Resisting Evidence Manipulation with Endogenous Skepticism

This study examines collective decision making and information design under different voting rules in a Bayesian-persuasion framework with strategic voting, potential noncommitment, and endogenous skepticism. A group of voters relies on the evidence provided by a sender (he) for information about the unobservable state. The sender may be honest or dishonest, and his type is his private information. An honest sender has full commitment power, while a dishonest sender provides evidence only generating signals favoring his preferred alternative. The sender can reduce the voters’ skepticism of his commitment power by taking a costly skepticism-reducing action with a constant marginal cost. We show that the sender takes this costly action only under the unanimous rule but never under nonunanimous rules. The honest sender may provide more, or less, or equally informative evidence under the unanimous rule than under nonunanimous rules. Compared to the situation without persuasion, the sender’s persuasion imposes no influence on the voters’ welfare under the unanimous rule, while it can make the voters better or worse off under nonunanimous rules. The honest sender’s expected payoff strictly decreases with the voters’ initial skepticism level under the unanimous rule, but is irrelevant with the latter under nonunanimous rules.