|
James G-A, You wrote (Fri.Mar.18): I agree that Raynaud is easy to explain. I don't know about Gross Loser, though... Winning votes is most intuitive to me. "This candidate was opposed by 60% of voters in a pairwise contest! Eliminate him! Bam!" I guess the GL equivalent would be "This candidate only got 30% of the vote in a pairwise contest! Eliminate him! Bam!" I dunno... maybe.The % sign here is a bit out of place and potentially misleading. I think GL is much more intuitive than WV (or PO) because the opposition could be from a subsequently eliminated candidate, which seems to render it less meaningful. In GL, you are looking at the pairwise matrix among remaining candidates and then you eliminate the loser with the smallest tally. What could be more natural than that? "Raynaud (GL): Until one candidate remains, repeatedly eliminate the candidate with the fewest votes in any of the pairwise comparisons among the remaining candidates." I think that I understand your definitions. Can you prove that Raynaud(GL) meets this criterion?Yes! Plurality says that if any x has more first-place votes than y has above-last-place votes, then y can't win. Of course x pairwise beats y, and x's first-place votes contribute to x's score in all x's pairwise contests. x has more of these votes than y has above-last-place votes; so while y is still around x can't be eliminated. Therefore y can't win. Raynaud(GL) meets (mutual)Majority, all the Condorcet properties, Plurality, Clone Independence, of course mono-add-plump Personally, I don't care a lot about random fill incentive... but are you sure that it doesn't exist in this method? It seems like it would generate some sort of queer incentive, but I don't know exactly what kind yet.I didn't mention random-fill incentives. I now think that with the right combination of other properties, a random-fill incentive can on balance be a good thing! I object far more to the "equal-rank near the top" incentive that exists for some voters (including "zero-info." voters) in equal-ranking allowed Winning Votes defeat-dropper. Am I sure that Raynaud(GL) meets NZIS? Yes. In the zero-info case, the voter declining to participate in a paiwise comparison in which the voter has a preference does nothing except make it more likely that the less preferred of the two candidates will win. Because it is far less vulnerable to Burying, I do actually prefer it to the "defeat droppers"! Hang on a moment... when did we establish that Raynaud was far less vulnerable to burying than defeat dropping methods?? I mean, if it is, that's great, but I don't remember anyone demonstrating that...Looking at it more closely, I may have exaggerated. Probably instead of "far less" I should have written "significantly". But I do have a weak Burial-related criterion that Raynaud(GL) meets and the Defeat-droppers fail, I'll save that for a later post. Chris Benham |
---- Election-methods mailing list - see http://electorama.com/em for list info
