[EM] 2-Balloting Approval

[MIKE OSSIPOFF]

When I mentioned strategies for 2-balloting Approval, where the
1st balloting doesn't elect anyone unless they have a vote total
equal to half the number of voters, or more, from an article
by Tideman and (I believe it was) Merrill, I should have said

"In the 2nd balloting, vote for whichever of the 1st balloting's
2 frontrunners you like better, and for everyone whom you like better."

Of course if that more preferred frontrunner came in 2nd instead
of 1st, then you might want to vote for candidates whom you
like less than him, but more than the other frontrunner. How far
down you vote would depend, of course, on what you feel it would
take to make someone defeat your less-liked of the 2 frontrunners.

That's using the voting-by-impressions that people usually use now.

Of course you could use Hoffman's method or Cranor's method, for
estimating Pij from a "how-will-you-vote" poll.

I must admit that I don't understand why Cranor's method should
predict tie/near-tie probabilities. I'd appreciate it if anyone
could explain that. As for Hoffman's method, it needs more dimensions
as we add more candidates. Geometry in many dimensions doesn't appeal to me, 
but if someone has written a program to apply Hoffman's method,
that would be a good way to determine strategy from "how-will-you-vote" 
polls.

I like geometry to be about, at most, 3 spatial dimensions, except maybe on 
Twilight Zone.

If I were to need to estimate Pij from "how-will-you-vote" polling
now, I'd probably use something similar to Cranor's method, but
more obvious, straightforward, & computationally inefficient.

I shouldn't say that I wouldn't use Tideman's, Hoffman's, or Cranor's
methods for estimating Pij, with very few voters, because, if the
information that those methods need were the only information
available, then of course it would make sense to use it.

Those methods, especially Tideman, are approximate anyway, but
it seems to me, at 1st glance, that having very few voters would
make them more approximate. But if all you have to go on is that
kind of polls, then Hoffman or Cranor makes sense. If all you have
to go on is impressions of winnability, prospects, or strength
as contenders, then Tideman makes sense.

But, as I said, polling is especially easy with very few voters,
as is preliminary balloting of everyone, and asking people their
1st choices, or their rankings, might be better.

Mike Ossipoff


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