One other bad mistake I noticed on http://scorevoting.net/MedianVrange.html : "Suppose this *"unhappy with all choices" scenario* happens. When it does, every candidate's median score will be exactly zero. (In contrast: Their * average* scores will generally be distinct nonzero values, and everything will be fine.) Hence Balinski & Laraki's tiebreaking procedure will be invoked. It will elect the candidate with the fewest 0s, which is exactly antiPlurality <http://scorevoting.net/Glossary.html#antipl> voting."
This is not antiplurality voting, it's just approval voting, with any non-zero value representing approval, and the additional assumption that no candidate has a majority of approval. It's a bad situation, with voters who overall dislike all candidates, but it's not the worst voting system to handle the situation. JQ 2011/10/12 Jameson Quinn <[email protected]> > > > 2011/10/12 Clay Shentrup <[email protected]> > >> On Wednesday, October 12, 2011 11:16:52 AM UTC-7, Jameson Quinn wrote: >>> >>> Warren and I had a long technical discussion about strategy incentive in >>> MJ versus range. He did some clever calculations, and I picked holes in >>> them, and we repeated it for several rounds. At the end we hadn't quite >>> completely converged on a consensus, but we both agreed that Range had a >>> greater strategy incentive than MJ. That result seems more robust than a >>> bald assertion from you. >>> >> >> I *think* you're confused. I presume that what you were talking about was >> how often strategy makes a difference, or how much of a difference it makes >> on average. I *don't* believe this changes the ideal strategy one iota. >> You give any candidate you like better than the expected value a max score, >> and others a min score. >> >> This should be *reeeally* obvious. If you think X=7, Y=3, and the scores >> are X={9, 7, 0}, Y={8, 8, 3}, then you vote X=10, Y=0. Now the scores are >> X={10, 9, 0}, Y={8, 8, 0}. X wins. I.e. you just polarize, so that you may >> get lucky enough to have your otherwise median score move the median up or >> down. >> > > This is true. But as the argued below, you can be essentially arbitrarily > certain of getting the same result, if you vote outside a certain band. For > instance, X=9, Y=1 would get you 99% certainty, and X=8, Y=2 would get you > 90% certainty, and your honest X=7 Y=3 would get you 70% certainty. (These > are arbitrary numbers; in real life, they'd be based on historical scores of > the top two candidates) > >> >> >>> The point is, even with zero information on a particular candidate, you >>> have a pretty good historical benchmark for the median scores of the first >>> and second place candidates. Outside of that range, you have a safe leeway >>> to be honest. >>> >> >> This is a flawed argument. You're saying it's very improbable that the >> scores will exceed those historical norms, so you should take the tiny risk >> of casting a weak vote, for the sake of honesty/expressiveness. But with >> ordinary Score Voting, there's an incredibly tiny probability that your vote >> will make a difference, so you might as well be honest. This is >> statistically equivalent. >> > > Not comparable at all. In any voting system at all, your chances of being > decisive are epsilon. In this case, your chances of even having any impact > at all on the margin of victory are epsilon. The chance of that impact then > being decisive are epsilon squared. Separate issues. > > >> >> >>> And it seems that MJ reacts much worse to such plausible behaviors. >>>> >>> >>> ??? What are you even talking about? If everyone exaggerates, MJ and >>> range are identical; they're both approval. And if a fixed X% of voters >>> exaggerate, it has a bigger effect on Range than MJ; that's an implication >>> Warren's result that I mentioned above. So you're 180 degrees wrong here. >>> >> >> If most (but not all) exaggerate, then you can get very weird results like >> Warren describes here. >> http://scorevoting.net/MedianVrange.html >> > > Are you talking about the bimodal distribution stuff at the bottom? That's > an issue when one candidate is exaggerated but others aren't. But if some > voters exaggerate across the board, it is at worst as bad as approval. It > degrades to approval less smoothly than range - that is, the effect of > exaggeration is smaller if few people exaggerate, and larger if many people > exaggerate. I believe that that's superior, because it makes > all-honest-voting into a more stable state (actually an equilibrium under > certain plausible assumptions, but even if not an equilibrium, still more > stable than Range). > > >> >> I speculate that you may be misunderstanding Warren's result. But it would >> be nice to see Warren's result instead of speculating. Could someone post it >> here or add it to the page? >> > > http://scorevoting.net/MedianAvg1side.html > >> >> Oh, and aside from calculations of how often strategies work and such, did >> Warren ever get actual BR figures for MJ? >> > > I don't know. > > JQ > >
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