Optimal Binary Prediction for Group Decision Making

In this paper we address the problem of optimally forecasting a binary variable for a het-erogeneous group of decision makers facing various (binary) decision problems that are only tied together by the unknown outcome. A typical example is a weather forecaster who needs to estimate the probability of rain tomorrow and then report it to the public. Given a conditional probability model for the outcome of interest (e.g., logit or probit), we introduce the idea of maximum welfare estimation and derive conditions under which traditional estimators such as maximum likelihood or (non-linear) least squares are asymptotically socially optimal even when the underlying model is misspecified