Condorcet method: Difference between revisions
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Any voting method can be made a Condorcet method by simply adding a condition that a Condorcet winner will win if one exists before running the voting method. It is possible to further make a voting method [[Smith-efficient]] by taking various approaches, such as eliminating candidates one by one until there is a Condorcet winner (like in [[Benham's method]]) or eliminating all candidates not in the [[Smith set]] before running the voting method's procedure. It is common terminology for Condorcet methods that start by electing the Condorcet winner if there is one, but otherwise run some other voting method, to be named as "Condorcet//voting method". For example, [[Condorcet//Score]] is [[Score voting]] modified to elect a CW. The Condorcet methods that start by eliminating all candidates not in a given set of candidates and then run some other voting method are named as "Given set//voting method" (sometimes with only one "/"). For example, [[Smith//IRV]] is [[IRV]] run on the [[Smith set]].
It is possible to do a first round where the [[Smith set]] of candidates is identified, and then a second round where another voting method is used to select among the Smith set (or any set). For example, [[Smith//Approval]] is the automatic form of doing this with [[Approval voting]].
Condorcet methods can be seen as highly related to [[Asset voting]]: the voters indicate their preferences on how they'd negotiate and form majority coalitions for their favorite candidates, and when those candidates aren't viable or aren't in consideration, would intervene to help elect some candidates they prefer more than others. In this sense, extending Condorcet to PR ([[Condorcet PR]]) is not too difficult: [[Droop proportionality criterion|Droop proportionality]] must be met, because Droop quotas can force their preference in any negotiation where each person can only maximally support up to a candidate, and certain other constraints must be met, such as allowing B to win in the following example:
26 A>B
25 B
49 C
because while A does pairwise beat B, C would always have 49 votes and thus actually win overall if the A-top voters try to only support A and not shift towards B, because A would have 26 votes, B 25, but C 49. In general, this type of "semi-solid coalition" where a group of voters are almost a [[solid coalition]] except that some in the group prefer another candidate over the solid coalition's candidates, with no voters outside of the coalition having preferences between the semi-solid coalition's candidates, has to always elect the candidate that everyone in the coalition supports to be related to Asset. In addition, the Condorcet PR method must be based on [[D'Hondt]], because Asset voting allows voters to split their votes to obtain more seats (similar to [[free riding]]).
All Condorcet methods pass the [[mutual majority criterion]] when there is a Condorcet winner. This is because the CW is guaranteed to be a member of any set of candidates that can pairwise beat all candidates not in the set, and the mutual majority set is such a set, because all candidates in it are ranked by a majority over all candidates not in the set. [[Smith-efficient]] Condorcet methods always pass the [[mutual majority criterion]].
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