...or Condorcet voting, Plurality, Borda Count, IRV, or whatever else you lke.
Or rather I will say that nearly any voting method can be Hayified. Standard Hay Voting is actually Hayified Random Ballot. I originally described Hay Voting by saying that we allocate voting mass to various candidates; a random ballot is chosen, and then a random point of voting mass is chosen from that ballot. I now think a more revealing description of Hayified Random Ballot would be to say that you allocate voting mass to all possible votes (in Random Ballot, the set of possible votes happens to equal the set of candidates). A random point of voting mass is selected from your ballot, and whatever lies on that point becomes "your vote." Then all votes are entered into a Random Ballot election. But we can substitute any election method for Random Ballot. What we discover about you, of course, is no longer your utility function over candidates, but your utility function over votes (in RB they happen to be equal). However, your utility function over votes is determined by your utility function over candidates and your beliefs about how the other voters will vote. As has been mentioned before, these beliefs can be measured with a prediction game. Then we can solve a system of linear equations to find your utility function over candidates. I conjecture that a Hayified voting method will asymptotically approach the original voting method (ie the probability of producing the same outcome approaches 1 as population size goes to infinity) if and only if the original method possesses the property that adding one more of every possible vote can never change the election outcome. Nearly all methods have this property, but Random Ballot doesn't, which is why Hayified Random Ballot is so much worse than ordinary Random Ballot. - Peter de Blanc ---- election-methods mailing list - see http://electorama.com/em for list info
