We consider multiattribute Bayesian optimization, where each feasible design is associated with a vector of attributes that can be evaluated via a time-consuming computer code, and the optimizer has not been provided with a utility function over attributes. Past work on multiattribute and multiobjective optimization has focused on estimating the Pareto frontier, measuring performance without a clear link to the value derived from the estimated frontier. We present a new decision-theoretic way to value the information derived from sampling in such multiattribute optimization problems. We assume that a decision-maker has a private utility function over attributes, according to which she may select attribute vectors, but which she cannot easily articulate to the optimizer. We model this utility function as drawn from a Bayesian prior distribution. The decision-maker will use this private utility function to select her most preferred design from a set identified by the sampling algorithm. The algorithm’s goal is to identify a set of designs that maximizes the expected utility of this most preferred design. We develop a novel algorithm using this approach, and show that it is better able to focus sampling effort on designs with attribute vectors that are more likely to be preferred.