While much of the rapidly growing literature on fair decision-making focuses on metrics for one-shot decisions, recent work has raised the intriguing possibility of designing sequential decision-making to positively impact long-term social fairness. In selection processes such as college admissions or hiring, biasing slightly towards applicants from under-represented groups is hypothesized to provide positive feedback that increases the pool of under-represented applicants in future selection rounds, thus enhancing fairness in the long term. In this paper, we examine this hypothesis and its consequences in a setting in which multiple agents are selecting from a common pool of applicants. We propose the Multi-agent Fair-Greedy policy, that balances greedy score maximization and fairness. Under this policy, we prove that the resource pool and the admissions converge to a long-term fairness target set by the agents when the score distributions across the groups in the population are identical. We provide empirical evidence of existence of equilibria under non-identical score distributions through synthetic and adapted real-world datasets. We then sound a cautionary note for more complex applicant pool evolution models, under which uncoordinated behavior by the agents can cause negative reinforcement, leading to a reduction in the fraction of under-represented applicants. Our results indicate that, while positive reinforcement is a promising mechanism for long-term fairness, policies must be designed carefully to be robust to variations in the evolution model, with a number of open issues that remain to be explored by algorithm designers, social scientists, and policymakers.

翻译：尽管快速增长的公平决策文献大多关注单次决策的度量标准，近期研究提出了通过设计序贯决策过程来积极影响长期社会公平性的有趣可能性。在诸如大学录取或招聘等选拔过程中，对来自代表性不足群体的申请人给予轻微偏袒的假设是：这种正向反馈将增加未来选拔轮次中代表性不足申请人的储备，从而在长期内提升公平性。本文在多个智能体从共同申请人池中进行选择的设定下，检验该假设及其影响。我们提出多智能体公平贪婪策略，该策略在贪婪分数最大化与公平性之间取得平衡。在此策略下，我们证明当不同群体间的分数分布相同时，资源池与录取结果将收敛于智能体设定的长期公平目标。通过合成数据集和经调整的真实数据集，我们为分数分布非相同情况下均衡点的存在提供了实证证据。随后，我们对更复杂的申请人池演化模型提出警示：在这些模型下，智能体间的不协调行为可能导致负向强化，从而降低代表性不足申请人的比例。我们的研究结果表明，虽然正向强化是实现长期公平性的有前景机制，但政策设计必须审慎考虑演化模型的变异性，算法设计者、社会科学家和政策制定者仍需探索诸多未决问题。