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

[Juho Laatu]

On 1.6.2012, at 6.38, Michael Ossipoff wrote:

> 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.

Is that a general claim that after seeing Approval polls, it is always easy for Approval voters (Greens and others) to decide how to vote?

> 
> 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.

Here you assume a special case where one of the candidates is a middle candidate (and there are max two potential winners, and a one-dimensional political space).

> 
> 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

I drafted one set of votes. There are multiple polls (maybe Approval based others) whose results are not very far from the election day sincere opinions that are given below. I wonder how the voters vote, who wins and who should win?

26:  A > B >> C
24:  B > A >> C
01:  B >> A = C
29:  C >> A > B
20:  C >> B > A

Juho