Statistical Discrimination in Stable Matchings
Résumé
Statistical discrimination results when a decision-maker observes an imperfect estimate of the quality of each candidate dependent on which demographic group they belong to. Prior literature is limited to simple selection problems with a single decision-maker. In this paper, we initiate the study of statistical discrimination in matching, where multiple decision-makers are simultaneously facing selection problems from the same pool of candidates (e.g., colleges admitting students). We propose a model where two colleges observe noisy estimates of each candidate's quality. The estimation noise controls a new key feature of the problem, namely the correlation between the estimates of the two colleges: if the noise is high, the correlation is low and vice-versa. We consider stable matchings in an infinite population of students. We show that a lower correlation (i.e., higher estimation noise) for one of the groups worsens the outcome for all groups. 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 to a college at all depends on their group, revealing the presence of discrimination coming from the correlation effect alone. Somewhat counter-intuitively the group that is subjected to more noise is better off.
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