Mutual majority criterion: Difference between revisions
→Bucklin approach
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==== Pairwise counting ====
Note that the mutual majority set is a pairwise-dominating set (every candidate in it [[pairwise]] beats every candidate not in it). So one way to find it would be to find the [[Smith set ranking]], and then look for the smallest group of candidates highest in the Smith ranking who are preferred by a mutual majority, if there is one.
The smallest mutual majority set can be found in part by looking for the [[Smith set]], because the Smith set is always a subset of the mutual majority set when one exists, and then adding in candidates into the mutual majority set who are preferred by enough of the voters who helped the candidates in the Smith set beat other candidates to constitute a mutual majority. Example:
35 A>B
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The Smith set is just B here. When looking at the 70 voters who helped B beat C and the 65 for B>A, it's clear that a majority of them prefer A over C, and that an absolute majority of voters prefer either A or B over C. So the smallest mutual majority set is A and B.
==== Bucklin approach ====
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