Recent work has proposed powerful frameworks, rooted in causal theory, to quantify fairness. Causal inference has primarily emphasized the detection of \emph{average} treatment effects (ATEs), and subsequent notions of fairness have inherited this focus. In this paper, we build on previous concerns about regulation based on averages. In particular, we formulate the "causal masking problem" as a linear program that optimizes an alternative objective, such as maximizing profit or minimizing crime, while retaining a zero ATE (i.e., the ATE between a protected attribute and a decision). By studying the capabilities and limitations of causal masking, we show that optimization under ATE-based regulation may induce significant unequal treatment. We demonstrate that the divergence between true and causally masked fairness is driven by confounding, underscoring the importance of full conditional-independence testing when assessing fairness. Finally, we discuss statistical and information-theoretic limitations that make causally masked solutions very difficult to detect, allowing them to persist for long periods. These results argue that we must regulate fairness at the model-level, rather than at the decision level.

翻译：近期研究提出了基于因果理论的强大框架来量化公平性。因果推断主要侧重于检测平均处理效应，而后续的公平性概念也继承了这一侧重点。本文基于先前关于基于平均值进行监管的关切展开研究。具体而言，我们将“因果掩蔽问题”表述为一个线性规划问题，该规划在保持零平均处理效应（即受保护属性与决策之间的ATE）的同时，优化替代目标（例如最大化利润或最小化犯罪率）。通过研究因果掩蔽的能力与局限，我们证明基于ATE的监管下的优化可能导致显著的不平等对待。我们论证了真实公平性与因果掩蔽公平性之间的差异是由混杂因素驱动的，这凸显了在评估公平性时进行完全条件独立性检验的重要性。最后，我们讨论了统计与信息论上的限制，这些限制使得因果掩蔽的解决方案极难被检测，从而允许其长期存在。这些结果表明，我们必须在模型层面而非决策层面对公平性进行监管。