  Systems based on machine learning may exhibit discriminatory behavior based
on sensitive characteristics such as gender, sex, religion, or race. In light
of this, various notions of fairness and methods to quantify discrimination
were proposed, leading to the development of numerous approaches for
constructing fair predictors. At the same time, imposing fairness constraints
may decrease the utility of the decision-maker, highlighting a tension between
fairness and utility. This tension is also recognized in legal frameworks, for
instance in the disparate impact doctrine of Title VII of the Civil Rights Act
of 1964 -- in which specific attention is given to considerations of business
necessity -- possibly allowing the usage of proxy variables associated with the
sensitive attribute in case a high-enough utility cannot be achieved without
them. In this work, we analyze the tension between fairness and accuracy from a
causal lens for the first time. We introduce the notion of a path-specific
excess loss (PSEL) that captures how much the predictor's loss increases when a
causal fairness constraint is enforced. We then show that the total excess loss
(TEL), defined as the difference between the loss of predictor fair along all
causal pathways vs. an unconstrained predictor, can be decomposed into a sum of
more local PSELs. At the same time, enforcing a causal constraint often reduces
the disparity between demographic groups. Thus, we introduce a quantity that
summarizes the fairness-utility trade-off, called the causal fairness/utility
ratio, defined as the ratio of the reduction in discrimination vs. the excess
loss from constraining a causal pathway. This quantity is suitable for
comparing the fairness-utility trade-off across causal pathways. Finally, as
our approach requires causally-constrained fair predictors, we introduce a new
neural approach for causally-constrained fair learning.
