An Accounting Identity for Algorithmic Fairness

TL;DR

This paper introduces an accounting identity linking accuracy and fairness in predictive models, revealing inherent tradeoffs and providing a unified framework for understanding fairness constraints in binary and regression tasks.

Contribution

It derives a novel identity connecting accuracy with fairness measures, explaining tradeoffs and impossibility results, and extends the analysis to non-binary outcomes.

Findings

Fairness interventions often trade off with accuracy.

Reducing fairness violations can expand the total unfairness budget.

The identity applies to both binary and regression prediction tasks.

Abstract

We derive an accounting identity for predictive models that links accuracy with common fairness criteria. The identity shows that for globally calibrated models, the weighted sums of miscalibration within groups and error imbalance across groups is equal to a "total unfairness budget." For binary outcomes, this budget is the model's mean-squared error times the difference in group prevalence across outcome classes. The identity nests standard impossibility results as special cases, while also describing inherent tradeoffs when one or more fairness measures are not perfectly satisfied. The results suggest that accuracy and fairness are best viewed as complements in binary prediction tasks: increasing accuracy necessarily shrinks the total unfairness budget and vice-versa. Experiments on benchmark data confirm the theory and show that many fairness interventions largely substitute between fairness violations, and when they reduce accuracy they tend to expand the total unfairness budget. The results extend naturally to prediction tasks with non-binary outcomes, illustrating how additional outcome information can relax fairness incompatibilities and identifying conditions under which the binary-style impossibility does and does not extend to regression tasks.