  This paper introduces a framework for measuring how much black-box
decision-makers rely on variables of interest. The framework adapts a
permutation-based measure of variable importance from the explainable machine
learning literature. With an emphasis on applicability, I present some of the
framework's theoretical and computational properties, explain how reliance
computations have policy implications, and work through an illustrative
example. In the empirical application to interruptions by Supreme Court
Justices during oral argument, I find that the effect of gender is more muted
compared to the existing literature's estimate; I then use this paper's
framework to compare Justices' reliance on gender and alignment to their
reliance on experience, which are incomparable using regression coefficients.
