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Intrinsic Fairness-Accuracy Tradeoffs under Equalized Odds

Meiyu Zhong, Ravi Tandon

TL;DR

The paper addresses the fundamental problem of fairness-accuracy tradeoffs for binary classification under equalized odds (EO). It derives a classifier-independent unconstrained upper bound on accuracy and, crucially, an EO-budget bound that incorporates subgroup TV distances and subgroup proportions, linking accuracy limits to data statistics via $d_{TV}(P_1^a,P_0^a)$, $d_{TV}(P_1^b,P_0^b)$, $\alpha$, and $\beta$. The bounds are demonstrated to be tight in simple regimes and are estimable from real data using variational TV estimators; experiments on COMPAS, Adult, and Law School datasets compare these bounds to the performance of EO-fair classifiers, illustrating fundamental limits when subgroup disparities are large. Overall, the work provides theoretical guarantees and practical guidance for designing and evaluating fair classifiers under EO constraints, with implications for policy and deployment in high-stakes domains.

Abstract

With the growing adoption of machine learning (ML) systems in areas like law enforcement, criminal justice, finance, hiring, and admissions, it is increasingly critical to guarantee the fairness of decisions assisted by ML. In this paper, we study the tradeoff between fairness and accuracy under the statistical notion of equalized odds. We present a new upper bound on the accuracy (that holds for any classifier), as a function of the fairness budget. In addition, our bounds also exhibit dependence on the underlying statistics of the data, labels and the sensitive group attributes. We validate our theoretical upper bounds through empirical analysis on three real-world datasets: COMPAS, Adult, and Law School. Specifically, we compare our upper bound to the tradeoffs that are achieved by various existing fair classifiers in the literature. Our results show that achieving high accuracy subject to a low-bias could be fundamentally limited based on the statistical disparity across the groups.

Intrinsic Fairness-Accuracy Tradeoffs under Equalized Odds

TL;DR

The paper addresses the fundamental problem of fairness-accuracy tradeoffs for binary classification under equalized odds (EO). It derives a classifier-independent unconstrained upper bound on accuracy and, crucially, an EO-budget bound that incorporates subgroup TV distances and subgroup proportions, linking accuracy limits to data statistics via , , , and . The bounds are demonstrated to be tight in simple regimes and are estimable from real data using variational TV estimators; experiments on COMPAS, Adult, and Law School datasets compare these bounds to the performance of EO-fair classifiers, illustrating fundamental limits when subgroup disparities are large. Overall, the work provides theoretical guarantees and practical guidance for designing and evaluating fair classifiers under EO constraints, with implications for policy and deployment in high-stakes domains.

Abstract

With the growing adoption of machine learning (ML) systems in areas like law enforcement, criminal justice, finance, hiring, and admissions, it is increasingly critical to guarantee the fairness of decisions assisted by ML. In this paper, we study the tradeoff between fairness and accuracy under the statistical notion of equalized odds. We present a new upper bound on the accuracy (that holds for any classifier), as a function of the fairness budget. In addition, our bounds also exhibit dependence on the underlying statistics of the data, labels and the sensitive group attributes. We validate our theoretical upper bounds through empirical analysis on three real-world datasets: COMPAS, Adult, and Law School. Specifically, we compare our upper bound to the tradeoffs that are achieved by various existing fair classifiers in the literature. Our results show that achieving high accuracy subject to a low-bias could be fundamentally limited based on the statistical disparity across the groups.
Paper Structure (5 sections, 2 theorems, 25 equations, 2 figures)

This paper contains 5 sections, 2 theorems, 25 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Preliminaries and Problem Statement
  3. Main Results and Discussion
  4. Experiments
  5. Conclusion

Key Result

Theorem 1

(Unconstrained Upper Bound on Accuracy) For any binary classifier $f$, its accuracy $Acc(f)$ satisfies $\text{Acc}(f) \leq \overline{\text{Acc}}$, where $\overline{\text{Acc}}$ is given as follows: Furthermore, the upper bound can be attained by the Bayes optimal classifier when $\alpha = 0, 0.5$ or $1$.

Figures (2)

  • Figure 1: (a) Illustration of the relationship between Theorem \ref{['The:generilized_le_cam']} and Theorem \ref{['the:tradeoff_acc_fair']}, where the red dotted line represents the bound established in Theorem \ref{['The:generilized_le_cam']}, while the orange fluorescent line depicts the minimum of the two functions $T_1$ and $T_2$ in Theorem \ref{['the:tradeoff_acc_fair']}, where $T_1$ and $T_2$ have slopes of $1-\beta$ and $\beta$, respectively. (b) Dataset-related parameters and upper-bound-related parameters in the real world datasets: COMPAS, Adult and Law School dataset.
  • Figure 2: Comparison of the upper bound of the test accuracy in real world datasets: (a) COMPAS dataset, (b) Adult dataset, (c) Law School dataset under three fair classifiers ($C_1$zhong2023learning, $C_2$bechavod2017learning and $C_3$zafar2017fairness1). We can observe that Theorem \ref{['the:tradeoff_acc_fair']} is consistently tighter than the unconstrained upper bound (Theorem \ref{['The:generilized_le_cam']}), and Theorem \ref{['the:tradeoff_acc_fair']} provides the tightly upper bound on the tradeoffs achieved by three classifiers for three real world datasets.

Theorems & Definitions (9)

  • Definition 1
  • Definition 2
  • Theorem 1
  • proof
  • Theorem 2
  • Remark 1
  • Remark 2
  • Remark 3
  • proof