  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.
