Rob LeGrand wrote >The problem is that the approval "voters" in CRAB don't know when the >balloting >will stop, so insincere strategy almost always backfires in the end, even if >it's effective at first. I've tried some tricky strategies in my simulations, >but they never help the voters using them in the long run. If anyone has >specific strategies for me to try, I'm taking suggestions.
Well, my standard example seems to work here, if we allow a little order-reversal. Once again, the sincere preferences are 49 Bush>Gore 12 Gore>Bush 12 Gore>Nader 27 Nader>Gore Now, with all voters using the "A" strategy from your previous post, the voting reliably settles on 49 Bush 24 Gore 27 Nader, Gore And Gore wins, 51 to 49 (Bush) to 27 (Nader). But what if 17 Bush voters decide to lock in with (Bush, Nader) in stead? If everyone else sticks to the "A" strategy, this insincere ranking sends the equilibrium to 17 Bush, Nader 33 Bush 12 Gore, Bush 39 Gore, Nader And now Bush wins, 61 to 56 (Nader) to 51 (Gore). Basically, the insincere ranking convinces the 12 Gore>Bush>Nader voters that they need to support Bush to prevent Nader from winning. I'll grant that it is difficult to spoof the system like this. If too many Bush voters insincerely rank, they will appear to hand the election to Nader, and they will quickly lose their resolve to vote insincerely. In this case, I've shown just the right number of Bush voters playing the game, such that Nader slots evenly between Gore and Bush. Getting back to the SVM, though... I'm beginning to believe it's possible. The simulation aspect of things makes the election harder to corrupt. The thing is that you can't "lock in" your vote to the SVM. All you can do is give it a set of rankings. If the 16 insincere voters gave the SVM a ranking of Bush>Nader>Gore, then the SVM would have them vote for only Bush, and Gore ends up emerging as the winner. But if they force the issue by reversing all the way to Nader>Bush, then they will end up giving the election to Nader. It may be that by limiting the voter to a certain set of strategies, we can prevent order-reversal and the like from being effective. In this case, a sort of simulated repeated approval balloting (SRAB) could be a viable election method, even for public elections. Rob, have you proven that universal use of the "A" strategy always settles on the Condorcet winner if one exists? If so, this could be a great election method. The thornier proof (but also very important) is to show that there is a unique equilibrium in all non-tied situations. If this is the case, then I think we should seriously examine SRAB as a public election method. -Adam ---- For more information about this list (subscribe, unsubscribe, FAQ, etc), please see http://www.eskimo.com/~robla/em
