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Minimax Condorcet method: Difference between revisions

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Minimax Condorcet method (view source)

Revision as of 16:16, 9 April 2024

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Rewrote the defeat-dropper note to clarify how they fail DMTBR.
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(Bolded the bad-example so it's clear where the ballots were truncated.)
(Rewrote the defeat-dropper note to clarify how they fail DMTBR.)
 
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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 whenwith there are 3three or fewer candidates with no pairwise ties between them. Because of this, defeat-droppersdropping methods that pass [[ISDA]] are equivalent to [[Smith//Minimax]] when the abovecycle conditionsinvolves holdonly for3 the Smith setcandidates. Example:
 
Since the defeat-droppers are equivalent to either Minmax or Smith//MinmaxMinimax when three or fewer candidates run, they all fail [[dominant mutual third burial resistance]]. This follows from the equivalence and the three-candidate Minimax DMTBR failure example given above.▼
{{ballots|
25: A>B>C
40: B>C>A
35: C>A>B
}}
 
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.
 
== References ==
Kristomun
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