Learning by Convex Combination

We study how an agent evaluates the optimality of an action when she only observes a sample of its outcomes, not the outcome distribution. We characterize a model where the agent assigns an ex-ante utility to the action and then, upon seeing the sample, “updates” her evaluation by taking a convex combination of this ex-ante utility and the average utility of the outcomes in the sample. The weight on the average utility in this convex combination increases with sample size. Asymptotically, actions are evaluated using their sample average utility. The model includes Bayesian benchmarks as special cases. More generally, it describes an agent that may learn imperfectly yet consistently with a rough intuitive understanding of the Law of Large Numbers; it also enables decision-theoretic definitions of important concepts in the descriptive study of probabilistic judgement.