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 \emph{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 optimal policies that are robust to model uncertainty. We then propose a range of identifying assumptions under which we can point or partially identify the QoTE. We establish the asymptotic bound on the regret of implementing the proposed policies. We consider both stochastic and deterministic rules. In simulations and two empirical applications, we compare optimal decisions based on the QoTE with decisions based on other criteria.

翻译：本文探讨了以分布福利为目标的优化处理分配政策。现有处理选择文献大多考虑基于条件平均处理效应（ATE）的功利主义福利。尽管平均福利直观易懂，但当个体异质性较大（例如存在异常值）时，它可能产生不理想的分配结果——这恰恰是最初引入个性化处理的根本原因。这一观察促使我们提出一种基于条件个体处理效应分位数（QoTE）的优化分配策略。根据分位数概率的选择，该准则可以容纳审慎或疏忽的政策制定者。识别QoTE的挑战在于需要掌握反事实结果的联合分布信息，而即使使用实验数据，该分布通常也难以恢复。因此，我们引入对模型不确定性具有鲁棒性的极小极大优化策略。随后，我们提出一系列可识别假设，在这些假设下我们可以点识别或部分识别QoTE。我们建立了实施所提策略的遗憾渐近界。我们同时考虑了随机规则和确定性规则。在模拟实验和两项实证应用中，我们将基于QoTE的最优决策与其他准则下的决策进行了比较。