I consider a class of statistical decision problems in which the policy maker must decide between two alternative policies to maximize social welfare based on a finite sample. The central assumption is that the underlying, possibly infinite-dimensional parameter, lies in a known convex set, potentially leading to partial identification of the welfare effect. An example of such restrictions is the smoothness of counterfactual outcome functions. As the main theoretical result, I derive a finite-sample, exact minimax regret decision rule within the class of all decision rules under normal errors with known variance. When the error distribution is unknown, I obtain a feasible decision rule that is asymptotically minimax regret. I apply my results to the problem of whether to change a policy eligibility cutoff in a regression discontinuity setup, and illustrate them in an empirical application to a school construction program in Burkina Faso.

翻译：本文考虑一类统计决策问题，其中政策制定者需基于有限样本在两种替代政策间选择以最大化社会福利。核心假设在于，潜在的（可能为无穷维）参数位于已知凸集中，这可能导致福利效应的部分识别。此类约束的一个例子是反事实结果函数的平滑性。作为主要理论结果，我在方差已知的正态误差假设下，推导出所有决策规则类中的有限样本精确极小最大遗憾决策规则。当误差分布未知时，我获得了一个可行的渐近极小最大遗憾决策规则。我将这些结果应用于回归间断点设计中是否改变政策资格阈值的决策问题，并在布基纳法索一所学校的建设项目实证分析中进行验证。