Strategic Classification Has a Missing Lever: Audit Risk

Raman Ebrahimi, Massimo Franceschetti

Strategic classification studies how a decision maker should choose a classifier when the agents being classified can adjust their features in response to it. In existing models, the classifier is the only instrument available to the decision maker, and therefore a feature that is predictive but easy to fake can only be down-weighted or discarded. However, in many settings the decision maker can also verify: lenders verify income, admissions offices check documents, and tax authorities audit returns. In this paper, we propose a model of strategic classification in which the firm jointly designs a linear classifier and an \emph{audit profile}, which assigns to each fakeable feature a probability of detection and a penalty when caught. We show that under linear costs, the classifier affects the audit problem only through the distribution of gaming rents it induces, so that the joint design problem decomposes into the choice of a score rule and an audit allocation problem. We use this decomposition to characterize the optimal audit allocation, to identify when the allocation problem is tractable and when it is NP-hard (namely, when agents can game through overlapping features under…