Persuasion by Dimension Reduction

TL;DR

This paper demonstrates that in multi-dimensional persuasion problems, optimal information transmission involves projecting data onto a lower-dimensional manifold, balancing revealing useful information and concealing extreme values based on utility shape.

Contribution

It introduces the concept of the 'optimal information manifold' for dimension reduction in persuasion, providing geometric characterizations and explicit solutions for various utility functions.

Findings

Optimal dimension reduction improves persuasion strategies.

Revealing full information is optimal with linear utility.

Concealing extremes is optimal with concave utility.

Abstract

How should an agent (the sender) observing multi-dimensional data (the state vector) persuade another agent to take the desired action? We show that it is always optimal for the sender to perform a (non-linear) dimension reduction by projecting the state vector onto a lower-dimensional object that we call the "optimal information manifold." We characterize geometric properties of this manifold and link them to the sender's preferences. Optimal policy splits information into "good" and "bad" components. When the sender's marginal utility is linear, revealing the full magnitude of good information is always optimal. In contrast, with concave marginal utility, optimal information design conceals the extreme realizations of good information and only reveals its direction (sign). We illustrate these effects by explicitly solving several multi-dimensional Bayesian persuasion problems.