Persuading sincere and strategic voters

A sender wants to persuade multiple homogeneous receivers to vote in favor of a proposal. Before the vote sender commits to a signal which sends private, potentially correlated, messages to receivers that are contingent on the true state of the world. The best equilibrium for sender in the resulting incomplete information game is unappealing: all receivers vote in favor of sender's preferred outcome, irrespective of their message. We therefore focus on the equilibrium where receivers vote sincerely, that is they vote in favor of the outcome that is optimal given their posterior. We characterize the optimal public and the optimal private signal, both for the case where receivers are behavioral and vote sincerely as well as the case where such behavior is a Bayes–Nash equilibrium (BNE). For the optimal public signal, sincere voting is a BNE, but the optimal private signal is subject to the swing voter's curse. Imposing the constraint that sincere voting be a BNE leads to an optimal signal where receivers are never pivotal.