Demorep wrote: >Will the voters be forced to state -- >this is my sincere vote --- [sincere vote] >this is my insincere vote --- [insincere vote]
No. Think of the election as a game, in the formal sense. Your sincere preference order represents your payoffs based on different outcomes, or at least the relative order of which outcomes you prefer. Your vote assigned by the computer, be it sincere or insincere, is your strategy. The computer assigns strategies to voters to find a Nash equilibrium. Although an election might have millions of voters, for a 3-candidate race we can think of the game as having only 6 players. If, for example, the rules of the game were plurality voting, each player would have 3 possible pure strategies. For player 1 his pure strategies might be give 1 million votes to candidate A, give one million votes to candidate B, or give 1 million votes to candidate C. For another player, representing a different bloc of voters with idential preference orders, the strategies might be give 2 million votes to any of the three candidates. Mixed strategies would be that bloc dividing its support among candidates. I'm not sure if there's an incentive to do so, but since I'm using terminology from game theory I might as well define the mixed strategies. Now, the computer looks at the strategies and payoffs available to each player and finds Nash equilibria, where each bloc of voters is following its best strategies given the strategies of all other blocs. Question: Can we come up with a voting method such that you never have an incentive to lie to the computer? If so, then it doesn't matter if your assigned strategy is insincere, we still satisfy strong FBC. Why do I say that? The concept of the computer assigning you a (possibly insincere) strategy based on your sincere input is just one more step in a voting method. We can think of a voting method as a black box: Input everybody's ballot, and it outputs a winner. If you have no disincentive to give sincere input, then whatever magic and churning it goes through, assigning convoluted insincere strategies, is all irrelevant. Strong FBC is satisfied. My hunch is that strong FBC cannot in general be satisfied. For a given set of players (with their associated payoffs) and available strategies, there can be instances where there are at least two Nash equilibria, and those 2 equilibria lead to different winners. I don't know if there exists a method in which insincere input cannot cause the computer to give at least one person a better result. If there is no such method then strong FBC is impossible. Maybe all I've done is make life more complicated without getting any closer to an answer, but it may be that by putting an intermediate stage between your sincere input and insincere strategy strong FBC can be satisfied. Something to think about... Alex ---- For more information about this list (subscribe, unsubscribe, FAQ, etc), please see http://www.eskimo.com/~robla/em
