Condorcet winner criterion: Difference between revisions
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{{Wikipedia}}
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The '''Condorcet candidate''', '''Pairwise Champion''' (PC), '''beats-all winner''', or '''Condorcet winner''' (CW) of an [[election]] is the candidate who is preferred by more voters than any other candidate.
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Range voting does not comply because it allows for the difference between 'rankings' to matter. E.g. 51 people might rate A at 100, and B at 90, while 49 people rate A at 0, and B at 100. Condorcet would consider this 51 people voting A>B, and 49 voting B>A, and A would win. Range voting would see this as A having support of 5100/100 = 51%, and B support of (51*90+49*100)/100 = 94.9%; range voting advocates would probably say that in this case the Condorcet winner is not the socially ideal winner.
== Multi-winner generalizations ==
Schulze has proposed a generalization of the Condorcet criterion for multi-winner methods:<ref name="Schulze 2018">{{cite web | last=Schulze | first=Markus | title=The Schulze Method of Voting | website=arXiv.org | date=2018-03-15 | url=https://arxiv.org/abs/1804.02973v6 | access-date=2020-02-11|page=351}}</ref> Suppose all but M+1 candidates are eliminated from the ballots, and the remaining candidates include candidate ''b''. If ''b'' is always a winner when electing M winners from the M+1 remaining candidates, no matter who the other M remaining candidates are, then ''b'' is an M-seat Condorcet winner.
A method passes the M-seat Condorcet criterion if its M-seat election outcome always contains such a ''b'' when he exists, and passes the multi-winner Condorcet criterion if it passes the M-seat Condorcet criterion for all M.
When M=1, the generalization reduces to the ordinary Condorcet criterion as long as the method passes the majority criterion.
== Abstract Condorcet Criterion ==
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