At 07:31 PM 8/29/2007, Paul Kislanko wrote: >I'd suggest that the zeroes in the last column are improbable if C is >acceptable to both A and B voters. That all A-first voters like C almost as >much as A but don't like B (or all B voters like C almost as much as B but >don't like A) is so improbable I can't believe it would happen.
On the contrary, I gave a travel example that explained the ratings as relative utilities. Then I showed how different absolute utilities underlying the relative utilities could lead to the conclusion that A was the best choice, B was the best choice, or C was the best choice. It's not common that we can determine absolute utilities so easily, but it *is* possible in some cases. And it gives us, I think, valuable information about how election methods behave. For example, where absolute utilities can be known, the majority criterion is almost preposterous. It happens to *usually* indicate the best winner, if a majority winner exists, but it can fail spectacularly. The most cogent objection to Range is not that it can fail MC. It is that it can fail to do what it is purported to do, which is to maximize social utility, and not only from "strategic voting," but merely from the normalization that we generally allow as still being sincere. Only if we have a way of encouraging voters to vote *absolute* utilities could we then be assured that Range would reliably elect the social utility winner. However, the extremes I have described are not the usual case. This is where Warren's simulations come in. With reasonable assumptions about absolute utilities for candidates would be formed (I think he has used an issue space model, the point is not whether or not that model is accurate, but only whether or not the utility distributions it generates are reasonably similar to those present in real elections, and that seems likely), we can then use these absolute utilities to judge the performance of election methods. Contrary to what so many claim about Warren's simulations of Range, he does not simply assume sincere votes. Range still performs quite well with various mixes of "strategic voters," and, of course, in the extreme, the election has been reduced to Approval, which is not a bad outcome, Approval also performs well, though not as well as Range. So, to me, the interesting question becomes whether or not we can detect what could be called S.U. failure in a Range election. I don't think there is any way to be sure of it, but there are, I strongly suspect, certain signs, and majority failure or the existence of a candidate who beats the Range winner pairwise, would be one. This is *not* a proof of SU failure, it is, however, something that can be associated with it. And so it becomes interesting, then, to test the preferences... by setting up a minor inconvenience in holding a runoff election. Voters with small preference strengths will be less likely to go to the trouble of voting, voters with strong preferences will be highly motivated, and there is more that I've described elsewhere. ---- Election-Methods mailing list - see http://electorama.com/em for list info
