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.

翻译：差分隐私已成为隐私保护机器学习系统的黄金标准。然而，后续研究主要聚焦于隐私与效用的权衡，使得公平性约束这一主题被低估且研究不足。本文系统性地探讨了三个研究脉络之间的联系：(1) Dalenius 关于语义隐私的不可能性结果，(2) Dwork 提出的差分隐私作为一种可实现的替代方案，以及 (3) 引入公平性要求后新出现的不可能性结果。通过具体案例和技术分析，本文论证了隐私、效用与公平性三者之间的帕累托前沿，揭示了可同时实现目标的基本限制。本研究刻画了这些限制，展示了其对少数群体的影响，并为权衡这些取舍提供了实践指导。这形成了一个统一框架，综合了分散的研究成果，以帮助从业者和政策制定者在部署隐私保护的公平学习系统时做出明智决策。