Institute for Mathematical Behavioral Sciences

In Condorcet’s model of information aggregation, a group of people decides among two alternatives, with each person getting an independent bit of evidence about which alternative is objectively superior. I define the “supermajority penalty” (SP) procedure and show that it is incentive compatible for all possible preferences and prior beliefs and is in this sense completely robust. I also show that for an unbiased person, the SP procedure is the optimal anonymous incentive compatible procedure when there are significant biases in both directions (when at least one person is biased toward one alternative and at least one person is biased toward the other). The SP procedure is not monotonic, but this is not unusual: I show that when there are significant biases in both directions, all nontrivial anonymous incentive compatible procedures are non-monotonic.