Prior-Free Predictions for Persuasion

We analyze robust predictions in the design of persuasion games: settings where receiver contracts their action on sender's choices of experiment and the realized signals. To do so, we characterize mechanisms which induce the same allocations (mappings from sender's type 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. When (and only when) sender's least favorite action is type-independent are all allocations robust, highlighting a connection between ordinal preference uncertainty and prior-dependent predictions. We apply our model to allocation settings with externalities and type-dependent outside options, and find efficient allocations are robust, even with significant preference heterogeneity. Additionally, we study school choice and uncover a novel informational justification for deferred acceptance when school preferences depend on students' unknown ability