[EM] B must be more than just above mean

[MIKE OSSIPOFF]

It's occurred to me that if Pbc(Ub-Uc) > Pab(Ua-Ub), and Pab > Pbc,
that doesn't must mean that Ub-Uc > Ua-Ub. It means that it must
be greater by a factor of at least Pab/Pbc. And so, if, as seems to be
the case, Pab > Pbc, then B must be more than just above the mean,
when there are very few voters.

I don't know if there will turn out to be something wrong with that
argument, or if there will turn out to be a situation where the
likelihood that your vote for i over j could be increased by
voting for k, rather than decreased, as seems to be the case so far.

So the fact that you're voting for A, & not for C, does seem to mess up the 
above-mean strategy when there are very few voters.

If that's right, and if we don't even have the above-mean strategy
when there are very few voters, then it's especially important to
conduct a preliminary balloting, by Approval, Plurality, or rankings
(depending on the conditions) and make that information available
to the voters before the 2nd balloting. Fortunately, as I said,
a preliminary balloting is especially feasible when there are very
few voters. If we can take its results as a sure prediction, then we
avoid the need to try to maximize expectation based on probability
estimates.

Mike Ossipoff

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