Abstract

There is a theorem that shows that it is impossible for an algorithm to jointly satisfy the statistical fairness criteria of Calibration and Equalized Odds non-trivially. But what about the recently advocated alternative to Calibration, Base Rate Tracking? Here we show that Base Rate Tracking is strictly weaker than Calibration, and then take up the question of whether it is possible to jointly satisfy Base Rate Tracking and Equalized Odds in non-trivial scenarios. We show that it is not, thereby establishing an even more general impossibility theorem.