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Attributes provide critical information about the alternatives that a decision-maker is considering. When their magnitudes are uncertain, the decision-maker may be unsure about which alternative is truly the best, so measuring the attributes may help the decision-maker make a better decision. This paper considers settings in which each measurement yields one sample of one attribute for one alternative. When given a fixed number of samples to collect, the decision-maker must determine which samples to obtain, make the measurements, update prior beliefs about the attribute magnitudes, and then select an alternative. This paper presents the sample allocation problem for multiple attribute selection decisions and proposes two sequential, lookahead procedures for the case in which discrete distributions are used to model the uncertain attribute magnitudes. The two procedures are similar but reflect different quality measures (and loss functions), which motivate different decision rules: (1) select the alternative with the greatest expected utility and (2) select the alternative that is most likely to be the truly best alternative. We conducted a simulation study to evaluate the performance of the sequential procedures and hybrid procedures that first allocate some samples using a uniform allocation procedure and then use the sequential, lookahead procedure. The results indicate that the hybrid procedures are effective; allocating many (but not all) of the initial samples with the uniform allocation procedure not only reduces overall computational effort but also selects alternatives that have lower average opportunity cost and are more often truly best.