Noisy Persuasion

Abstract

We study the effect of noise due to exogenous information distortions in the context of Bayesian
persuasion. In particular, we ask whether more noise (a la Blackwell) is always harmful for
the information designer, i.e., the sender. We show that in general this is not the case. We
provide a necessary and sufficient condition for the sender to always be worse off when noise
increases in a binary noisy channel. There are two ways to read our result: (a) the sender always
dislikes additional noise if and only if we start with little noise in the first place, (b) the sender
always dislikes additional noise if and only if this additional noise is modelled by a sufficiently
symmetric channel. Finally, we provide sufficient conditions that extend this result to channels
of arbitrary cardinality.

Keywords: Bayesian Persuasion; Data Distortions; Optimal Signal; Garbling

JEL Classification: C72, D72, D82, D83, K40, M31