Optimal Information Disclosure: Quantity vs. Quality

A sender chooses ex ante how her information will be disclosed to a privately informed receiver who then takes one of two actions. The sender wishes to maximize the probability that the receiver takes the desired action. The sender faces an ex ante quantity-quality tradeoff: sending positive messages more often (in terms of the sender's information) makes it less likely that the receiver will take the desired action (in terms of the receiver's information). Interestingly, the sender's and receiver's welfare is not monotonic in the precision of the receiver's private information: the sender may find it easier to influence a more informed receiver, and the receiver may suffer from having more precise private information. Necessary and sufficient conditions are derived for full and no information revelation to be optimal.