Suppose you were given a set of voted CR ballots, perhaps with supplemental information such as a tentative approval cutoff. What rule would you use to adjust the approval cutoff by taking into account the popularity of the various candidates as manifested by the ballots themselves, as opposed to published opinion polls?
What supplemental information would you solicit from the voters (through modified CR ballots) if you could have it? Suppose, for example, that you asked all voters to submit (along with their cardinal ratings) the probabilities for each of the candidates being the final winner of the election, along with a number w between zero and 100 percent expressing their confidence in these probabilities. Suppose that voters had no strategic incentive to exaggerate any of these numbers. Then weighted averages (using the w's for the weights) of these probability estimates could be used as a pooled estimate of the probabilities of the various candidates winning. These pooled probabilities could be used to estimate the expected "cardinal payoff" (i.e. expected utility if the CR values are utilities) on each ballot, and the cutoff could be a weighted average of the pooled estimate and the individual estimate. If the individual is 100 percent confident, then the pooled estimate would count for nothing. If the individual is zero percent confident, then the pooled estimate counts for everything. If the individual is 50% confident, then the pooled estimate and his own estimate receive equal weight. If the voter wanted to manipulate, he would have to express high confidence in his estimate or else it wouldn't effect the outcome much. But if he expresses high confidence, then he has to live with the results, since his cutoff will be determined accordingly. To simplify things, instead of estimating all of the candidate probabilities, just have each voter indicate which candidate is most likely to win (in his opinion) along with a confidence number w as before. These results can still be used to find a pooled estimate, and averaging the pooled estimate with the cardinality of the most likely candidate on the ballot is still a reasonable way to pick a cutoff. In fact, this weighted average will be between the expected CR according to the pooled estimate of probabilities and the CR level judged most likely by the voter, and closer to the one that the voter has expressed more confidence in. That's just one example. Let's see some creativity! Forest ---- Election-methods mailing list - see http://electorama.com/em for list info
