Externally Valid Selection of Experimental Sites via the k-Median Problem

TL;DR

This paper links the problem of selecting experimental sites for external validity to the k-median problem, providing a decision-theoretic foundation and practical algorithms for optimal site selection.

Contribution

It introduces a decision-theoretic approach to site selection using the k-median problem, with conditions for optimality and empirical applications demonstrating its effectiveness.

Findings

Minimizing worst-case regret aligns with finding central site covariates.

The k-median formulation can be solved via linear integer programming.

Empirical applications show practical benefits of the method.

Abstract

We present a decision-theoretic justification for viewing the question of how to best choose where to experiment in order to optimize external validity as a $k$-median problem, a popular problem in computer science and operations research. We present conditions under which minimizing the worst-case, welfare-based regret among all nonrandom schemes that select $k$ sites to experiment is approximately equal - and sometimes exactly equal - to finding the k most central vectors of baseline site-level covariates. The k-median problem can be formulated as a linear integer program. Two empirical applications illustrate the theoretical and computational benefits of the suggested procedure.