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An interactive algorithm is proposed for the problem of selecting one of a finite number of alternatives where each is evaluated in terms of a number of conflicting criteria. A simple form of utility function is assumed, and the possibility is modeled probabilistically that the decisionmaker may at any time indicate a preference between alternatives in conflict with his true utility. On this basis, a formal Bayesian inferential procedure is applied to a sequence of pairwise choices between alternatives made by the decisionmaker to yield estimates of the unknown parameters of the utility function. This ultimately implies probability distributions on the utilities of each alternative. The sequence of pairwise comparisons continues until a satisfactorily short list of alternatives remains after elimination of those inferred to be significantly worse than the best.