As society increasingly relies on AI-based tools for decision-making in socially sensitive domains, investigating fairness and equity of such 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).