Reputational cheap talk with misunderstanding

We consider a cheap talk game with a sender who has a reputational concern for an ability to predict a state of the world correctly, and where receivers may misunderstand the message sent. When communication between the sender and each receiver is private, we identify an equilibrium in which the sender only discloses the least noisy information. Hence, what determines the amount of information revealed is not the absolute noise level of communication, but the extent to which the noise level may vary. The resulting threshold in transmission noise for which information is revealed may differ across receivers, but is unrelated to the quality of the information channel. When information transmission has to be public, a race to the bottom results: the cut-off level for noise of transmitted information now drops to the lowest cut-off level for any receiver in the audience.