On Fri, 20 Sep 2002, Rob LeGrand wrote in part: > Sincere preferences: > > 45:Reagan>Anderson>Carter > 35:Carter>Anderson>Reagan > 20:Anderson>Carter>Reagan > > Plurality equilibrium: > > 45:Reagan > 35:Carter > 20:Carter <--- insincere > > IRV equilibrium: > > 45:Anderson>Reagan>Carter <--- insincere > 35:Carter>Anderson>Reagan > 20:Anderson>Carter>Reagan > > Note that there are two other plurality equilibria. In fact, there's a > plurality equilibrium for each sincere pairwise majority in an > election, so there's always at least one that elects the Condorcet > winner. I believe the IRV equilibrium above is unique, so all of the > plurality and IRV equilibria for this electorate entail insincerity. >
Very informative examples, but the existence of different equilibria doesn't quite answer the original question, which was formulated in terms of near optimal strategy given near perfect information. Given the sincere preferences of your example it seems more likely to me that optimal (and near optimal) strategy for plurality would lead to the other equilibrium that you mentioned: 45:Anderson <--- insincere 35:Carter 20:Anderson The Reagan faction knows that more than 50 percent of the voters rank Reagan dead last so that he has no chance of winning, therefore they have nothing to lose by voting for Anderson. In the plurality equilibrium that you suggested the Anderson faction had to defect even while they knew there was a good chance of winning if they didn't defect. Perhaps you were assuming that the plurality voters had only plurality polling information, but I'm assuming that both had the same near perfect information. Forest ---- For more information about this list (subscribe, unsubscribe, FAQ, etc), please see http://www.eskimo.com/~robla/em
