Geometric Control of Decisions' Affordability

This paper studies the performance of data-driven decisions from a geometric perspective. A policymaker learns from an innovated donor population to decide whether to innovate groups in a distinct target population, and must compensate for any mistake. I introduce certification: an estimator yields certified decisions when it controls the probability of a mistake, whenever intervention effects are sufficiently large in magnitude. First, I show that certification implies a bound on worst-case compensation. Then, I study matching estimators with positive weights and show that, in a large-sample regime, affordability by certification becomes a purely geometric problem. I prove that a Delaunay interpolant, whose properties are well-known from results in computational geometry, delivers the best affordability guarantee. Finally, I show how this result can be leveraged to guide donor-data collection plans to bring worst-case compensation cost below a target level. I illustrate the gains of adopting this geometric point of view in targeting and collection plans with a semi-synthetic empirical application in development economics.