Enforcing Group Fairness in Algorithmic Decision Making: Utility Maximization Under Sufficiency

TL;DR

This paper investigates how to implement fairness constraints like sufficiency, PPV parity, and FOR parity in binary classifiers, revealing optimal decision rules and counter-intuitive outcomes in utility maximization.

Contribution

It characterizes optimal decision rules under various fairness constraints, highlighting when simple thresholds suffice and when more complex rules are necessary, including counter-intuitive results.

Findings

Group-specific thresholds are optimal for PPV and FOR parity.

Upper-bound thresholds can be optimal, sometimes selecting individuals with lowest utility.

Complex decision rules are needed for sufficiency, causing within-group unfairness.

Abstract

Binary decision making classifiers are not fair by default. Fairness requirements are an additional element to the decision making rationale, which is typically driven by maximizing some utility function. In that sense, algorithmic fairness can be formulated as a constrained optimization problem. This paper contributes to the discussion on how to implement fairness, focusing on the fairness concepts of positive predictive value (PPV) parity, false omission rate (FOR) parity, and sufficiency (which combines the former two). We show that group-specific threshold rules are optimal for PPV parity and FOR parity, similar to well-known results for other group fairness criteria. However, depending on the underlying population distributions and the utility function, we find that sometimes an upper-bound threshold rule for one group is optimal: utility maximization under PPV parity (or FOR parity) might thus lead to selecting the individuals with the smallest utility for one group, instead of selecting the most promising individuals. This result is counter-intuitive and in contrast to the analogous solutions for statistical parity and equality of opportunity. We also provide a solution for the optimal decision rules satisfying the fairness constraint sufficiency. We show that more complex decision rules are required and that this leads to within-group unfairness for all but one of the groups. We illustrate our findings based on simulated and real data.