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 ---- Election-Methods mailing list - see http://electorama.com/em for list info
