When I replied to David, I said that if he told me his utilities for the candidates, I could calculate those 2 probabilities that Markus mentioned. Of course really I wouldn't need any utilities to calculate those probabilities. The probabilities are calculated from the assumption that we have no information about some situations being more likely than others. Markus's formula uses utilities to determine which course of action would be better. Of course if one were doing mathematical strategy, one would determine the expectation-improving value of each pair-ordering that you could vote, and, from that, determine what ranking is the best. Of course it could be a strict ranking, or a ranking with equally-ranked candidates. It could be a complete ranking, or a truncated one. Of course I'm not saying that some particular count rule wouldn't preclude one or more of those possibilities. So the result of the strategy calculation would be a ranking-- your best ranking for that election. *** By the way, if Blake's suggestion of wv with automated strategy assistance was intended as a way of saying that wv strategy is more complicated than that of Margins--it isn't. Margins, like Condorcet, would require checking out all of those situations I described. The difference is that Margins would require more computation, because your ordering of A & B can change the the margin of the defeat between them regardless of the direction of the defeat. Any method has a mathematical strategy, and rank methods have very complicated strategies. Someone might criticize some method by saying that there could be strategic incentive to do this or that. Sure, those strategies are so complicated, with so many possible situations, that no doubt they could give you all sorts of incentives, depending on your utilities. But I caution against assuming that that's what we should judge the methods by. The real problems are the _gross_ problems, where a majority are strategically forced to do something that often will give away the election, in order to make a lesser-evil keep a greater evil from winning. The fact that it's horrendously complicated to calculate mathematical strategy with rank methods, without a computer program for it, shouldn't be counted against those methods in general. So what? If you don't know the exptectation-optimizing strategy, then you can rank sincerely with Condorcet. Is there some meaningful sense in which someone who calculates his mathematical strategy in the same election will have an unfair advantage over you? Condorcet's unique basic guarantees say that he won't be able to steal the election by thwarting majority wishes. Sure, that other guy is doing better to achieve his maximum possible expectation than you are. But it isn't something that he can use against you to cheat a majority out of a rightful win. I've never heard of anyone willing to spend the time, or use up the paper, to write a strategy for IRV. IRV, very unlike Condorcet, is a method where strategy is very much needed. Good luck figuring out what your strategy should be in IRV. Sure, it isn't easy to calculate it in Condorcet (or Margins), but in Condorcet you don't really need it to protect you, though you might like it for that extra tweak to increase your utility expectation. I'd conjecture that with Condorcet, there's only a small improvement in using mathematical strategy vs sincere ranking anyway. Mike Ossipoff ______________________________________________________ Get Your Private, Free Email at http://www.hotmail.com
