Statistical Discrimination in Stable Matching

Rémi Castera (1, 2) , Patrick Loiseau (3) , Bary Pradelski (2)

1 LIG - Laboratoire d'Informatique de Grenoble
2 POLARIS - Performance analysis and optimization of LARge Infrastructures and Systems
3 FAIRPLAY - IA coopérative : équité, vie privée, incitations

We study statistical discrimination in matching, where multiple decision-makers are simultaneously facing selection problems from the same pool of candidates. We propose a model where decision-makers observe different, but correlated estimates of each candidate's quality. The candidate population consists of several groups that represent gender, ethnicity, or other attributes. The correlation differs across groups and may, for example, result from noisy estimates of candidates' latent qualities, a weighting of common and decision-maker specific evaluations, or different admission criteria of each decision maker. We show that lower correlation (e.g., resulting from higher estimation noise) for one of the groups worsens the outcome for all groups, thus leading to efficiency loss. Further, the probability that a candidate is assigned to their first choice is independent of their group. In contrast, the probability that a candidate is assigned at all depends on their group, and --- against common intuition --- the group that is subjected to lower correlation is better off. The resulting inequality reveals a novel source of statistical discrimination.

Domains: Computer Science and Game Theory [cs.GT]; Modeling and Simulation; Probability [math.PR]

Rémi Castera, Patrick Loiseau, Bary Pradelski. Statistical Discrimination in Stable Matching. 2023. ⟨hal-03672270v2⟩