[EM] non-transitive ranked pairs

[Jameson Quinn]

At a first glance, this seems to be a definition that's equivalent to
Schulze.

2011/11/1 Ross Hyman <rahyman at 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
>
>
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.electorama.com/pipermail/election-methods-electorama.com/attachments/20111101/96d6619b/attachment-0004.htm>