We study the compatibility between the optimal statistical parity solutions
and individual fairness. While individual fairness seeks to treat similar
individuals similarly, optimal statistical parity aims to provide similar
treatment to individuals who share relative similarity within their respective
sensitive groups. The two fairness perspectives, while both desirable from a
fairness perspective, often come into conflict in applications. Our goal in
this work is to analyze the existence of this conflict and its potential
solution. In particular, we establish sufficient (sharp) conditions for the
compatibility between the optimal (post-processing) statistical parity $L^2$
learning and the ($K$-Lipschitz or $(\epsilon,\delta)$) individual fairness
requirements. Furthermore, when there exists a conflict between the two, we
first relax the former to the Pareto frontier (or equivalently the optimal
trade-off) between $L^2$ error and statistical disparity, and then analyze the
compatibility between the frontier and the individual fairness requirements.
Our analysis identifies regions along the Pareto frontier that satisfy
individual fairness requirements. (Lastly, we provide individual fairness
guarantees for the composition of a trained model and the optimal
post-processing step so that one can determine the compatibility of the
post-processed model.) This provides practitioners with a valuable approach to
attain Pareto optimality for statistical parity while adhering to the
constraints of individual fairness.

我们研究了最优统计公平性解决方案与个别公平性之间的兼容性，并分析了它们之间的冲突以及潜在解决方案。通过放宽前者到 Pareto 边界，我们确定了满足个体公平性要求的 Pareto 边界区域，从而使统计公平的 Pareto 最优性与个体公平性的约束相适应。