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Condorcet winner criterion: Difference between revisions
→Multi-winner generalizations
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3 B1(>A)</blockquote>Now both of A and B1 are weak CWs, because they both pairwise tie each other. In this particular example, since there is nothing that distinguishes either candidate from the other, the neutrality criterion requires that both A and B1 must have an equal probability of winning i.e. both must have a 50% chance. This means that removing clones of B1 increased B1's chances of winning (which were originally at 0%, since A was guaranteed to win earlier i.e. had a 100% chance of winning.) <ref>https://arxiv.org/abs/1804.02973v6 p. 206-207</ref>
Note that the Condorcet criterion also implies the following criterion which is somewhat related to Independence of Irrelevant Alternatives: removing losing candidates can't change the result of an election if there is a Condorcet winner. <ref>https://arxiv.org/abs/1804.02973 The Schulze Method of Voting p.351 "The Condorcet criterion for single-winner elections (section 4.7) is important because, when there is a Condorcet winner b ∈ A, then it is still a Condorcet winner when alternatives a1,...,an ∈ A \ {b} are removed. So an alternative b ∈ A doesn’t owe his property of being a Condorcet winner to the presence of some other alternatives. Therefore, when we declare a Condorcet winner b ∈ A elected whenever a Condorcet winner exists, we know that no other alternatives a1,...,an ∈ A \ {b} have changed the result of the election without being elected."</ref>
== Multi-winner generalizations ==
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When M=1, the generalization reduces to the ordinary Condorcet criterion as long as the method passes the majority criterion.
Note that Bloc Ranked Pairs and Bloc Score voting (if scored methods are considered) would pass this criterion, though they are not proportional, and the latter is not a Condorcet method in the single-winner case. So it may make more sense to consider Schulze's criterion as one of several that a multi-winner method ought to pass to be considered a Condorcet multi-winner or Condorcet PR method, rather than the definitive one.
== Abstract Condorcet Criterion ==
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