In this paper, we explore optimal treatment allocation policies that target distributional welfare. Most literature on treatment choice has considered utilitarian welfare based on the conditional average treatment effect (ATE). While average welfare is intuitive, it may yield undesirable allocations especially when individuals are heterogeneous (e.g., with outliers) - the very reason individualized treatments were introduced in the first place. This observation motivates us to propose an optimal policy that allocates the treatment based on the conditional quantile of individual treatment effects (QoTE). Depending on the choice of the quantile probability, this criterion can accommodate a policymaker who is either prudent or negligent. The challenge of identifying the QoTE lies in its requirement for knowledge of the joint distribution of the counterfactual outcomes, which is generally hard to recover even with experimental data. Therefore, we introduce minimax policies that are robust to model uncertainty. A range of identifying assumptions can be used to yield more informative policies. For both stochastic and deterministic policies, we establish the asymptotic bound on the regret of implementing the proposed policies. In simulations and two empirical applications, we compare optimal decisions based on the QoTE with decisions based on other criteria. The framework can be generalized to any setting where welfare is defined as a functional of the joint distribution of the potential outcomes.

翻译：本文探讨了以分配福利为目标的最优治疗分配政策。现有关于治疗选择的大部分文献都基于条件平均处理效应（ATE）来考虑功利主义福利。虽然平均福利直观易懂，但在个体存在异质性（例如存在异常值）的情况下，它可能产生不可取的分配结果——而这正是个性化治疗最初被提出的原因。这一观察促使我们提出一种基于个体治疗效应条件分位数（QoTE）的最优政策。通过选择不同的分位数概率，该准则能够适应谨慎或疏忽的政策制定者。识别QoTE的挑战在于需要了解反事实结果的联合分布，而这即使在有实验数据的情况下通常也难以恢复。因此，我们引入了对模型不确定性具有稳健性的极小极大政策。一系列识别假设可用于生成更具信息量的政策。对于随机政策和确定性政策，我们建立了实施所提政策的遗憾渐近界。在模拟实验和两个实证应用中，我们比较了基于QoTE的最优决策与基于其他准则的决策。该框架可推广至任何福利定义为潜在结果联合分布函数的场景。