Pivotal persuasion.

A sender seeks to persuade a group of heterogeneous voters to adopt an action. We analyze the sender's information-design problem when the collective decision is made through a majority vote and voting for the action is personally costly. We show that the sender can exploit the heterogeneity in voting costs by privately communicating with the voters. Under the optimal information structure, voters with lower costs are more likely to vote for the sender's preferred action when it is the wrong choice than those with higher costs. The sender's preferred action is, therefore, adopted with a higher probability when private communication is allowed than when it is not. Nevertheless, the sender's preferred action cannot be adopted with probability one if no voter, as a dictator, is willing to vote for it without being persuaded.