Persuasion and Limited Communication

This paper studies optimal persuasion. A speaker must decide which arguments to present and a listener which arguments to accept. Communication is limited in that the arguments available to the speaker depend on her information. Optimality is assessed from the listener's perspective assuming that the listener can commit to a persuasion rule. I show that this seemingly simple scenario--introduced by Glazer and Rubinstein (2006)--is computationally intractable (formally, NP-hard). However under the assumption known as normality, which validates the revelation principle in mechanism design environments with evidence (Green and Laffont 1986, Bull and Watson 2007), I show that the persuasion problem reduces to a classic optimization problem, leading to a simple procedure for its solution. This procedure finds not only the optimal rule, but also the credible implementation of the optimal rule, i.e., the equilibrium of the game without commitment leading to the same outcome as the optimal rule. Normality also has qualitative consequences for the optimal rule. In particular, under normality, there always exists an optimal rule which is symmetric: i.e., ex ante equivalent evidence is treated equivalently. When normality fails, all optimal rules may be asymmetric; in other words, the listener may categorize evidence in an arbitrary manner, and base his decisions on these categories in order to influence the speaker's reporting behavior.