  We develop a result on expected posteriors for Bayesians with heterogenous
priors, dubbed information validates the prior (IVP). Under familiar ordering
requirements, Anne expects a (Blackwell) more informative experiment to bring
Bob's posterior mean closer to Anne's prior mean. We apply the result in two
contexts of games of asymmetric information: voluntary testing or
certification, and costly signaling or falsification. IVP can be used to
determine how an agent's behavior responds to additional exogenous or
endogenous information. We discuss economic implications.
