An Accounting Identity for Algorithmic Fairness

2026-01-28

AI Summary

This study reveals an inherent trade-off between accuracy and fairness in binary prediction, elucidating why multiple fairness criteria are often mutually incompatible. By establishing the first quantitative identity linking overall accuracy to diverse group fairness metrics, the authors decompose global calibration error into within-group and between-group components, unifying them under a “total unfairness budget.” This framework extends classical impossibility theorems to non-binary settings. Drawing on probability calibration theory, mean squared error analysis, and group-based statistical modeling—supported by both theoretical derivation and empirical validation—the work demonstrates that improving model accuracy effectively reduces the total unfairness budget. In contrast, most fairness interventions merely redistribute bias across different fairness violations and, when pursued at the expense of accuracy, may inadvertently exacerbate overall unfairness.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Computer Vision: Bias, Fairness & Privacy
• Game Theory and Economic Paradigms: Fair Division

Application Category

• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Social Networks and Social Media: Fairness and bias in social network and social media analysis
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics

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.

Problem

• algorithmic fairness
• accuracy-fairness tradeoff
• calibration
• impossibility results
• predictive modeling

Innovation

• algorithmic fairness
• accuracy-fairness tradeoff
• calibration
• impossibility theorems
• unfairness budget