Long-Term Fairness in Sequential Multi-Agent Selection with Positive Reinforcement

TL;DR

This paper explores how sequential multi-agent selection processes can be designed to promote long-term fairness through positive reinforcement, analyzing policies that balance fairness and score maximization, with theoretical and empirical insights.

Contribution

It introduces the Multi-agent Fair-Greedy policy, proving convergence to fairness under identical score distributions and highlighting potential risks of negative reinforcement in complex models.

Findings

Convergence to long-term fairness with identical score distributions

Existence of equilibria in non-identical score distribution scenarios

Uncoordinated behavior can cause negative reinforcement and reduce fairness

Abstract

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.