Prior-Free Predictions for Persuasion

We analyze prior-free predictions in the design of persuasion games: settings where Receiver contracts their action on Sender's choices of experiment and realized signals about some state. To do so, we characterize robust mechanisms - those which induce the same allocation rules (mappings from the state to actions) regardless of prior beliefs. These mechanisms take a simple form: they (1) incentivize fully revealing experiments, (2) depend only on the induced posterior, and (3) maximally punish pooling deviations. We then highlight a tight connection between ordinal preference uncertainty and prior-dependent predictions - all such rules are implementable if and only if the sender has a state-independent least favorite action. This, in turn, implies all (and only) ordinally monotone allocation rules are robust in binary action problems. We apply our model to school choice and uncover a novel informational justification for deferred acceptance when school preferences depend on students' unknown ability. Finally, we study good allocation settings with externalities and state-dependent outside options and show all efficient allocation rules are robust, even with significant preference heterogeneity.