I accidentally said "order-reversal", when I meant "falsification of a preference", in the definition of conditional complete expressiveness.
Blake once objected to wv's defensive truncation strategy, to deter offensive order-reversal, on the grounds that, whether or not the opponet order-reverses, the defensive truncation can only worsen the outcome for the truncators. So defensive truncation is a dominated strategy, one that can only worsen the outcome, if it affects it at all, if it's used instead of some other particular strategy. But defensive truncation is part of a desirable equilibrium, an equilibrium that the defensive truncator likes. There's ample precedent for using a dominated strategy when it's part of a desired equilibrium. For instance, say there's a crime for which statistics indicate that it's very unlikely that its perpetrator will again commit a crime. If we incarcerate the perpetrator, we add the cost of incarceration to the cost of the crime itself. So if we have a policy of incarcerating people who commit that crime, having that policy is a dominated strategy. It's dominated by the strategy of not having that policy. Whether the person commits the crime or not, our cost can be greater if we have that policy, but can't be less. But that dominated strategy is part of an equilibrium that society likes: No crime, no incarceration. The person worsens his outcome if he commits a crime and is incarcerated. Society doesn't improve its outcome if it drops the policy when the person doesn't change his strategy of not committing the crime. With many people, for many crimes, that equilibrium usually obtains, even if they'd considered the crime. So, as I said, there's ample precedent for using a dominated strategy that's part of a desired equilibrium. wv's deterrence of offensive order-reversal is similar to the justice system example that I described above. It works there, and it will work for wv too. You might say, "Yes, but there's still crime." Sure, but not as much, because, as I said, that equilibrium apparently obtains for most people. And, as I said, offensive order-reversal would be impossible to plan & organize without getting caught. And Margins doesn't deter offensive order-reversal; it merely prevents it from working, if enough people rank a compromise over their favorite. If people don't have compunction about order-reversing, as Rob LG contends, then they have nothing to lose by trying it, in many situations, in Margins. Specialists on game theory have said that if a strategy configuration is an equilibrium, it will be found by the players. But if there's no equilibrium in which order-reversal doesn't occur, that isn't at all promising for such a method. If, as Rob LG contends, people will use any strategy that would improve their outcome, then that any non-equilibrium non-reversing strategy configuration won't last. Maybe one more method description is needed: methods that--even if voting of a false preference is ruled out as a strategy--have situations that have no equilibria in which no one votes a less-liked candidate equal to another candidate that he votes for and the CW wins. Maybe methods like that, and conditionally completely expressive ones, should be defined together in a separate section starting with: "If falsification of a preference is ruled out as a strategy:". Condorcet(margins) is such a method. That's a long way from wv's complete expressiveness under those same conditions. Whether or not people will offensively order-reverse, margins has nothing to offer in the way of sincere equilibria. Mike Ossipoff _________________________________________________________________ Chat with friends online, try MSN Messenger: http://messenger.msn.com
