Beat-the-plurality-winner method: Difference between revisions
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'''BPW''' (for ''' |
'''BPW''' (for '''Beat the Plurality Winner''') is a Condorcet completion method invented and studied by Eivind Stensholt as an attempt to reduce burial incentive.<ref>{{cite journal | last=Stensholt | first=Eivind | title=Condorcet Methods - When, Why and How? | journal=SSRN Electronic Journal | publisher=Elsevier BV | year=2008 | issn=1556-5068 | doi=10.2139/ssrn.1145304}}</ref> It is mainly described for the case of three candidates. In the absence of a CW, one elects the candidate who defeats the [[FPP]] winner pairwise. |
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== Notes == |
== Notes == |
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Stensholt suggests defining BPW 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. |
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One could potentially extend BPW to all elections by 1) first eliminating everyone not in a particular set (i.e. the [[Smith set]]) before running BPW, and/or 2) using another voting method to reduce the number of candidates down to three. |
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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. |
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== References == |
== References == |
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Revision as of 18:13, 3 May 2022
BPW (for Beat the Plurality Winner) is a Condorcet completion method invented and studied by Eivind Stensholt as an attempt to reduce burial incentive.[1] It is mainly described for the case of three candidates. In the absence of a CW, one elects the candidate who defeats the FPP winner pairwise.
Notes
Stensholt suggests defining BPW 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.
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.
References
- ↑ Stensholt, Eivind (2008). "Condorcet Methods - When, Why and How?". SSRN Electronic Journal. Elsevier BV. doi:10.2139/ssrn.1145304. ISSN 1556-5068.