Investigating fairness and equity of automated systems has become a critical
field of inquiry. Most of the literature in fair machine learning focuses on
defining and achieving fairness criteria in the context of prediction, while
not explicitly focusing on how these predictions may be used later on in the
pipeline. For instance, if commonly used criteria, such as independence or
sufficiency, are satisfied for a prediction score $S$ used for binary
classification, they need not be satisfied after an application of a simple
thresholding operation on $S$ (as commonly used in practice). In this paper, we
take an important step to address this issue in numerous statistical and causal
notions of fairness. We introduce the notion of a margin complement, which
measures how much a prediction score $S$ changes due to a thresholding
operation. We then demonstrate that the marginal difference in the optimal 0/1
predictor $\widehat Y$ between groups, written $P(\hat y \mid x_1) - P(\hat y
\mid x_0)$, can be causally decomposed into the influences of $X$ on the
$L_2$-optimal prediction score $S$ and the influences of $X$ on the margin
complement $M$, along different causal pathways (direct, indirect, spurious).
We then show that under suitable causal assumptions, the influences of $X$ on
the prediction score $S$ are equal to the influences of $X$ on the true outcome
$Y$. This yields a new decomposition of the disparity in the predictor
$\widehat Y$ that allows us to disentangle causal differences inherited from
the true outcome $Y$ that exists in the real world vs. those coming from the
optimization procedure itself. This observation highlights the need for more
regulatory oversight due to the potential for bias amplification, and to
address this issue we introduce new notions of weak and strong business
necessity, together with an algorithm for assessing whether these notions are
satisfied.

通过因果分解从真实世界中存在的偏见与优化过程本身导致的因果差异中解脱出来，研究论文引入了边界互补的概念，并提出了衡量预测分数变化的新方法，以解决自动化系统的公平性和公正性问题。同时，还介绍了部分业务必要性的概念和评估算法，以应对潜在的偏见放大问题。