Inscribing Diversity Policies in Algorithmic Hiring Systems : Theory and Empirics

In algorithmic hiring systems, diversity policies are often inscribed as algorithmic fairness constraints. But algorithms rarely work in isolation; almost always, humans make the ultimate hiring decision based on recommendations from the algorithm. To better understand the downstream effects of algorithmic fairness constraints in Human+AI hiring systems, we present, solve and empirically estimate a 2-stage hiring model consisting of: (1) an algorithmic screener, which screens and shortlists candidates from a pool of applicants, and (2) an unbiased hiring manager, who hires from the shortlist. There is an optional parity constraint (i.e., a diversity policy) imposed on the algorithm to shortlist an equal number of men and women. We solve this model analytically and show that even when both the algorithm and the hiring manager are unbiased, the parity constraint can be ineffective in increasing the diversity of the hires. Its effectiveness depends on parameters such as the size of the applicant pool, gender differences in the screening algorithm's predictive power, and most importantly, the correlation between the algorithm's and the hiring manager's assessment of candidate quality. The more correlated the screening algorithm's and the hiring manager's quality estimates are, the less effective the parity constraint becomes in increasing workforce diversity. We empirically estimate these parameters using hiring data from IT firms and show via counterfactual policy simulation that parity constraint can improve the average proportion of female hires by a modest amount; however, there will be a high level of heterogeneity in the effectiveness across job types. We discuss the algorithmic design implications of these findings and propose a method that would increase the effectiveness of algorithmic diversity policies