Condorcet loser criterion: Difference between revisions
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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.
Note that it is very unlikely for a candidate with any significant amount of support to be a CL, even if they have significantly less support than other candidates, because they will still beat any candidates with negligible support i.e. [[Write-in candidate|Write-in candidat]]<nowiki/>es marked on only one ballot. Because of this, it is common to discuss the CL criterion when only looking at matchups between the major candidates. <ref>{{Cite web|url=https://www.fairvote.org/more-on-warren-smiths-and-anthony-gierzynskis-flawed-analysis|title=More on Warren Smith's and Anthony Gierzynski's flawed analysis.|last=FairVote.org|first=|date=|website=FairVote|url-status=live|archive-url=|archive-date=|access-date=2020-05-10|quote=In fact, Bucklin, Approval and Range voting quite possibly would have elected Kurt Wright (the Condorcet-loser among the top three)}}</ref>
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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