Multi Stage Screening: Enforcing Fairness and Maximizing Efficiency in a Pre-Existing Pipeline

Consider an actor making selection decisions (e.g., hiring) using a series of classifiers, which we term a sequential screening process. The early stages (e.g. resume screen, coding screen, phone interview) filter out some of the applicants, and in the final stage an expensive but accurate test (e.g. a full interview) is applied to those individuals that make it to the final stage. Since the final stage is expensive, if there are multiple groups with different fractions of positives in them at the penultimate stage (even if a slight gap), then the firm may naturally only choose to apply the final (interview) stage solely to the highest precision group which would be clearly unfair to the other groups. Even if the firm is required to interview all those who pass to the final round, the tests themselves could have the property that qualified individuals from some groups pass more easily than qualified individuals from others. Accordingly, we consider requiring Equality of Opportunity (qualified members of each group have the same chance of reaching the final stage and being interviewed). We then examine the goal of maximizing quantities of interest to the decision maker subject to this constraint, via modification of the probabilities of promotion through the screening process at each stage based on performance at the previous stage. We exhibit algorithms for satisfying Equal Opportunity over the selection process and maximizing precision (the fraction of interviews that yield qualified candidates) as well as linear combinations of precision and recall (recall determines the number of applicants needed per hire) at the end of the final stage. We also present examples showing that the solution space is non-convex, which motivate our combinatorial exact and (FPTAS) approximation algorithms for maximizing the linear combination of precision and recall. Finally, we discuss the ‘price of’ adding additional restrictions, such as not allowing the decision-maker to use group membership in its decision process.