  Machine learning models are often used to decide who receives a loan, a job
interview, or a public benefit. Models in such settings use features without
considering their actionability. As a result, they can assign predictions that
are fixed $-$ meaning that individuals who are denied loans and interviews are,
in fact, precluded from access to credit and employment. In this work, we
introduce a procedure called recourse verification to test if a model assigns
fixed predictions to its decision subjects. We propose a model-agnostic
approach for recourse verification with reachable sets $-$ i.e., the set of all
points that a person can reach through their actions in feature space. We
develop methods to construct reachable sets for discrete feature spaces, which
can certify the responsiveness of any model by simply querying its predictions.
We conduct a comprehensive empirical study on the infeasibility of recourse on
datasets from consumer finance. Our results highlight how models can
inadvertently preclude access by assigning fixed predictions and underscore the
need to account for actionability in model development.
