ABSTRACT
This chapter has three thrusts: (a) It formulates in a common framework mathematical representations of two global sensory procedures: summation of intensity and the method of ratio production (Luce, 2002, 2004). Until recently, these two topics have not been treated together in the literature, (b) Although the psychophysical representations we arrive at include both free parameters and free functions, a message of this work, especially illustrated in Steingrimsson and Luce (2005a, 2005b), 3 is that one can evaluate the adequacy of the representations without ever estimating either the parameters or the functions, but rather by just evaluating parameter-free behavioral properties that give rise to the representations, (c) A closely related message is that, to the degree that the theory holds, no individual differences arise in the defining behavioral properties except, of course, for the fact that each person has his or her own sense of the relative intensities of two stimuli, that is, the subjective intensity ordering. At the same time, the potential exists for substantial individual differences in the representations in the following sense: there is a strictly increasing psychophysical function and a strictly increasing function that distorts numerical responses but that is not otherwise constrained without additional axioms. The work on the forms of these functions, although quite well developed, is not yet in final manuscript form. Nonetheless, we cover it in some detail in Sections 5 and 6. A number of interesting open problems are listed.
