Censorship as optimal persuasion

Abstract

We consider a Bayesian persuasion problem where a sender's utility depends only on the expected state. We show that upper censorship that pools the states above a cutoff and reveals the states below the cutoff is optimal for all prior distributions of the state if and only if the sender's marginal utility is quasi‐concave. Moreover, we show that it is optimal to reveal less information if the sender becomes more risk averse or the sender's utility shifts to the left. Finally, we apply our results to the problem of media censorship by a government.

The Economics of Partisan Gerrymandering

“…x ∈ [0, s * ] and is risk-averse in x "on average" for x ∈ [s * , 1], so voters below s * are segregated and voters above s * are pooled. Similar results were established by Gul and Pesendorfer (2010) and, in the persuasion literature, Kolotilin (2018) and Kolotilin, Mylovanov, and Zapechelnyuk (2022).…”

“…Proof of Proposition 4. The proposition follows from Theorem 1 in Kolotilin, Mylovanov, and Zapechelnyuk (2022). The proof is similar to the proof of Proposition 2.…”

Optimal persuasion via bi‐pooling

“…Consider the setting of Kolotilin, Mylovanov, and Zapechelnyuk (2022). A receiver has to decide whether or not to accept a project whose quality is known to the sender.…”

“…Upon rejection, the receiver's utility, denoted by V , is her private information while the sender's utility is zero. Kolotilin, Mylovanov, and Zapechelnyuk (2022) focus on the case where the distribution over the value of V has a unimodal density function. The unimodal density function induces an S‐shaped indirect utility function (a convex interval followed by a concave interval).…”

“…Our results about feasible bi‐pooling policies are shown to be useful in imposing significant restrictions on the structure of feasible price functions, so that the search for the right price function (and hence for the optimal policy) can become much more straightforward. In particular, we revisit the framework of Kolotilin, Mylovanov, and Zapechelnyuk (2022), where the receiver has an outside option whose value is her private information. We provide an intuition to their characterization of the optimal policy for S‐shaped utility functions.…”