A Rothschild Stiglitz Approach to Bayesian Persuasion
Rothschild and Stiglitz (1970) represent random variables as convex functions (integrals of the cumulative distribution function) Combining this representation with Blackwell's Theorem (1953) we characterize distributions of posterior means that can be induced by a signal. This characterization provides a novel way to analyze a class of Bayesian persuasion problems.