# Minmax

**Minmax** is the name of several election methods based on electing the candidate with the lowest score, based on votes received in pairwise contests with other candidates.

**Minmax(winning votes)** elects the candidate whose greatest pairwise loss to another candidate is the least, when the strength of a pairwise loss is measured as the number of voters who voted for the winning side.

**Minmax(margins)** is the same, except that the strength of a pairwise loss is measured as the number of votes for the winning side *minus* the number of votes for the losing side.

Both of these methods satisfy the Condorcet criterion, and both fail the Smith criterion. Minmax(winning votes) also satisfies the Plurality criterion. In the three-candidate case, Minmax(margins) satisfies the Participation criterion.

**Minmax(pairwise opposition)** or **MMPO** elects the candidate whose greatest *opposition* from another candidate is minimal. Pairwise wins or losses are not considered; all that matters is the number of votes for one candidate over another.

Minmax(pairwise opposition) does not strictly satisfy the Condorcet criterion or Smith criterion. It also fails the Plurality criterion, and is more indecisive than the other Minmax methods. However, it satisfies the Later-no-harm criterion, and in the three-candidate case, the Participation criterion.