Who is Afraid of Bayesian Persuasion?

Abstract

Bayesian persuasion (Kamenica and Gentzkow 2011) refers to the optimal signalling of a Sender with informational advantage over the Receiver, under the constraint that the expected posterior (over the state space) equals the common prior. In the basic example of a judicial system with a prosecutor (Sender) and a judge (Receiver) who needs to convict or acquit a defendant, the mechanism of Bayesian persuasion entails the detriment of the third party (absent in the model): innocent subjects who get convicted suffer from this optimal signalling scheme. If the judge is concerned about errors of convicting innocent defendants, or about the overall sustainability of the judicial system, then different outcomes may arise.