1. This paper and a following paper deal with problems, such as the following, that arise in experimental studies of the neural mechanisms underlying sensory discrimination: What measures of neural activity are relevant in such a study? How can sample data from the responses of single neurons be combined to represent the information relayed by a population of neurons? How can neural data be compared with results from psychophysical studies? What assumptions are implicit in any such comparison? What are the implications of assumptions that neurons respond independently or that they have homogeneous response properties? How can neural codes be assessed in a systematic way? Can psychophysical and neurophysiological observations be combined to infer mechanisms or relationships in the processes underlying discrimination? All of these questions require some theoretical framework before they can be answered. These papers set out such a framework, they deal with most of those questions, and they provide practicable formulas for relating sample data from neurophysiological experiments to behavioral measures derived from psychophysical experiments. 2. The processes that intervene between a relatively peripheral array of neural activity and a subject's decision in a discrimination task are split into two sections: a) the ascending sensory processes that provide the final patterns of neural activity on which discrimination is based, and b) a process that yields decisions of the type required by the experimental design used in the psychophysical study. The approach is to develop a theory of the decision process in this paper, and then to expand it to incorporate the ascending processes in the following paper. 3. The decision theory deals with a class of experimental designs in which a subject is required to make a decision about two stimuli S1 and S2 (e.g., S1 is larger than S2, S2 is the same as S1, S2 was the modified stimulus, and so on). A mathematical representation for experimental designs of this type is developed. 4. The decision process is analyzed in two forms: a) a multivariate form in which the discrimination decision results directly from multidimensional neural representation of the two stimuli, and b) a vivariate form in which the final representation of each stimulus is a unidimensional variable. Conditions required for equivalence of these formulations are examined. 5. The theory includes as explicit variables a) the experimental design, b) the subject's discrimination strategy, c) bias, d) memory variance, e) bias variance, f) variance in the final neural representations of the stimuli, and g) their functional dependence on the stimuli that they represent. 6. Formulas are developed for the expected values of commonly used psychophysical measures such as the classical psychometric function, receiver operating characteristic (ROC) functions, discriminatory separation index (d'), and the difference limen. 7. Optimum discrimination behavior is analyzed.