Differential coupling of sensory discriminations inferred from a survey of stable decision models for Weber's Law

Differential coupling of sensory discriminations to the physical stimuli is here established by showing that the contrary supposition, direct coupling, leads to empirical predictions which are at variance with well‐established experimental findings. Certain plausible assumptions about the initial stages of sensory processing suggest that the distributions to be combined in a statistical model for sensory discrimination should be stable; these assumptions are first set out together with the experimental evidence which gives them plausibility. The notion of direct coupling to the physical stimuli suggests, in addition, that the stable distributions should be unidimensional. A survey of stable decision models shows that, to accommodate Weber's Law, the distributions must be either Cauchy distributions or strictly stable. The unidimensional Cauchy model is shown to be incompatible with the typical shape of the psychometric function for a discrimination between two separate stimuli; and unidimensional, strictly stable, decision models are shown to have inadequate resolving power in relation to the discriminative sensitivity of human subjects. The suggestion that the decision variables should be unidimensional is thereby shown to be untenable. Sensory discriminations can be satisfactorily represented by a strictly stable model with an unspecified, possibly large, number of independent components, and an example (the normal model) is given to show what such a model might look like. Estimates are given with respect to this model of the numbers of independent components required to support the accuracy of discrimination typically achieved with different stimulus attributes.