[EM] An alternative to Tideman

[MIKE OSSIPOFF]

Yesterday, when I said that, having estimated the 2 top votegetters,
and their probabilities of outpolling eachother, one could then
estimate their win probabilities. But if that's done based on
those other estimates named here, that can lead to mutually contradictory 
estimates, and that suggests that, if it seems
easiest to estimate the top-2, and their probabilities of outpolling
eachother, and if we want to use Weber, then there might be a better
way of using that information.

I'm only talking about 2-way ties. When I say "tie" I mean
"tie or near-tie".

Joe showed that the probability of a certain 2 candidates being
the top two votegetters isn't necessarily the same as their probability
of being the candidates in a tie for 1st, if there is one. But
if we have no information suggesting that the likelihood of a tie
for 1st is more or less likely depending on who the frontrunners are,
then isn't it ok to make that assumption that those probabilities
are the same?

Say it's 80% that X & Y are the top 2, and 70% that X outpolls Y,
and 30% that Y outpolls X (not counting the tiny probability that
they poll the same).

For Weber's method, Pxy is .8   Say we estimate a 2% chance that
neither X nor Y will be a frontrunner.
The probability of a tie between X & Z is (.18)(.7)*Pfz,
where Pfz is Pz divided by the sum of the Pi of everyone but
X & Y.

Those other candidates' Pi can be gotten by Tideman, as I've
talked about, and can be used to determine tie probabilities of
their pairs.

Mike Ossipoff


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