On Monotone Persuasion

TL;DR

This paper investigates the design of monotone persuasion strategies in linear settings, identifying when optimal signals are monotone or require nonmonotone approaches, with applications to media censorship.

Contribution

It characterizes conditions under which monotone signals are optimal versus when nonmonotone signals are necessary in persuasion problems.

Findings

Optimal monotone signals are upper censorship for s-shaped objectives with discrete states.

Optimal monotone signals are interval disclosures for m-shaped objectives with continuous states.

Unrestricted signals may require nonmonotone pooling or randomization, unlike monotone solutions.

Abstract

We study monotone persuasion in the linear case, where posterior distributions over states are summarized by their mean. We solve the two leading cases where optimal unrestricted signals can be nonmonotone. First, if the objective is s-shaped and the state is discrete, then optimal monotone signals are upper censorship, whereas optimal unrestricted signals may require randomization. Second, if the objective is m-shaped and the state is continuous, then optimal monotone signals are interval disclosure, whereas optimal unrestricted signals may require nonmonotone pooling. We illustrate our results with an application to media censorship.