At 06:25 PM 7/31/2007, Peter Barath wrote: > >>"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."
The statement is not correct. With some patterns of utilities and probabilities, intermediate votes are not suboptimal at all. I'll give an obvious counterexample. I'm working on exact numbers, but it looks currently like the suboptimality of the "sincere" Range vote takes place when it is *not* fully sincere, because the resolution does not allow an exact sincere expression. The error can then make the Range vote suboptimal. And this is a work in progress, and I'm not aware of any formal study, only theories, which can be drastically incorrect unless rigorous. At the time that Warren Smith wrote the above, he had not read, I think, Schudy's paper, he was responding to the comment as made, which was made here without the qualification. The study I'm working on is the zero-knowledge case. It's obvious that if you have a two-candidate election, your sincere vote is Approval style, even if the election method allows more resolution, and the same is effectively the case when there are more candidates, but you judge them moot, even if they include your favorite. With a large number of voters in the simple Range 2 election, the sincere vote we postulated of 2, 1, 0 had the same expected utility as 2, 2, 0 or 2, 0, 0. But to come to this result we had to neglect three-way ties; the greatly increased possibility of this is the reason that the optimal Approval vote is not balanced in the small election case. If the utility is the same, it cannot be said that voting sincerely is "suboptimal." Rather, what can be said about this case is that either strategy is "optimal," there is no cost to voting sincerely. And there is a cost in regret to having voted insincerely. If you vote sincerely and lose, you will think, "I did my best." If you exaggerate, and lose because of that, you will be kicking yourself. "Why didn't I just tell it like it was?" Hard to quantify this, but it is a reasonable assumption that there is a value to sincerity and accuracy, independent from actual strategy, such that if strategies are equally effective, the sincere one is better. >"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." Okay, counterexample to the principle. A group of people are going to place bets on the number of beans in a jar, to win a prize. They look at the jar, and use some method to estimate the number. If they guess it exactly, they get a much bigger prize than if they are merely the closest guess. Now, you are ten of these people, say you are all one family, there is no competition between you. Any one of you winning the prize is the same as any other one, your interests coincides. How should you guess? If you only had one chance, you would use your estimate, best shot. But if you have ten chances, you would spread them. Further, there is a specific problem here. In order to prove that the optimal strategy is to vote Approval style, Ossipoff is *assuming* that the optimal strategy is approval style.... He merely does not give the individual voter a chance to vote any other way. Now, if I look only at the situations where the voter can influence the outcome, in a Range 2 3-candidate election with sincere utilities of 2, 1, 0, zero knowledge, the sincere vote and the two possible Approval Votes all have the same expectation, 40% over not voting. If I do the same, making the election Approval, the expected utility is 33% over not voting. There is an assumption in Ossipoff's "proof" that a series of decisions, optimized, must be the same as a set of individual decisions multiplied by the number in the series. Suppose we were trying to make a course correction. We can do it with ten small moves or one large one. What is the optimum move to make? If we look at the small correction, we will see that it is binary, perhaps. We make a full move to swing our direction in one way. If we make a series of these identically, however, we overcorrect. If we are going to make a series, we will make some in one direction, and some in the other, with some net effect. If we do it all at once, we would want to use some intermediate force. So I'm highly suspicious of the "proof," and attaching words like "linear programming" to it doesn't help, unless the specific principle and its application is examined. >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. But this clearly doesn't work in control systems where some precision is involved. >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. Well, this is a different case than saying, "Optimal strategies never vote anything other than 0 or 1, so range voting complicates ballots and confuses voters for little or no gain." The first part is false, as stated. It can be equally optimal to vote "sincerely." (The language is loaded, I do not define an Approval style vote as "insincere," as long as preferences are not reversed.") Secondly, the conclusion does not follow. It presumes that the only function of elections is to determine the winner. The performance of losers is also of great interest and effect. Intermediate ratings, we think, have a value in expressing much more accurately what the gap was between winner and loser. *How* much would a candidate have had to rise in rating to win*? If people vote Approval style, which they properly are free to do, this information is lost. There is a value to the information. Further, the zero knowledge case is a special one. I used it for my study because it is simpler. But it is not realistic. Most people have some idea who is likely to win the election, and especially they usually know if it is a certain pair, and sometimes there are three. Approval style votes can make very much sense if you know a pairwise contest is the real one. It is obvious that if this knowledge is strong, your optimal vote is Approval style. For those two candidates. What about others? To claim that there is no value to these other votes is utterly without basis. It is an *opinion* of the voter, not a fact, that this is the pairwise contest. And voting intermediate votes for candidates that the voter does not expect to win can have no negative impact on the expected utility for that voter. And it has another value: individual voting strategy does not determine the overall benefit of the election to society. It may be true that voting Approval style is optimal strategy for the individual, but it does not follow that this optimizes the value to society of the election. We consider public methods and procedures based on overall public benefit, and it is clear that voting Approval style reduces the information available for doing this. It is like having a series of sensors for light. We could have analog sensors that give us a range of values for the light, or binary ones that tell us that the light is above a certain threshhold. Which one can give us better vision for making decisions? If we have the analog ones, and we want to, we can convert them to binary. But we can't convert the binary to analog, particularly if there is a systemic bias. Sometimes we can average together a lot of binary values and get a refined value, but as it was described above, if you take each example and make a determination on it, which way should it go, you can bias the outcome. When you are going to average together a lot of binary values, it helps to introduce noise, which causes the binary information to become far more accurate when averaged together. It is as if you are making a lot of binary measurements with different cutoff levels. And this may explain why the expected outcome is better, under the conditions stated, for Approval Voting strategy, if the election is Range. Maybe. At this point this is a conjecture. (To really know that the expected outcome is better, I need to determine the absolute utilities, I haven't done that yet.) >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 ---- Election-Methods mailing list - see http://electorama.com/em for list info
