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A general theory of signal detectability, constructed after the model provided by decision theory, is applied to the performance of the human observer faced with the problem of choosing among multiple signal alternatives on the basis of a fixed, finite observation interval. An extension of the theory, previously reported, of deciding among two alternatives, is developed in detail, permitting the treatment of the two simple cases involving multiple alternatives that are studied experimentally. In both cases, a priori probabilities are assigned to the occurrence of the relevant signal alternatives, and values are assigned to the possible decision outcomes. This assignment permits definition of the expected value of a decision, and specifies as the optimum decision criteria those that maximize expected value. The experiments are primarily concerned with determining the ability of the human observer to successively establish optimum decision criteria in accordance with changes in the a priori probabilities and risk functions. The experimental results are portrayed in the form of comparisons of the payoff obtained by the observer and the theoretically maximum payoff attainable, and comparisons of the response-frequency tables generated by the theory and by the observer. The results indicate that a highly simplified theory is adequate for prediction of the obtained payoff and response-frequency tables to within a few percent. They also indicate the fairly large extent to which intelligence may influence a sensory process usually assumed to involve fixed parameters.