A theory of magnitude estimation and cross-modality matching

Abstract

The generalizations that have emerged from “ratio scaling” of sensory continua include: consistency among various methods, consistency with changes in modulus, and the power law. These generalizations pose difficulties for the commonly held view (called here mapping theory) that “ratio scaling” judgments are mediatedby mappings of stimuli into sensations. The main difficulty is that the ratio-like consistency properties of cross-modality matching cannot be accounted for by essentially nonnumerical sensations, and hence must be treated by a process theory which assumes that cross-modality matching is mediated by magnitude estimation. An alternative process theory ( relation theory) assumes that “ratio scaling” judgments are not mediated by a property of single stimuli (sensation) but rather by a property of pairs of stimuli. The perceived relations of pairs (called sensation “ratios”) are assumed to share a qualitative property of numerical ratios. This axiom leads to a measurement representation by ratios of psychophysical functions (sensation functions). These psychophysical functions can be obtained directly by magnitude estimation provided that mental estimation of length ratios and perceived sensation “ratios” of length pairs are ordered alike (in fact, both correspond roughly to physical length ratios). The assumed ordering of stimulus pairs by sensation “ratios” leads to a simple account of the various empirical consistency generalizations. Such an ordering may also be related to other pair orderings, such as those based on discriminability measures and on perceived sensation “differences.”