🤖 AI Summary
This study addresses the challenge of uncontrolled compensation costs arising from erroneous interventions in cross-population data-driven decision-making. To ensure affordability, the authors propose a geometry-inspired framework that incorporates a certification mechanism to tightly bound the probability of decision errors when intervention effects are substantial. For the first time, they integrate decision affordability with computational geometry, rigorously demonstrating that Delaunay interpolation yields optimal worst-case cost guarantees. By synergistically combining matching estimators with computational geometry theory, the approach not only refines target population selection but also informs efficient data collection strategies. Empirical validation on semi-synthetic datasets from development economics confirms the method’s significant advantages in controlling compensation costs while enhancing decision efficacy.
📝 Abstract
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.