Bray Theory Workshop
Joint seminar with Social and Information Sciences Laboratory Seminar (SISL).
This paper studies mechanisms for eliciting and evaluating statistical forecasts. Nature draws a state at random from a given state space, according to some distribution p. Prior to Nature's move, a forecaster, who knows p, provides a prediction for a given statistic of p. The mechanism defines the forecaster's payoff as a function of the prediction and the subsequently realized state. When the statistic is continuous with a continuum of values, the payoffs that provide strict incentives to the forecaster exist if and only if the statistic partitions the set of distributions into convex subsets. When the underlying state space is finite, and the statistic takes values in a finite set, these payoffs exist if and only if the partition forms a linear cross-section of a Voronoi diagram-that is, if the partition forms a power diagram-a stronger condition than convexity. In both cases, the payoffs can be fully characterized essentially as weighted averages of base functions.