[EM] Few-voters strategy approaches?

[MIKE OSSIPOFF]

In Approval,
a voter is just as likely to vote A over B as B over A.
And isn't a voter equally likely to vote A & B the same as vote them
different? And isn't he just as likely to vote them the same by
voting for both as vote them the same by voting for neither?

If so, then that suggests that there are 4 equally likely ways for
him to vote, between A & B. A over B, B over A, A & B, Neither A nor B.

Maybe, from those facts it can be determined how likely it is that
A will get the same number of votes as B. And how likely it is that
A will get one vote fewer than B.

Is that problem something that would be helped by the binomial distribution 
or something like it? Joe, I'll bet that you could
write the very-few-voters, 0-info, Approval strategy.

And would that enable the calculation
of the probability that a certain set of candidates will share 1st
place, and a certain set will have one voter fewer? Of course
those are the same no matter which candidates are in those sets.
So could that lead to the probability that n candidates will be in
1st place, with m having one vote fewer?--before you vote?

Each tie with some particular n candidates in 1st place & some particular
m candidates with one vote fewer gives a certain worth to your vote for
some particular candidate, given some fixed assumption about your other
votes.

The 1st assumption is that you're voting for your favorite, and not
for anyone lower than 2nd choice, for the purpose of determining the
worth of voting for your 2nd choice. Then, if you're not voting for him,
you're done. If you're voting for him then, with the assumption that
you're voting for your 1st & 2nd choices, but for no one lower than
3rd choice, determine the worth of voting for your 3rd choice...etc.

I don't know if this overall approach would get anywhere. I just mention
it because it occurred to me. My voting system work, discussion &
debate hasn't involved this kind of a probability/statistics problem,
and so I'm out of my element when I talk about it.

The goal of course would be a formula for determining the worth of
voting for a particular one of your ranked choices, based on the
candidates' utilities for you, the number of candidates, and the number of 
voters. I don't know if the suggestions in this letter are on the
right track, but I wanted to mention them. One would hope that that
formula could be evaluated in a convenient amount of computing time,
unlike the task of looking at every way that every voter could vote.

Mike Ossipoff


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