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：我考虑一类统计决策问题，其中决策者必须基于有限样本在两种替代政策间做出选择以最大化社会福利。核心假设是潜在的（可能为无限维）参数位于一个已知凸集中，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，我在已知方差的正态误差假设下，推导出所有决策规则类中具有有限样本精确极小极大遗憾的决策规则。当误差分布未知时，我获得了一个可行的决策规则，该规则具有渐近极小极大遗憾性质。我将结果应用于回归间断点设计框架下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建设项目中通过实证分析进行案例说明。