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Line 1: The "'''~~BPW~~beat-the-plurality-winner method'''" (~~for~~or "'''~~Beats~~BPW ~~Plurality Winner~~method'''") 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 ~~only~~mainly ~~defined~~described for upthe tocase of three candidates ~~and doesn't have an obvious way of being expanded to more~~. In the absence of a CW[[Condorcet winner]], one elects the candidate who defeats the [[~~FPP~~first-past-the-post]] winner pairwise. == 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. This may be prone to ties. 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. Kevin Venzke suggests generalizing the method using a modification of the chain climbing mechanism (e.g. "[[total approval chain climbing]]" or "TACC"). The steps: # 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 "beat-the-plurality-winner" 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 ==