Anthony Duff asked: > I am interested in the question of the frequency > of non-existence of a sincere CW. I personally > do not know that it is probable.
Here's another reason to occasionally expect sincere cycles at the top, when we're electing candidates to offices: Candidates want to win! In other words, they'll position themselves on the issues in such a way as to give themselves a good shot at winning. Assuming a Condorcetian voting method, there figures to be a bunch of candidates competing to be the most popular centrist compromise, adopting positions similar to each other. I think this implies simulations using random electorates provide a reasonable estimate of the frequency of sincere cycles at the top. Peter Ordeshook's book, Game Theory and Political Theory, has a table on p.58 listing such estimates. Here are its percentages assuming a large number of voters: #alternatives noCW fraction --------------- --------------- 3 .088 4 .176 5 .251 6 .315 7 .369 (Interpret the #alternatives column as the number of alternatives competing to be the centrist compromise.) --Steve ---- Election-methods mailing list - see http://electorama.com/em for list info