[EM] Another reason why Greens won't vote Dem, due to previous count results.

[Michael Ossipoff]

As I was saying in a recent previous post about this, Approval's count
results will tell Green-preferrers whether or not they need Dem to protect
against Repub.

And I gave a reason why that is: Preferrers of the middle of 3 parties have
no reason to approve either extreme. I told of a reason why that is.

Now I'd like to tell of another:

On EM, it's been shown by at least three people, in at least two ways, that
the expectation-maximizing strategy of Approval is to approve the
above-expectation candidates.

It's obvious why that's so: Your expectation is the sum, over all of the
candidates, of the product of a candidate's win-probability and hir utility.
It's obvious that when you increase the win-probability of a candidate who
is better than your expectation (you do that when you approve hir), that
will raise your expectation. 

Well, suppose you're a Democrat-preferrer (if there really are any). Say
it's Green, Dem, Repub. If it's certain that some particular candidate will
win, then your expectation is the utility of that candidate. Otherwise your
expectation is somewhere between the utility of the Green and the Dem, or
somewhere between the utility of the Repub and the Dem.

Say it's somewhere between the Green and the Dem. As I said above, your best
expectation-maximizing strategy is to approve  (only) all of the
above-expectation candidates. By assumption, the Green is farther from you
than is the point representing the utility equal to your expectation. So you
don't approve the Green.

What would it take to make your expectation worse than the Green? No, even
if it were almost certain that the Repub would win, that wouldn't do it,
because Dem and Repub are so close that you couldn't squeeze an amoeba
between them. The expected utility for you would have to be a candidate
farther away from you than the Green and the Repub. And that would be
impossible with just 3 candidates.

So then, what if there were more candidates? Maybe there's a candidate who,
as seen by you (a Dem-preferrer) is beyond the Green, in the same direction.
Maybe the it looks as if someone that far away from you, in that direction,
will win. Well, if that's so, then we can forget all about the Repub as a
threat, can't we. In that case, the Green preferrers certainly have no
reason to approve Dem.

So, if there are any Democrat-preferrers, they aren't going to vote for the
Green, except under conditions that would make the Rep is so unwinnable that
the Dems aren't needed as a compromise. 

And with the Dems not approving in either direction, the count totals of
Greens and Repubs will be a good estimate of their preferrers' numbers. And
when the Green shows as bigger than the Repub (as s/he immediately will) it
will be obvious that Green can beat Repub, and that Green preferrers don't
need to approve Dem.

As I was saying, in fact, I suggest that, in the 1st Approval election, the
Repubs count-total will be so low the suggestion of Dem as a necessary
compromise would be quite out of the question.

Aside from all this, remember that, when non-Republocrats are seen as
viable, there will be statisticians and (honest) poll-takers who are very
interested in finding out about the relative numbers of preferrers of the
various parties.

Mike Ossipoff