  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.
