Ranking Treatment Saturations: Regret Bounds and Experimental Design

Seungjin Han, Julius Owusu and Youngki Shin

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Abstract: We study the statistical decision problem of ranking treatment saturations, the treated shares of a cluster. Planners need a ranking, not only the best saturation, when rollouts are phased or the preferred saturation becomes infeasible. Using a two-stage randomized saturation experiment, we analyse the empirical success (ES) ranking, a simple and widely used rule. We derive finite-sample regret bounds for ES under the welfare-weighted Kendall distance loss that allow arbitrary within-cluster interference and need no network data. In a local asymptotic framework, ES on efficient welfare estimates has maximum regret at most about 1.4 times the minimax regret, for any number of saturations and any covariance. This bound guides the allocation of clusters by balancing cost against the variance of cluster means under each saturation. In the Malawi cash-transfer experiment, ES ranks full saturation of unconditional transfers first and zero last for marriage, and the realized allocation nearly minimizes the bound.

Date: 2026-06, Revised 2026-10
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