Robust Narrative Persuasion
Abstract: This paper studies a sender who designs a public menu of narratives for a heterogeneous population whose cross-sectional distribution of priors is known only through moment restrictions. After each signal realization, receivers select the narrative that best explains it under their prior and act on its posterior. With binary states, any menu is weakly dominated by a menu using one narrative to set each realization’s threshold. I characterize implementable thresholds by a frontier that is piecewise linear in odds coordinates and reduce robust menu design to a moment problem that admits a least favorable distribution with finite support. In a political application, an optimal menu concentrates persuasion on the more valuable realization. Tighter dispersion raises the sender’s optimal value, while a higher mean prior can lower it by reducing the least favorable mass above the persuasion threshold.