Eliciting Information on the Distribution of Future Outcomes

This paper studies the problem of inducing a presumably knowledgeable expert to reveal true information regarding the probability distribution of a future random outcome. I consider general information that includes, in particular, the statistics of probability distributions (such as mean, median, variance), and all categorical information (such as the most correlated pair of variables). I examine two types of incentive schemes: Those that reward the expert for being truthful, and, for the case of numerical and ordinal information, those that reward the expert increasingly with the accuracy of the prediction. For both cases, I establish simple criteria to determine the information that can be elicited, and offer a complete characterization of the associated schedule fee.