Persuasion under the Threat of Verification

Public communication is often followed by private fact-finding.

We study a sender who commits to a costly public experiment before heterogeneous receivers decide whether to pay to verify the state, and ask whether cheaper private verification disciplines the sender or instead lets her shift the informational burden onto receivers.

The answer turns on the sender's own cost of public information.

When that cost is low, cheaper verification makes the optimal experiment weakly more informative; once the discipline margin is active, the favourable signal becomes more decisive and realized verification falls.

When public information is costly, the sender instead tolerates more private fact-finding, weakly coarsens the experiment, and may eventually pool.

A benchmark with uniformly distributed verification costs and quadratic persuasion costs delivers this phase reversal in closed form.

For general symmetric convex persuasion costs, primitive curvature and supporting-line conditions recover each side of the reversal; an explicit counterexample shows that a first-order stochastic reduction in verification costs alone does not sign the response.

Public informativeness and private verification, in short, need not move together.