Incorporating Preferences Into Treatment Assignment Problems

Abstract: This study investigates the problem of individualizing treatment allocations using stated preferences for treatments. If individuals know in advance how the assignment will be individualized based on their stated preferences, they may state false preferences. We derive an individualized treatment rule (ITR) that maximizes welfare when individuals strategically state their preferences. We also show that the optimal ITR is strategy-proof, that is, individuals do not have a strong incentive to lie even if they know the optimal ITR a priori. Constructing the optimal ITR requires information on the distribution of true preferences and the average treatment effect conditioned on true preferences. In practice, the information must be identified and estimated from the data. As true preferences are hidden information, the identification is not straightforward. We discuss two experimental designs that allow the identification: strictly strategy-proof randomized controlled trials and doubly randomized preference trials. Under the presumption that data comes from one of these experiments, we develop data-dependent procedures for determining ITR, that is, statistical treatment rules (STRs). The maximum regret of the proposed STRs converges to zero at a rate of the square root of the sample size. An empirical application demonstrates our proposed STRs.