Rational distance functions for multidimensional scaling

Abstract

A rational distance function is a numerical measure of psychological distance whose geometric properties are deducible from psychological truths about some particular judgmental task. In this paper, we review two theoretical analyses that have led to proposed rational distance functions. These analyses are based on two different tasks: paired-associate learning and similarity judgments. A generalization of the theory on similarity judgments is presented. Empirical results concerning similarity judgments seriously conflict with the basic psychological assumptions in the generalized treatment of similarity judgments. We conclude form these results that the construction of valid psychologically-based distance functions from analysis of choice probabilities in similarity judgments requires, as an initial step, the development of scaling models that take into account the influence of “irrelevant” dimensions on choice probability.