Bayesian Persuasion with Multiple Receivers

Abstract

This paper investigates the role of persuasion mechanisms in collective decision-making. A biased sender adopts a Bayesian persuasion mechanism to provide a committee of uninformed receivers with signals about the unknown state of the world. We compare public persuasion with private persuasion. We find that the sender can always reach the concave closure of the set of possible expected payoffs under public persuasion, regardless of the number of generated signals. The sender is weakly worse off under private persuasion. We also provide conditions under which the receivers' welfare from private persuasion dominates that from public persuasion. Moreover, voting fully aggregates receivers' private information in the state where the sender and receivers' preferences are perfectly aligned, while full information aggregation may fail in other states.