Learning Where to Look: Delaunay Matching for Policy Choice and Data Collection

This paper studies data-driven policy choices from a geometric perspective. A sample from a donor population fully exposed to an innovation informs a policymaker (PM) on whether to innovate groups in a target population where the innovation was not introduced. Any wrong decision must be compensated from a finite budget and the PM seeks an estimator of the innovation's effect that guarantees an affordable compensation cost. I focus on matching estimators with positive weights and derive affordability guarantees when finite and large samples of the populations of interest are available. In the latter case, Delaunay interpolants, whose properties are well-known from results in computational geometry, deliver the smallest budget that covers the compensation cost uniformly over the admissible target populations, and conditional on the donor collection design. This result informs where to look for new donor observations to decrease the worst-case compensation cost the most. In an empirical application, I show that such collection plans halve the cost by adding three donor units, while random sampling fails to reach the same target within twenty additions.