At a first glance, this seems to be a definition that's equivalent to Schulze.
2011/11/1 Ross Hyman <rahy...@sbcglobal.net> > Ranked Pairs and all of its variants that I am aware of abhor > non-transitivity. Here is a variant of Ranked Pairs that embraces > non-transitivity. Despite being non-transitive, it elects a unique > winner, the Condorcet winner if there is one. In the cases I have looked > at, the winner is also the Schulze winner. Is it always? > > > > Candidates are classed in two categories: Winners and Losers. Initially, > all candidates are Winners. Every candidate has an associated List of > candidates that have defeated it. Every candidate initially has a List > composed of itself and no other candidates. The method is so affirming > of non-transitivity that it even treats each candidate as a > non-transitivity loop unto itself. Winners are those candidates who have > no Winners in their List aside from themselves. > > > > Rank the pairs in a strict order, in the same order one would use for your > favorite strict order transitive variant of Ranked Pairs. Affirm each > pair in order, from highest ranked to lowest. When A > B is affirmed, > the List for candidate A is added to every List that includes candidate B > (not just candidate B’s list). All Winners that now have other Winners > in their List are reclassified as Losers. The count can be ended when > only one Winner remains since affirming the remaining pairs cannot make the > Winner a Loser. Provided that every pair is ranked into a strict > ranking, and each pair expresses a definite ranking between the two > candidates in the pair, there is guaranteed to be one Winner. > > > > Example election from: http://www.cs.wustl.edu/~legrand/rbvote/desc.html > > Brad > Erin 623, 298 > > Erin > Dave 610, 311 > > Dave > Brad 609, 312 > > Abby > Erin 511, 410 > > Abby > Dave 485, 436 > > Brad > Abby 463, 458 > > Abby > Cora 461, 460 > > Brad > Cora 461, 460 > > Dave > Cora 461, 460 > > Erin > Cora 461, 460 > > > > Each Candidate begins as a Winner with only itself on its List. > > Abby(W): Abby(W) > > Brad(W):Brad(W) > > Cora(W): Cora(W) > > Dave(W): Dave(W) > > Erin(W): Erin(W) > > > > The first affirmed pair is Brad> Erin. Brad’s List is added to Erin’s > List, the only one that includes Erin. > > Abby(W): Abby(W) > > Brad(W):Brad(W) > > Cora(W): Cora(W) > > Dave(W): Dave(W) > > Erin(L): Erin(L), Brad(W) > > Erin is now a Looser. > > > > The next pair to be affirmed is Erin > Dave. Erin’s List is added to > Dave’s List, the only one that includes Dave. > > Abby(W): Abby(W) > > Brad(W):Brad(W) > > Cora(W): Cora(W) > > Dave(L): Dave(L), Erin(L), Brad(W) > > Erin(L): Erin(L), Brad(W) > > Dave is now a Looser. > > > > The next pair to be affirmed is Dave > Brad. Dave’s List is added to > Brad’s and Erin’s Lists, since both include Brad. > > Abby(W): Abby(W) > > Brad(W):Brad(W), Dave(L), Erin(L) > > Cora(W): Cora(W) > > Dave(L): Dave(L), Erin(L), Brad(W) > > Erin(L): Erin(L), Brad(W), Dave(L) > > Brad is still a Winner. > > > > The next pair to be affirmed is Abby > Erin. Abby’s List is added to > Brad’s, Dave’s, and Erin’s Lists, since they all include Erin. > > Abby(W): Abby(W) > > Brad(L):Brad(L), Dave(L), Erin(L), Abby(W) > > Cora(W): Cora(W) > > Dave(L): Dave(L), Erin(L), Brad(L), Abby(W) > > Erin(L): Erin(L), Brad(L), Dave(L), Abby(W) > > Brad is now a Looser. > > > > The next pair to be affirmed is Abby > Dave. The Lists do not change. > > > > The next pair to be affirmed is Brad > Abby. > > Abby(W): Abby(W), Brad(L), Dave(L), Erin(L) > > Brad(L):Brad(L), Dave(L), Erin(L), Abby(W) > > Cora(W): Cora(W) > > Dave(L): Dave(L), Erin(L), Brad(L), Abby(W) > > Erin(L): Erin(L), Brad(L), Abby(W), Dave(L) > > Abby is still a Winner. > > > > The next affirmed pair is Abby > Cora. > > Abby(W): Abby(W), Brad(L), Dave(L), Erin(L) > > Brad(L):Brad(L), Dave(L), Erin(L), Abby(W) > > Cora(L): Cora(L), Abby(W), Brad(L), Dave(L), Erin(L) > > Dave(L): Dave(L), Erin(L), Brad(L), Abby(W) > > Erin(L): Erin(L), Brad(L), Abby(W), Dave(L) > > Cora is now a looser. > > > > Abby is the winner of the election. > > ---- > Election-Methods mailing list - see http://electorama.com/em for list info > >
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