Information design for weighted voting

We consider a sender who wishes to persuade multiple receivers to vote in favor of a proposal and sends them private correlated messages that are conditional on the true state of the world. The receivers share a common prior, wish to implement the outcome that matches the true state, and have homogeneous preferences. However, they are heterogeneous in their voting weights. We consider both behavioral and sophisticated voters. When voters are behavioral, public communication is optimal if and only if there is a veto player. For sophisticated voters, we establish lower bounds on the sender’s gain from persuasion for general voting quotas and show that the sender can often improve upon public communication. Finally, in an extension, we show that even when behavioral voters have heterogeneous prior beliefs, public communication is optimal if and only if there is a veto player.