EM list-- I'd like to further clarify an answer that I made in my most recent letter: I'd previously said: "If you don't [protect a certain preferred candidate by sharing 1st place with him], for instance, one of them could turn out to be a sincere CW who lost because of truncatiion, and because you didn't insincerely share 1st place with him." Blake then said: "But can you give an argument for why in a 0-knowledge situation, falsely ranking 2 candidates as equal can maximize expected utility, in margins? All you have done is suggested that in some cases, equal ranking can help. But unless you know that you are dealing with one of those cases, that isn't a good reason to vote a particular way." My answer was ok as far as it went, but it wasn't complete, and left out what was most necessary to say in that reply: Of course you don't know what situation you're dealing with. It's a decision under uncertainty. Even with probabililty information it would be a decision under uncertainty & we wouldn't know what situation it is. But with 0-info, we don't even have probability information. Either way, when we don't know what situation it is, we calculate, based on our specific probability information (of which we have none here) the probability of each possible situation. One aspect of each situation is what's the way in which we'd be able to affect the result if there were a way in which we could. What pairwise comparison is it that's the close one that would be affectable by us if any of them is. Considering all the combinations of pair-defeats, and, for each of those, the ways we could pick a comparison to be the near-tied one (there are especially unlikely to be two), we know that all of those possible situations are equally likely. Then, for each of those possible situations, we determine the utility difference between the 2 outcomes that it's teetering between, and which we could make go either way. With those situation probabilities and utility differences, we can assign utility expectation improvement values to each pair-ordering we could vote, as compared to the utility of the outcome if we didn't vote or if we voted the other way. Having that, we could calculate the improvement of each possible ranking of the candidates by us, compared to if we didn't vote. So we pick the ranking, partial, complete, strict or position- sharing, etc., that gives the most improvement over not voting, in terms of its improvement of utility expectation. *** I'm not saying that I've got all of that right, but it's got to be something like that, doesn't it? *** The point that I was trying to make was that of course we don't know what the situation is, or that it's a situation where we're saving a SCW from truncation. But we consider all the situations that it might be, and how our utility would be affected in each situation. So my argument doesn't depend on our knowing that it's some particular kind of situation. *** Mike Ossipoff ______________________________________________________ Get Your Private, Free Email at http://www.hotmail.com
