Prior-Free Information Design

Abstract: This paper introduces a prior-free framework for information design based on partial identification and applies it to robust causal inference. The decision maker observes the distribution of signals generated by an information structure and ranks alternatives by their worst-case payoff over the state distributions consistent with those signals. We characterize the set of robustly implementable actions and show that each can be implemented by an information structure that withholds at most one dimension of information from the decision maker. In the potential outcomes model, every treatment is implementable via an experiment that is almost fully informative.