I said:
Find, somehow, the probability of all the possible n-member ties & near-ties, before your vote is cast (last). For each of the 2^N ways that you could vote, a sum can be written, each of whose terms multiplies the probability of a tie or near-tie by the difference in the utility of what would happen if you didn't change that tie or near-tie and what would happen if you did. Find the way of voting that maximizes that sum. I meant: Using Hoffman, or individual candidates' vote total probability distributions, etc, find the probabilities of all of the possible n-member ties & n-member near-ties, before your ballot (the last ballot) is cast. For each of the 2^N ways of voting, a sum can be written, with a term for each possible n-member tie or n-member near-tie, with the probability of that tie or near-tie multiplied by the utility difference between the outcome if the tie or near-tie occurs and you vote and your ballot would change that tie or near-tie, and if you don't vote. Of course the utility of a tie in the final count is the average of the utilities of the candidates in the tie, since they're all equally likely to be chosen by the random tiebreaker. Find the way of voting that maximizes that sum. [end of definition] That's what I mean by Weber's method. Of course it has a very simple implementation when the many-voter simplifying assumptions are permissible. 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
