Yesterday, when I said that, having estimated the 2 top votegetters, and their probabilities of outpolling eachother, one could then estimate their win probabilities. But if that's done based on those other estimates named here, that can lead to mutually contradictory estimates, and that suggests that, if it seems easiest to estimate the top-2, and their probabilities of outpolling eachother, and if we want to use Weber, then there might be a better way of using that information.
I'm only talking about 2-way ties. When I say "tie" I mean "tie or near-tie". Joe showed that the probability of a certain 2 candidates being the top two votegetters isn't necessarily the same as their probability of being the candidates in a tie for 1st, if there is one. But if we have no information suggesting that the likelihood of a tie for 1st is more or less likely depending on who the frontrunners are, then isn't it ok to make that assumption that those probabilities are the same? Say it's 80% that X & Y are the top 2, and 70% that X outpolls Y, and 30% that Y outpolls X (not counting the tiny probability that they poll the same). For Weber's method, Pxy is .8 Say we estimate a 2% chance that neither X nor Y will be a frontrunner. The probability of a tie between X & Z is (.18)(.7)*Pfz, where Pfz is Pz divided by the sum of the Pi of everyone but X & Y. Those other candidates' Pi can be gotten by Tideman, as I've talked about, and can be used to determine tie probabilities of their pairs. Mike Ossipoff _________________________________________________________________ Chat with friends online, try MSN Messenger: http://messenger.msn.com ---- For more information about this list (subscribe, unsubscribe, FAQ, etc), please see http://www.eskimo.com/~robla/em
