Majorized Bayesian Persuasion and Fair Selection

TL;DR

This paper introduces a new approach to fair selection under uncertainty using Bayesian persuasion, proposing an efficient information revelation policy that approximates fairness measures within a logarithmic factor.

Contribution

It presents the first non-trivial majorization result in Bayesian persuasion with multi-dimensional information, offering a polynomial-time policy for approximate fairness.

Findings

Achieves a logarithmic-approximation to majorization in polynomial time.

No policy can achieve a constant-approximation to majorization.

First non-trivial majorization result in multi-dimensional Bayesian persuasion.

Abstract

We address the fundamental problem of selection under uncertainty by modeling it from the perspective of Bayesian persuasion. In our model, a decision maker with imperfect information always selects the option with the highest expected value. We seek to achieve fairness among the options by revealing additional information to the decision maker and hence influencing its subsequent selection. To measure fairness, we adopt the notion of majorization, aiming at simultaneously approximately maximizing all symmetric, monotone, concave functions over the utilities of the options. As our main result, we design a novel information revelation policy that achieves a logarithmic-approximation to majorization in polynomial time. On the other hand, no policy, regardless of its running time, can achieve a constant-approximation to majorization. Our work is the first non-trivial majorization result in the Bayesian persuasion literature with multi-dimensional information sets.