Thank you for the article, as it was informative. It is very true that Elimination methods tend to eliminate candidates who could go onto become winners.
QLTD doesn't have a single loser to eliminate (it doesn't mention losers much either). In fact I worn against first-past-the-post methods (vanilla QLTD) (that's why I go with the "converse" way--the elimination way), as they are susceptible to Burying mentioned here http://en.wikipedia.org/wiki/Tactical_voting what I think the original article (http://www.mcdougall.org.uk/VM/ISSUE6/P4.HTM) tries to show is QLTD has a problem with a subset criterion to monotocity he called mono-add-top (which is very close to the Participation criterion). My method doesn't have that problem. Let me use his example (though I have some mild problems with the Droop Quota now, I'll still use it for these calculations). Election 2: abcdef 12 votes cabdef 11 votes bcadef 10 votes def 27 votes when adding: ad 6 votes Pre add: Votes: 60 Quota: 31 Round 1: 1: 2.8 2: 2.818182 3: 2.833333 4: 3.121212 5: 4.121212 6: 5.121212 Candidate 6 has the worst multiplier and was removed. Round 2: 1: 2.421053 2: 2.450000 3: 2.476190 4: 3.121212 5: 4.121212 Candidate 5 has the worst multiplier and was removed. Round 3: 1: 1.950000 2: 2.000000 3: 2.047619 4: 3.121212 Candidate 4 has the worst multiplier and was removed. Round 4: 1: 1.500000 2: 1.571429 3: 1.578947 Candidate 3 has the worst multiplier and was removed. Round 5: 1: 0.849315 2: 1.205479 Candidate 2 has the worst multiplier and was removed. Final order from worst to best: 6, 5, 4, 3, 2, 1. Post add: Votes: 66 Quota: 34 Round 1: 1: 2.500000 2: 2.960000 3: 2.962936 4: 3.030303 5: 4.115942 6: 5.072464 Candidate 6 has the worst multiplier and was removed. Round 2: 1: 2.263158 2: 2.545455 3: 2.565217 4: 3.030303 5: 4.085714 Candidate 5 has the worst multiplier and was removed. Round 3: 1: 1.800000 2: 2.130436 3: 2.166667 4: 3.030303 Candidate 4 has the worst multiplier and was removed. Round 4: 1: 1.350000 2: 1.625000 3: 1.636364 Candidate 3 has the worst multiplier and was removed. Round 5: 1: 0.800000 2: 1.247059 Candidate 2 has the worst multiplier and was removed. Final order from worst to best: 6, 5, 4, 3, 2, 1. (Notice, it was unchanged. Not very "chaotic", wouldn't you say?) On 6/9/12, Kevin Venzke <[email protected]> wrote: > Hi Nicholas, > > I think that your basic method (page 2 of html version) is the same as > > QLTD: > http://www.mcdougall.org.uk/VM/ISSUE6/P4.HTM > > I say this because the multiplier is expressed in terms of ranking slots > and a candidate is allowed to win with only part of a subsequent slot > instead of only in increments of entire slots. > > > So your full method is what I would call "QLTD elimination" because you > repeatedly eliminate the QLTD loser. (Hopefully I haven't misunderstood > > the definition.) > > > Elimination+Recalculation methods are bad for monotonicity because the > > way information can be used for or against candidates is usually not > > predictable. It would need to be quite clear how other candidates will > > fare when another candidate is eliminated. > > Participation is satisfied by simple point scoring methods. I doubt it is > compatible with elimination+recalculations. The problem is that you need > to guarantee each voter that information will only work in certain ways, > but eliminations tend to have chaotic results. > > > ______________________________ >> De : Nicholas Buckner <[email protected]> >>À : Kristofer Munsterhjelm <[email protected]> >>Cc : [email protected] >>Envoyé le : Samedi 9 juin 2012 4h04 >>Objet : Re: [EM] Throwing my hat into the ring, possibly to get trampled >> >>Thank you for that information. I thought IIA referred to adding of >>irrelevant alternatives, not removing them. As a consequence I didn't >>look as strongly at criterions I thought were incompatible, from the >>Condorcet criterion group. > > Basically adding them is a problem if removing them is. If there are only > two > candidates A and B and you add a new candidate C, and change the winner from > > A to B, then you could also take the new situation, and remove C from it, > and > thereby change the winner from B to A. > > You wrote originally "I developed an alternative method that takes the > > Independence of Irrelevant Alternatives path over the Condorcet path." Do > you > know that we don't have *any* serious rank methods that satisfy IIA? For > example, STV doesn't satisfy it either. > > Kevin > > ---- Election-Methods mailing list - see http://electorama.com/em for list info
