>>"Range voting is a generalisation of approval voting where you can >> give each candidate any score >>between 0 and 1. Optimal strategies never vote anything other than >> 0 or 1, so range voting >>complicates ballots and confuses voters for little or no gain." >> >>Ossipoff: Warren Schude's statement was correct
>--CORRECTION: optimal strategies can vote other than 0 and 1, and >voting 0 or 1 can be suboptimal. Seems you were not so assiduous as to actually read the footnotes in Warren Schudy's paper, which in this particular case (footnote number 1) reads: "As long as the population is sufficiently big and uncertain." And in that case we may nicely agree, I guess. I think Michael Ossipoff's analysis: "Suppose that the method is 0-10 RV... Now, suppose that you consider the points that you're awarding one-at-a-time, as if it were a series of 10 Approval elections... We're assuming that it's a public election, so that there are so many voters that your own votes have no significant effect on the probabilities. Your Approval strategy is based on two things: The candidates' utility to you, and the probabilities that you estimate... Your utilities don't change during that series of 10 Approval elections that you vote. The probability estimates don't change either... If you give to a candidate any points at all, you give hir 10 points." is informal, but fully correct. (Which doesn't mean I agree with him in everything else.) And those who refer to linear programming essentially say the same thing. If the field is big enough, a small part of it may be considered as having linear probability-distribution (or whatever) functions, so the optimum lies somewhere on the border. So if you started to go to a direction you have to stay on that course. So, they say if the number of voters goes toward infinity, the probability of a case where Approval-style voting is suboptimal goes toward zero. The counterexamples? most of them have extremally small number of votes. And even which does not so, uses the less-then infinite, non-linear attributes or simply wrong. http://beyondpolitics.org/Range2Utility.htm when shifts from Range(0,1,2) to Approval, calculates like those "odd number" cases would simply vanish. And vanishing some good vote value, the average worsens when Approval becomes the method. But those cases don't vanish. The logical statistic assumption is that they evenly distribute themselves among the neighboring cases. And some of previously irrelevant cases become relevant cases, so the probability of decisive vote rises. This rise exactly compensates for the loss of utility rise. As for http://rangevoting.org/RVstrat5.html it's more reality, but only by using the three-candidate-tie event, attributed with a T probability. If T=0, the classic case happens: giving the in-between B candidate max or min is optimal, or all the same. And if the number of voters goes toward infinity, T goes toward zero. So, please, don't infer "which graduation is best for range voting" type statements from these calculations. We can go back to the consensus (used even in your simulations) that _essentially_ a strategic Range vote is an Approval vote. Which doesn't decide which one is better. Valid arguments exists on both sides. Range voters can choose from more possibilities, but is this choice a pleasant one? I can be a "sucker" or a "cheater", maybe I would be more glad without it. I think they are so close that even their fans can be close and fight side by side. I'm looking for the future when TV-personalities as well as people at the coffee machine dispute about whether Approval or Range is better method. Peter Barath ____________________________________________________________________ Tavaszig, most minden féláron! ADSL Internet már 1 745 Ft/hó -tól. Keresse ajánlatunkat a http://www.freestart.hu oldalon! ---- Election-Methods mailing list - see http://electorama.com/em for list info