Algorithmic fairness with monotone likelihood ratios

Wes Camp

Abstract: We show that inequalities of many commonly used fairness metrics (true/false positive/negative rates, predicted positive/negative rates, and positive/negative predictive values) are guaranteed for groups with different outcome rates under a monotonically calibrated model whose risk distributions have a monotone likelihood ratio, extending existing impossibility results. We further provide lower bounds on the FNR/FPR disparities and PPR/PNR disparities in the same setting, showing that either the FNR disparity or FPR disparity is at least as large as the positive outcome rate disparity (for FNR disparity) or negative outcome rate disparity (for FPR disparity), and either the PPR disparity or PNR disparity is at least as large as the positive outcome rate disparity (for PPR disparity) or negative outcome rate disparity (for PNR disparity). While incompatibilities of some combinations of these metrics have been demonstrated previously, we are unaware of any work that has demonstrated direct incompatibility of calibration with these individual equalities, equivalence of these inequalities, or lower bounds for the disparity in these values under distributional assumptions about a model's predictions.

Submission Length: Regular submission (no more than 12 pages of main content)

Assigned Action Editor: ~Geoff_Pleiss1

Submission Number: 4684