Adam was quoted:
>Adam was more helpful, with a rule I could follow: Approve whichever >candidate I prefer among the expected front runners, and approve all the >candidates I like better than that one. That's an easily-applied strategy, since one thing oftenr relatively obvious is who the 2 strongest contenders are. The above strategy of course is the one that voters use in Plurality. Say we call the two strongest contenders X & Y. It can be fancied up a bit, though. Say the top-2 are equally likely to be the one that outpolls the other. Then, for any other candidate Z, if Z managed to get into a tie for 1st, Z would be equally likely to tie X & Y. So Z should be approved if Z is better than the halfway point between X & Y. That's the strategy described in an journal article that someone once sent me a copy of. I don't remember the authors. We can get a little more elaborate if we estimate the probability that X will outpoll Y, or that Y will outpoll X. If there's a 70% chance that X will outpoll Y, then Z is correspondingly more likely to be in a tie for 1st with X than with Y. Those probabilities for Z, and Z's utility relative to X and to Y, can be used to decide whether we should approve Z. Of course we're talking about some Z whose utility is somewhere between that of X & Y. Of course now we're judging Z by his relative chances of tying X or Y, but we're ignoring the smaller chance of 2 candidates other than X or Y tying eachother. That would be the next natural step, then, in a smooth gradation in elaboratenes: Having identified the 2 strongest contenders, and estimated their probabilities of outpolling eachother, write how likely each is to win, and consider how less likely to win are the other candidates. That's a small additional task. Then we have the Wi, the win probabilities that Weber-Tideman uses. Mike Ossipoff _________________________________________________________________ Join the world�s largest e-mail service with MSN Hotmail. http://www.hotmail.com ---- For more information about this list (subscribe, unsubscribe, FAQ, etc), please see http://www.eskimo.com/~robla/em
