Discriminatory Persuasion: How to Convince a Group

We study a Bayesian persuasion game between a sender and a set of voters. A collective decision is made according to a majority rule. The sender can influence each voter's choice by persuading her individually and privately. Voters are heterogenous in thresholds of doubt, so some of them are easy to convince while others are hard. The optimal persuasion signal provides voters with discriminatory and correlated information. Furthermore, it has several pivotal realizations, each of which results in a distinctive winning coalition. An individual voter belongs to multiple winning coalitions and she cannot distinguish them given her private signal; and thus information aggregation among voters is inefficient.