Theories of choice may be regarded as having two principal features: a representation of indecision and a decision rule stating the conditions which must be satisfied for a choice to occur. Three ways of representing indecision are described and evaluated. I n terms of one of these representations, several theoretical models of choice are developed by considering the consequences of two kinds of decision rule. A way of determining the properties of the models is described, but is not used in more than an illustrative fashion. A detailed examination of these properties will be given elsewhere, when comparisons will be made with empirical data.The relationship between two measuresThe relation of response latency and speed to the intervening Behavior Theory and Conditioning. Englewood Cliffs: Prentice- Signal Detection and Recognition by Human Observers.Part I. Psychol. Rev. 59, 431-442. P S.P.

The relation between response latency and probability is discussed with particular reference to differences between mean times for correct and incorrect responses in difficult two-choice discriminations. The predictions of some finite Markov chain models for this situation are considered, and possible modifications of these simple systems which may bring about features of observed data are discussed. Some results, in the form of curves of the latency-probability relation, are presented from earlier work and new discrimination experiments. These data are discussed in relation to theoretical interpretations based on a particular stochastic model which describes psychophysical discrimination in terms of the accumulation of units contributing to the overt response.

A general class of stochastic models for choice behaviour is described, which can be regarded as finite Markov chains with absorbing states and which subsumes some particular models discussed by Audley and Pike (1965). The equations for response probabilities and moments of response latency distributions are obtained from the properties of such chains and a very general approach is given in terms of ‘transition‐similar’ systems, which includes discrete time and continuous time processes. Generating functions for the systems are obtained and variations in parameters controlling the rate of occurrence of events in time are also considered. A brief discussion centres around some of the problems which arise in such a general treatment and the reasons for its usefulness.

A model for two-choice discrimination based on a process of simple counting is described, and two experiments are performed to test the predictions of the model concerning the graph of latency as a function of response proportion. Two main forms of this graph are identified and predicted to arise in different circumstances. The experimental results support the model, and its possible extension to other psychophysical situations, especially signal detection, are then discussed. It is compared with a model derived directly from the detection situation, and the usefulness of testing these models is pointed out.

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