Beat-the-plurality-winner method: Difference between revisions

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== Notes ==

Stensholt suggests defining the "Beat the Plurality Winner" for more than three candidates by reducing to the Smith set and conducting the basic method on each possible set of three candidates, awarding a point to the BPW winner of each set, so that the overall winner is the one who wins the greatest number of these contests.

Stensholt suggests defining the "Beat the Plurality Winner" for more than three candidates by reducing to the Smith set and conducting the basic method on each possible set of three candidates, awarding a point to the BPW winner of each set, so that the overall winner is the one who wins the greatest number of these contests. This may be prone to ties.

Kevin Venzke suggests generalizing the method using a modification of the chain climbing mechanism of e.g. [[TACC]]. Initialize an empty set. Consider each candidate in order of descending first preference count. When a candidate pairwise defeats all (if any) candidates currently in the set, then add them to the set. The last candidate who can be added to the set is elected. This agrees with BPW in the three-candidate case since, in the absence of pairwise ties, the winner is always either the Condorcet winner or the candidate of the cycle who pairwise beats the first preference count winner.

Kevin Venzke suggests generalizing the method using a modification of the chain climbing mechanism of e.g. [[TACC]]. Initialize an empty set. Consider each candidate in order of descending first preference count. When a candidate pairwise defeats all (if any) candidates currently in the set, then add them to the set. Otherwise continue to the next candidate. The last candidate who can be added to the set is elected. This agrees with BPW in the three-candidate case since, in the absence of pairwise ties, the winner is always either the Condorcet winner or the candidate of the cycle who pairwise beats the first preference count winner.

== References ==