Minimax Condorcet method: Difference between revisions

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This contrasts with [[Schulze]], which alternates between eliminating all candidates not in the [[Schwartz set]] and dropping defeats.

All [[:Category:Defeat-dropping Condorcet methods|defeat-dropping Condorcet methods]] become equivalent to Minimax when there are 3 or ~~fewer~~ candidates ~~with no pairwise ties between them~~. Because of this, defeat-~~droppers~~ that pass [[ISDA]] are equivalent to [[Smith//Minimax]] when the ~~above~~ ~~conditions~~ ~~hold~~ ~~for~~ ~~the~~ ~~Smith set.~~ ~~Example~~:

All [[:Category:Defeat-dropping Condorcet methods|defeat-dropping Condorcet methods]] become equivalent to Minimax when there are fewer than 3 candidates. Because of this, defeat-dropping methods that pass [[ISDA]] are equivalent to [[Smith//Minimax]] when the cycle involves only 3 candidates. For example:

{{ballots|

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The pairwise victories are 60 A>B, 65 B>C, 75 C>A. The A>B defeat is weakest by winning votes, so dropping it results in B being undefeated (alternatively, B's win can be explained as them being on the losing end of this defeat, and this defeat being their strongest defeat, since it's their only defeat).

Since the defeat-droppers are equivalent to either Minmax or Smith//Minmax when three or fewer candidates run, they all fail dominant mutual third burial resistance.

Since the defeat-droppers are equivalent to either Minmax or Smith//Minmax when three or fewer candidates run, they all fail [[dominant mutual third burial resistance]].{{Citation needed}}{{Clarify|reason=Even with equal ranks and winning votes?|date=April 2024}}

== References ==