On minima of discrimination functions

摘要

A discrimination function psi (x, y) assigns a measure of discriminability to stimulus pairs x, y (e.g., the probability with which they are judged to be different in a same-different judgment scheme). If for every x there is a single y least discriminable from x, then this y is called the point of subjective equality (PSE) for x, and the dependence h (x) of the PSE for x on x is called a PSE function. The PSE function g (y) is defined in a symmetrically opposite way. If the graphs of the two PSE functions coincide (i.e., g = h(-1)), the function is said to satisfy the Regular Minimality law. The minimum level functions are restrictions of psi to the graphs of the PSE functions. The conjunction of two characteristics of psi, (1) whether it complies with Regular Minimality, and (2) whether the minimum level functions are constant, has consequences for possible models of perceptual discrimination. By a series of simple theorems and counterexamples, we establish set-theoretic, topological, and analytic properties of psi which allow one to relate to each other these two characteristics of (C) 2008 Elsevier Inc. All rights reserved.