I keep getting kicked off the list because of alleged bounced e-mails I'm forwarding eskimo.com's returned copy to the list, hence the ">" marks: >This never occurred to me before: With many voters, as in public >elections, we've been assuming, reasonably, that any tie is a 2-way >tie. But I've been continuing to use that assumption, unjustifiably, >for very few voters. > >So anything that I tried to demonstrate about very few voters isn't >really demonstrated. Only my strategies for Richard's original puzzle >example, and the one with thousand-voter blocs are valid. > >It's still true that when Richard's 3 voters are replaced by same-voting >1000-voter blocs, we maximize our expectation by voting only for A, >just as in the original puzzle. This is contrary to Richard's suspicion >that the best strategy in the X1000 election would be to vote for >A & B. > >Also, when we were all talking about Pij, because we thought ties would >be 2-way, Richard said that in his example, the Pij are all the same. >At first it does seem that the 3 candidates are related to eachother in >the same way, before you vote. But they aren't: There's a 50% probability >that the A voter will vote for B, but there's a zero probabililty that the >B >voter will vote for A. That cycle only goes >one way. The candidates aren't related to eachother in the same way. > >Anyway, not it's not demonstrated what 0-info strategy would be when >there are very few voters. It would be necessary to extend the 2-way >tie discussion of many-voter strategy to n-way ties. > >With N candidates, you influence the election by changing an outcome >with a certain n winners to an outcome with m winners who aren't the >same ones. m & n are numbers from 1 to N. > >There are n = 1 to N candidates who share highest vote total before >you vote, and there are 0 to N-n candidates whose >vote totals, before you vote, are 1 less than those other ones. > >If the 1st set contains more than 1, or the 2nd one contains more than >0, then you can affect the outcome. > >I expect that my demonstrations can be extended to n-way ties in this >way, and that it will turn out that even with very few voters, the >expectation-maximizing strategy with 0-info is to vote for all the >above-mean candidates, and for no one else. > >Maybe this has been demonstrated somewhere already. > >Mike Ossipoff > >_________________________________________________________________ >Get your FREE download of MSN Explorer at http://explorer.msn.com > _________________________________________________________________ Get your FREE download of MSN Explorer at http://explorer.msn.com
