From Statistical Disclosure Control to Fair AI: Navigating Fundamental Tradeoffs in Differential Privacy

TL;DR

This paper investigates the fundamental limits of private data release by linking Dalenius's impossibility with differential privacy and emerging fairness constraints. It formalizes a three-way Pareto frontier among privacy, utility, and fairness, derives lower bounds showing how minority groups suffer more DP noise, and presents an $n^* = \Theta(d/(\\varepsilon^2 p F^2))$ threshold beyond which simultaneous optimization of all three objectives becomes feasible. Through theoretical results, empirical insights, and practical guidelines, it provides a unified framework and decision toolkit for practitioners and policymakers deploying private fair learning systems. The work highlights that while differential privacy offers rigorous guarantees, achieving strong fairness without sacrificing utility requires large sample sizes or innovative strategies such as synthetic data, adaptive privacy budgeting, and fairness-aware architecture, making the tradeoffs central to real-world impact.

Abstract

Differential privacy has become the gold standard for privacy-preserving machine learning systems. Unfortunately, subsequent work has primarily fixated on the privacy-utility tradeoff, leaving the subject of fairness constraints undervalued and under-researched. This paper provides a systematic treatment connecting three threads: (1) Dalenius's impossibility results for semantic privacy, (2) Dwork's differential privacy as an achievable alternative, and (3) emerging impossibility results from the addition of a fairness requirement. Through concrete examples and technical analysis, the three-way Pareto frontier between privacy, utility, and fairness is demonstrated to showcase the fundamental limits on what can be simultaneously achieved. In this work, these limits are characterized, the impact on minority groups is demonstrated, and practical guidance for navigating these tradeoffs are provided. This forms a unified framework synthesizing scattered results to help practitioners and policymakers make informed decisions when deploying private fair learning systems.

Figures (3)

• Figure 1: Laplace noise distributions for different privacy parameters $\varepsilon$. The scale parameter is $b = 1/\varepsilon$ for sensitivity $\Delta f = 1$. Higher privacy (smaller $\varepsilon$) results in wider distributions and more noise added to the true answer.
• Figure 2: The Privacy-Utility Tradeoff
• Figure 3: A Decision Tree for Tradeoff Mitigation Selection

Theorems & Definitions (13)

• Example 1: The Smoking Dataset
• Theorem 1: Informal
• Theorem 2: Impossibility of Semantic Security dwork_differential_2006
• Proof 1: Proof Sketch
• Definition 1: Differential Privacy dwork_differential_2006
• Definition 2: Sensitivity
• Theorem 3: Privacy Guarantee of Laplace Mechanism dwork_differential_2009
• Proof 2
• Theorem 4: Basic Composition dwork_differential_2006
• Definition 3: Demographic Parity