A speaker wishes to persuade a listener to take a certain action. The conditions under which the request is justiﬁed, from the listener’s point of view, depend on the state of the world, which is known only to the speaker. Each state is characterized by a set of statements from which the speaker chooses. A persuasion rule speciﬁes which statements the listener ﬁnds persuasive. We study persuasion rules that maximize the probability that the listener accepts the request if and only if it is justiﬁed, given that the speaker maximizes the probability that his request is accepted. We prove that there always exists a persuasion rule involving no randomization and that all optimal persuasion rules are ex-post optimal. We relate our analysis to the ﬁeld of pragmatics.
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