We study persuasion mechanisms in linear environments. A privately informed receiver chooses between two actions. A sender designs a persuasion mechanism that can condition the information disclosed to the receiver on the receiver's report about his type. We establish the equivalence of...

We consider a Bayesian persuasion problem where a sender's utility depends only on the expected state. We provide a necessary and sufficient condition for the optimality of upper censorship that pools the states above a cutoff and reveals the states below the cutoff. This condition is equivalent...

A sender designs a signal about the state of the world to persuade a receiver. Under standard assumptions, an optimal signal censors states on one side of a cutoff and reveals all other states. This result holds in continuous and discrete environments with general and monotone partitional...