This paper studies delegation in a model of discrete choice. In the delegation problem, an uninformed principal must consult an informed agent to make a decision. Both the agent and principal have preferences over the decided-upon action which vary based on the state of the world, and which may not be aligned. The principal may commit to a mechanism, which maps reports of the agent to actions. When this mechanism is deterministic, it can take the form of a menu of actions, from which the agent simply chooses upon observing the state. In this case, the principal is said to have delegated the choice of action to the agent. We consider a setting where the decision being delegated is a choice of a utility-maximizing action from a set of several options. We assume the shared portion of the agent's and principal's utilities is drawn from a distribution known to the principal, and that utility misalignment takes the form of a known bias for or against each action. We provide tight approximation analyses for simple threshold policies under three increasingly general sets of assumptions. With independently-distributed utilities, we prove a $3$-approximation. When the agent has an outside option the principal cannot rule out, the constant approximation fails, but we prove a $\log \rho/\log\log \rho$-approximation, where $\rho$ is the ratio of the maximum value to the optimal utility. We also give a weaker but tight bound that holds for correlated values, and complement our upper bounds with hardness results. One special case of our model is utility-based assortment optimization, for which our results are new.

翻译：本文研究离散选择模型中的委托问题。在委托问题中，一个不知情的主体必须咨询知情代理以做出决策。代理和主体对选定行动的偏好均随世界状态变化，且二者偏好可能不一致。主体可承诺采用一种机制，将代理的报告映射为具体行动。当该机制为确定性时，其可表现为行动菜单的形式，代理在观测状态后直接从中选择。此时，我们称主体将行动选择权委托给了代理。我们考虑这样一种设定：被委托的决策是从若干选项中选择一个效用最大化的行动。我们假设代理与主体效用中共享部分的分布为主体的已知信息，而效用偏差则表现为对每个行动的已知偏好或厌恶。我们在三组渐次放宽的假设条件下，对简单阈值策略给出了紧近似分析。对于独立分布效用，我们证明了3-近似比。当代理存在主体无法排除的外部选项时，常数近似比不再成立，但我们证明了log ρ/log log ρ-近似比，其中ρ为最大效用值与最优效用之比。我们还给出了适用于相关效用的较弱紧界，并通过硬度结果补充了上界分析。我们模型的一个特例是基于效用的品类优化问题，本文结论对该领域具有创新性。