Condorcet loser criterion: Difference between revisions
Undo revision 10958 by BetterVotingAdvocacy (talk) Turns out a "Condorcet non-loser" is actually a weak Condorcet winner.
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(Undo revision 10958 by BetterVotingAdvocacy (talk) Turns out a "Condorcet non-loser" is actually a weak Condorcet winner.) Tag: Undo |
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== Notes ==
Any voting method that operates by having or being able to be reduced to a final runoff will always pass the Condorcet loser criterion, since either the Condorcet loser is not in the runoff and thus can't win, or is in the runoff and is by definition defeated by their opponent; this includes [[IRV]], [[STAR voting|STAR]], Top-two runoff, etc. A generalization of the Condorcet loser criterion is the Smith loser criterion: a candidate in the [[Smith loser set]] (the smallest group of candidates such that more voters prefer anyone not in the group over anyone in the group) should never win unless all candidates are in the Smith loser set. The [[Smith criterion]] implies the Smith loser criterion, since the Smith set only overlaps with the Smith loser set when both sets include all candidates.<ref>[[Talk:Condorcet ranking]] Look for "I think I can prove" on the message with a timestamp date of 21 February 2020.</ref> The Smith loser criterion implies the Condorcet loser criterion, since a Condorcet loser, when they exist, will always be the only candidate in the Smith loser set. Many non-Smith efficient methods that pass the Condorcet loser criterion fail the Smith loser criterion.
== See also ==
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