At 04:36 AM 7/26/2007, Michael Ossipoff wrote: >I'm not replying to Lomax's rebuttals because that would be sending >some unnecessarily long postings to you, and because I'm firmly >convinced that everything he says is answered in my recent postings. >I won't read any posting that I don't intend to reply to. Why >subject myself to it if I'm not going to subject you to it? :-)
Excellent advice, he's giving himself. Helps us, too. However, one point. I'm offering a counterexample to what he's been claiming, over and over, without proof other than abstract theorizing that bristles with assumptions that may not be true. I would suggest one thing to Mr. Ossipoff if he is truly interested in the matter. I have proposed a method for easily determining the exact expected utility for various vote patterns for a voter, voting in a many-voter environment with zero knowledge, Range 2, and the results show higher utility for sincere range strategy than for approval strategy. I've given the exact numbers, and have described the method in detail. Anyone could do it with a sheet of paper and a pencil. I also offered the spreadsheet, just to make it simple for those with access to a spreadsheet program. (There is also googledocs for people without their own computer, even, writing at a library, as Ossipoff used to do sometimes.) Ossipoff has not responded *at all* to the many-voter claim. Perhaps he was misled by the fact that I first described the 2-voter situation, and made an error in it, an error, interestingly, that I was led into by assuming that something Ossipoff had written was correct, that the vote 220 was of the same utility as 200, if the voter had sincere utilities of 210. Seems obvious. Isn't true, *unless* the number of voters is large. Put it another way. It isn't true, period. The optimal vote is 200, if we are limited to approval style votes. The difference in utility disappears in large elections, gradually decreasing with size, because it depends on three-way ties, which cause a loss of utility for the Approval vote. Three-way ties become vanishingly rare. If a two way tie has probability of P, then three-way ties should have, roughly, zero-knowledge, a probability of P^2. I neglect them in my many-voter analysis, which, not surprisingly, shows both Approval votes as having the same utility. But that utility difference remains, albeit increasingly small, so the statement that there is no difference was false, and blatantly false in the 2-voter case, which I was examining at the time. I then moved on to the many-voter case, finding a way to generalize the approach. If there is something wrong with that, all that I've been asserting could be wrong. I really would appreciate it if anyone, including Ossipoff, irritating as it might be, would find any errors in it. The approach is simple and has been described many times. I won't describe it again here, at least not now. ---- Election-Methods mailing list - see http://electorama.com/em for list info
