On the law of Regular Minimality: Reply to Ennis

Ennis's critique touches on issues important for psychophysics, but the points he makes against the hypothesis that Regular Minimality is a basic property of sensory discrimination are not tenable.(1) Stimulus variability means that one and the same apparent stimulus value (as measured by experimenter) is a probabilistic mixture of true stimulus values. The notion of a true stimulus value is a logical necessity: variability and distribution presuppose the values that vary and are distributed (even if these values are represented by processes or sets rather than real numbers). Regular Minimality is formulated for true stimulus values. That a mixture of probabilities satisfying Regular Minimality does not satisfy this principle (unless it also satisfies Constant Self-Similarity) is an immediate consequence of my 2003 analysis. Stimulus variability can be controlled or estimated: the cases when observed violations of Regular Minimality can be accounted for by stimulus variability corroborate rather than falsify this principle. In this respect stimulus variability is no different from fatigue, perceptual learning, and other factors creating mixtures of discrimination probabilities in an experiment.(2) Could it be that well-behaved Thurstonian-type models are true models of discrimination but their parameters are so adjusted that the violations of Regular Minimality they lead to (due to my 2003 theorems) are too small to be detected experimentally? This is possible, but this amounts to admitting that Regular Minimality is a law after all, albeit only approximate: nothing in the logic of the Thurstonian-type representations per se prevents them from violating Regular Minimality grossly rather than slightly. Moreover, even very small violations predicted by a given class of Thurstonian-type models can be tested in specially designed experiments (perhaps under additional, independently testable assumptions). The results of one such experiment, in which observers were asked to alternately adjust to each other the values of stimuli in two observation areas, indicate that violations of Regular Minimality, if any, are far below limits of plausible interpretability.