A speaker wishes to persuade a listener to accept a certain request. The conditions under which the request is justified, from the listener's point of view, depend on the values of two aspects. The values of the aspects are known only to the speaker and the listener can check the value of at most one. A mechanism specifies a set of messages that the speaker can send and a rule that determines the listener's response, namely, which aspect he checks and whether he accepts or rejects the speaker's request. We study mechanisms that maximize the probability that the listener accepts the request when it is justified and rejects the request when it is unjustified, given that the speaker maximizes the probability that his request is accepted. We show that a simple optimal mechanism exists and can be found by solving a linear programming problem in which the set of constraints is derived from what we call the L-principle.

A new model of persuasion is presented. A listener first announces and commits to a codex (i.e., a set of conditions). The speaker then presents a (not necessarily true) profile that must satisfy the codex in order for the listener to be persuaded. The speaker is boundedly rational in the sense that his ability to come up with a persuasive profile is limited and depends on the true profile and the content and framing of the codex. The circumstances under which the listener can design a codex that will implement his goal are fully characterized.