CPO-STV: Difference between revisions

It has not been proven whether CPO-STV is proportional for Droop solid coalitions. However, if it can be, then its cycle resolution method likely must choose from the [[Smith set|Smith Set]] of winner sets in order to do so, as Smith-efficiency guarantees Droop proportionality (the [[Mutual majority criterion|mutual majority]] criterion) in the single-winner case. One procedure that requires among the fewest pairwise comparisons to find one of the Smith Set winner sets is "pair any two winner sets, eliminate the one that loses their pairwise matchup, then repeat until only one winner set remains." Since a winner set in the Smith Set can only be eliminated by another Smith winner set by this procedure, the final remaining winner set will guaranteeably be in the Smith Set. If desired, it is then possible to discover the rest of the Smith Set by checking which winner sets beat or tie the final remaining winner set, which beat or tie these winner sets, etc. One well-known procedure that works along these lines is [[BTR-IRV]].