This paper introduces a novel information-theoretic perspective on the
relationship between prominent group fairness notions in machine learning,
namely statistical parity, equalized odds, and predictive parity. It is well
known that simultaneous satisfiability of these three fairness notions is
usually impossible, motivating practitioners to resort to approximate fairness
solutions rather than stringent satisfiability of these definitions. However, a
comprehensive analysis of their interrelations, particularly when they are not
exactly satisfied, remains largely unexplored. Our main contribution lies in
elucidating an exact relationship between these three measures of (un)fairness
by leveraging a body of work in information theory called partial information
decomposition (PID). In this work, we leverage PID to identify the granular
regions where these three measures of (un)fairness overlap and where they
disagree with each other leading to potential tradeoffs. We also include
numerical simulations to complement our results.

这篇论文介绍了一种新颖的信息论视角，探讨了机器学习中著名的群体公平性概念之间的关系，即统计平衡、平等几率和预测平衡。通过利用信息论中称为部分信息分解（PID）的工作，我们准确阐明了这三个 (不) 公平性度量之间的精确关系，并确定了它们重叠和相互矛盾的细节区域，从而引发了潜在的权衡。我们还包括了数值模拟来补充我们的结果。