Anonymous Procedures for Condorcet’s Model: Robustness, Nonmonotonicity, and Optimality^* Available to Purchase

In Condorcet’s model of information aggregation, a group of people decides among two alternatives a and b, with each person getting an independent bit of evidence about which alternative is objectively superior. I consider anonymous procedures, in which the group’s decision depends only on the number of people who report a or b, not their identities. A procedure is called incentive compatible for a person if she wants to report truthfully given that others report truthfully. I show that if an anonymous procedure is incentive compatible for both a person who is significantly biased toward a and a person who is significantly biased toward b, then it is incentive compatible for any person, regardless of his preferences and prior beliefs; also, if it is not trivial, it must be nonmonotonic, with an additional report for a sometimes decreasing the probability the group chooses a. I define the “supermajority penalty” (SP) procedure and show that when there are significant biases in both directions, the SP procedure is the optimal anonymous incentive compatible procedure from the point of view of an unbiased person.