We propose an approach to recommendation systems that optimizes over possible sets of recommended alternatives in a decision-theoretic manner. Our approach selects the alternative set that maximizes the expected valuation of the user’s choice from the recommended set. The set-based optimization explicitly recognizes the opportunity for passing residual uncertainty about preferences back to the user to resolve. Implicitly, the approach chooses a set with a diversity of alternatives that optimally covers the uncertainty over possible user preferences. The approach can be used with several preference representations, including utility theory, qualitative preferences models, and informal scoring. We develop a specific formulation for multi-attribute utility theory, which we call maximization of expected max (MEM). We go on to show that this optimization is NP-complete (when user preferences are described by discrete distributions) and suggest two efficient methods for approximating it. These approximations have complexity of the same order as the traditional k-max operator and, for both synthetic and real-world data, perform better than the approach of recommending the k-individually best alternatives (which is not a surprise) and very close to the optimum set (which is less expected).