  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.
