[EM] Few voters make n-way ties.

[MIKE OSSIPOFF]

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
>
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