Persuasion by Dimension Reduction
This provides a theoretical framework for multi-dimensional Bayesian persuasion, with potential applications in economics and communication, but it is incremental as it builds on existing persuasion models.
The paper tackles the problem of how an agent should persuade another by optimally reducing the dimensionality of multi-dimensional data, showing that projecting onto an 'optimal information manifold' is always optimal and characterizing when to reveal full magnitude versus only direction of good information.
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.