking x above y minus the number of voters ranking y above x. This is called using margins.
3. The number of voters ranking x above y, regardless of whether more voters rank x above y or vice versa. This interpretation is sometimes called pairwise opposition.

When one of the first two interpretations 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. Any election method conforming to the Condorcet criterion is known as a Condorcet method. ...

Minimax using winning votes or margins satisfies Condorcet and the majority criterion, but not the Smith criterion, mutual majority criterion, or Condorcet loser criterion. When winning votes is used, Minimax also satisfies the Plurality criterion. The Condorcet candidate or Condorcet winner of an election is the candidate who, when compared in turn with each of the other candidates, is preferred over the other candidate. ... The majority criterion is a voting system criterion, used to objectively compare voting systems. ... In voting systems, the Smith set is the smallest set of candidates in a particular election who, when paired off in pairwise elections, can beat all other candidates outside the set. ... The mutual majority criterion is a criterion used to compare voting systems. ... Given a vote where voters rank options in order of preference, a Condorcet loser is an option that loses all of its pairwise comparisons. ... Plurality criterion is a voting system criterion devised by Douglas Woodall. ...

When the pairwise opposition interpretation is used, minimax also does not satisfy the Condorcet criterion. However, it satisfies the favorite betrayal criterion when equal-ranking is permitted. It also satisfies the Later-no-harm criterion, which means that by listing additional, lower preferences in one's ranking, one cannot cause a preferred candidate to lose. The Condorcet candidate or Condorcet winner of an election is the candidate who, when compared in turn with each of the other candidates, is preferred over the other candidate. ... In social choice theory, the favorite betrayal criterion (or FBC) is a voting system criterion devised by Mike Ossipoff for evaluating voting systems. ...

External resources

• Voting methods survey: minimax by James Green-Armytage
• Description of ranked ballot voting methods: Simpson by Rob LeGrand
• Single-winner electoral methods: minmax by Blake Cretney
• Electowiki: minmax