Polarizing persuasion

We introduce an equilibrium model of polarizing communication between a sender and two receivers. The sender's payoff is a function of the receivers' beliefs on a binary payoff relevant variable. All agents share a common prior about this variable. But we assume disagreement about a second binary variable, which enters no utility functions. We characterize the joint distribution of receiver posterior beliefs on the payoff relevant variable that can be implemented. An immediate consequence of this characterization is that the sender's payoff is non-decreasing in the prior disagreement between the two receivers. We measure polarization as the sender's expectation of the absolute difference between the receivers' posterior beliefs on the payoff relevant variable, and solve for the maximum polarization across all message services. Given extreme prior disagreement between the receivers, we solve for the optimal message service when the sender has monotone payoffs that are bi-concave or bi-convex.