Your DP and ABE criteria are talking about systems not having a problem with the chicken dilemma. Unfortunately, while satisfying these criteria is a good thing if the honest preferences have a chicken dilemma situation (Two near-clones and one opposition candidate who could beat either but not both of them); it is also bad in some cases (a three-way near-tie with sincere bullet-like utilities).
So I suggest you look at how SODA handles the chicken dilemma. Without satisfying your criteria, I believe that it resolves the underlying problem of the chicken dilemma better than any other system I know. JQ 2011/11/1 MIKE OSSIPOFF <[email protected]> > For my definition of 3PD, I should define "discriminate": > > A voter discriminates among a set of candidates iff s/he votes some of > them over others in any order she wants to. > > I referred to a method that I call "DP". That stands for Defection-Proof. > It was proposed by Chris Benham. It doesn't meet CD, > and I guess that only pairwise-count methods can, but it doesn't fail in > the Approval bad-example, something that can be said for > only very few methods. > > Definition of DP: > > Voting is 3-slot: Preferred, Middle, and Bottom. > > Bottom is the default for a candidate not ranked on a ballot. > > To rank a candidate other than at bottom is to "approve" that candidate. > > If the number of voters approving X but not Y is greater than the number > of voters approving Y, then disqualify Y. > > Among the undisqualified candidates, elect the one preferred on the most > ballots. > > [end of DP definition] > > DP meets FBC and 3P, and doesn't fail in the Approval bad-example. > > CD is probably too demanding, referring, as it does, to a Condorcet > candidate. > > Maybe a criterion an be written that better reflects the Approval bad > example (the ABE). > > Maybe something like: > > If a majority prefer A and B to all the other candidates, and if, A would > win if the 1st choice supporters of both candidates > voted both over all the others, then A should win even if A's 1st choice > voters vote B over the others, but the B > voters don't vote A over the others. > > [end of tentative CD definition] > > When I have a good definition to reflect the ABE, I'll call it CD. > > As for the criterion that I've previously called CD, I'll call it CCD > (Condorcet Co-operation/Defection Criterion). > > Maybe someone has already posted about this, but Bucklin gives the voter a > lot more than 3 protection-levels, as I've > defined that term. It gives the voter as many protection levels as there > are rank positions in the voter's ballot. > > So I'll modify the 3P criterion to say "..at least three...", instead of > "...three..." > > And, if a method, like Bucklin, gives an unlimited number of protection > levels, then it meets the > Unlimited-Protection-Levels Criterion, which I abbreviate "UP". > > MDDA meets 3P and 3PD, but fails UP. Bucklin meets 3P, 3PD and UP. > > But, regrettably, Bucklin fails in the ABE. > > Can a method meet UP and not fail in the ABE? > > Yes. IRV (= whole) meets FBC and UP, and doesn't fail in the ABE. > > I now consider IRV (= whole) to be the best method. Certainly the best for > public political elections. > > Between MDDA and DP, I prefer DP, because I consider the ABE to be more > important than > discrimination among candidates protected at a protection-level. > > (Below "ABE" means "doesn't fail in the ABE") > > > A criterion compliance chart: > > -----------------FBC--------3P-----3PD--------UP----ABE > > Bucklin---------Yes--------Yes-----Yes--------Yes----No > MDDA----------Yes---------Yes----Yes---------No----No > DP--------------Yes---------Yes-----No---------No----Yes > MCA------------Yes---------Yes-----No---------No----No > MAMPO---------Yes---------No-----No----------No---No > IRV(= whole)---Yes-------Yes-----Yes--------Yes---Yes > > Mike Ossipoff > > ---- > Election-Methods mailing list - see http://electorama.com/em for list info > >
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