Prior-Free Blackwell

Abstract

This paper develops a prior-free model of data-driven decision making in which the decision maker observes the entire distribution of signals generated by a known experiment under an unknown distribution of the state variable and evaluates actions according to their worst-case payoff over the set of state distributions consistent with that observation. We show how our model applies to partial identification in econometrics and propose a ranking of experiments in which E is robustly more informative than E' if the value of the decision maker's problem after observing E is always at least as high as the value of the decision maker's problem after observing E'. This comparison, which is strictly weaker than Blackwell's classical order, holds if and only if the null space of E is contained in the null space of E'.