Thurstonian-type representations for ``same-different'' discriminations: deterministic decisions and independent images.
The original Thurstonian representation idea applies to greater-less comparison of given pairs of stimuli (e.g.\ noise), and the presumption is that individuals map stimuli into a perceptual space (`loudness'), so that to each stimulus one can assign a probability distribution on the perceptual space representing the possible values the stimulus can be mapped to, and relative probabilities; to test this presumption the theory starts with data on stimuli comparisons, and seeks a pair of probability distributions on the perceptual space which generate the given data; and the theorems seek conditions on the data which guarantee the existence of a representation in terms of probability pairs. The author's present work is concerned with extending this Thurstonian ideas to same-different comparisons (where naturally the perception space is no longer unidimensional but can be much more general), and presents a negative `regularity' result. In the present setting the data are represented by `psychometric' functions describing the probability with which a pair of stimuli (in The Euclidean space) are distinguished; and the result reported is roughly that for psychometric functions satisfying some `reasonable' properties there exists no `smooth' probabilistic representation in any perceptive space. The reason is that such smooth representations generate `smooth' psychometric functions, while `reasonable' functions of this kind naturally lack the given smoothness. In fact it is is not difficult to imagine that the latter functions' graphs may look like pointed cones, with minima for pairs of stimuli most likely perceived as `same'. The author concludes with a word of skepticism about Thurstonian-type representations for same-different comparisons, because if one wants to stick to such probabilistic representations one has to look for distributions with singularities; but on the other hand, the latter does not seem to be a natural constraint in psychophysics where on the contrary there is a time-honoured practice of working with normal or other `nice' distributions.
scientific article; zbMATH DE number 1956183