Robust Predictions for Persuasion

Abstract: We study persuasion games -- environments where Receiver contracts their action on Sender's choice of experiment and the realized signals about some state -- and identify which predictions can be made absent knowledge about the prior. To do so, we characterize robust mechanisms: those which induce the same allocation rules (mappings from the state to actions) for all priors. 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. This characterization uncovers a tight relationship between ordinal preference uncertainty and prior-independent predictions -- allocation rules are robust if and only if Sender has a state-independent least favorite action. Furthermore, all (and only) ordinally monotone allocation rules are robust in binary action problems. We then apply our model to school choice and uncover a novel informational justification for deferred acceptance when school preferences depend on students' unknown ability. Finally, in general good allocation settings, we show all efficient allocations are robust, even when agent preferences feature state-dependent outside options and allocation externalities.