EM list-- First, let me correct something that I missed in this letter: >>then with >> >>N1 AB N2 >>N3 BC N4 >>N5 AC N6 >> >>the N numbers must all be rather close for "you" (i.e. John/Mary Q. voter) >>by >>yourself (without any other devious voters) to change the results >>sincerely >>or insincerely. No. In any 1 particular situation there need only be _one_ pairwise defeat that's close enough for us to change, or one pair of pairwise defeats whose magnitudes are close enough for us to tip the balance. Sure, there could be more than one such way that we could change the outcome in a particular situation-- but, given a situation where we can change the outcome, the chance that there'd be two ways we could change it is negligibly small. So always we just look at the situations where there's one way that we could influence the outcome. *** In my reply to David, I got it right in the 2nd to last paragraph, and in the last paragraph, but, because I said it misleadingly througout the rest of the letter, I should clarify it better here: When we have no knowledge about the other voters, it isn't that we _assume_ that all the situations have equal probability-- they _do_ have equal probability from our point of view. So the fact that we have no information about the other voters is itself a piece of information from which we know probabilities, by which we can calculate how various pair-orderings that we vote would affect our utility expectation. *** Of course one reason why this topic is of interest is for the practical purpose of calculating strategy in an actual election. Also, it's interesting to find out what utility-maximization would have us do, with various methods, with various utilities. But maybe, for the purpose of looking at methods in this way, an interesting to find out would be the utility expectation that goes with voting sincerely with various methods and various candidate utilities. We could compare in that way Condorcet, Margins, IRV, Plurality, & Approval. If it turned out that Margins excelled in that respect, that would tend toward weighing against its problems in other areas, somewhat, especially if the good results continued when various kinds of probability information are available. *** Voting sincerely in Approval with 0-info seems naturally to mean using Approval's strategy of voting for all the above-mean candidates. Though it's a mathematical strategy, it's one that doesn't require any calculations to implement, and it sounds sincere to me. *** But speaking of utility, it's been pointed out that if we're considering elections in the future, and we don't know which voter in the example we'll be, then it's in our best interest to want a voting system that maximizes the voters' average utility in the outcome. One that maximizes the sum of the utilities for all the voters. One that maximizes the "social utility" of the outcome. If the distribution of the voters is even, or if its density increases with decreasing distance from the mean & median position, then a candidate at the voter median will also be the one who maximizes social utility. The candidate at the voter median is the SCW too. So if a method does well at picking SCWs, then we can expect it do do excellently by social utility. I don't think anyone's denied that Condorcet does better at picking SCWs than Margins does, and better than IRV does. Therefore, Condorcet does the best job of maximizing your utility expectation for some election in the future after Condorcet is adopted, when you don't know what the example will be or which voter in the example you'll be. Approval, like any method, picks the SCW if voters have complete information about eachother. With 0-info, it does a good job of picking the voter median candidate (and therefore a good job of maximizing social utility) to the extent that the mean position of the candidates coincides with the voter median. That condition can't be guaranteed, though candidates will quickly move toward that position & cluster around it when a better method like Approval is in use. But even if it isn't exactly so, it's a condition that will be approached reasonably well. Mike Ossipoff ______________________________________________________ Get Your Private, Free Email at http://www.hotmail.com
