> A buries A truncates A sincere >B buries C wins C wins B wins >B truncates C wins C wins AB equal >B sincere A wins AB equal AB equal
Truncation is a dominated strategy (it never beats sincerity). So you can basically get rid of Truncation and just look at burying vs. sincerity. There are two Nash equilibrium. Each involves one side burying, and the other side truncating. In these cases, neither side can improve their odds by changing their strategy (one side has guaranteed victory, and the other side can only make things worse for itself). Both sides have an incentive to claim they will bury, whether they do or not. Both sides have an incentive to bury, AS LONG AS they think the other side will not. Say you're an A supporter. I'll denote your utility for A as U_a, B as U_b, and C as U_c. I'll denote the probability that B voters will bury as T. I'll denote your probability of winning the sincere contest between A and B as P_a. Your expected return on burying is: T(U_c) + (1-T)(U_A) And your expected return on sincerity is: T(U_b) + (1-T)(P_a*U_a + (1-P_a)U_b) so, you should bury when the first number is bigger than the second. The ironic effect of this is that, if you really want everyone to vote sincerely, the best thing is for everyone to loudly proclaim that they are going to bury their second-favorite. This way, nobody really has the incentive to bury (assuming they do hate C). If everyone promises to play nice, then you actually have an incentive to backstab once you're behind the curtain. -------- Really, once you start talking about complex strategic options like this, a lot of the voting theory arguments go out the window. IRV is basically equally vulnerable in this case, I think. The fact that you have to bury in a "more violent" fashion is mostly irrelevant to any voter who is willing to consider this sort of strategy. -Adam ---- Election-methods mailing list - see http://electorama.com/em for list info
