Equalised Odds is not Equal Individual Odds: Post-processing for Group and Individual Fairness

TL;DR

This paper explores the incompatibility of group and individual fairness in predictive models, proposing a method to reconcile them through continuous probability functions constrained by Lipschitz conditions.

Contribution

It introduces a novel post-processing approach that achieves both group and individual fairness by constructing continuous probability functions with Lipschitz constraints.

Findings

The method preserves predictive power and robustness.

It ensures group fairness without violating individual fairness.

The approach effectively balances fairness objectives in calibrated models.

Abstract

Group fairness is achieved by equalising prediction distributions between protected sub-populations; individual fairness requires treating similar individuals alike. These two objectives, however, are incompatible when a scoring model is calibrated through discontinuous probability functions, where individuals can be randomly assigned an outcome determined by a fixed probability. This procedure may provide two similar individuals from the same protected group with classification odds that are disparately different -- a clear violation of individual fairness. Assigning unique odds to each protected sub-population may also prevent members of one sub-population from ever receiving equal chances of a positive outcome to another, which we argue is another type of unfairness called individual odds. We reconcile all this by constructing continuous probability functions between group thresholds that are constrained by their Lipschitz constant. Our solution preserves the model's predictive power, individual fairness and robustness while ensuring group fairness.