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.

翻译：我们通过贝叶斯劝说的视角建模不确定性下的选择这一基本问题。在我们的模型中，信息不完全的决策者总是选择期望值最高的选项。我们旨在通过向决策者揭示额外信息来影响其后续选择，从而实现选项间的公平性。为度量公平性，我们采用主控序概念，力求同时近似最大化所有关于选项效用的对称、单调、凹函数。作为主要成果，我们设计了一种新颖的信息揭示策略，可在多项式时间内实现对主控序的对数近似。另一方面，任何策略（无论其运行时间如何）都无法实现对主控序的常数近似。我们的工作是贝叶斯劝说文献中首个在多维信息集上取得非平凡主控序结果的研究。