Multidimensional similarity: an experimental and theoretical comparison of vector, distance, and set theoretical models: I. Models and internal consistency of data

Abstract

In an experiment (conducted by the senior author) subjects were instructed to give three kinds of quantitative judgment on pairs of simple geometrical stimuli: similarity, commonality ratio and magnitude ratio. It was assumed that the different kinds of judgments could be interpreted in terms of one cognitive structure, and that formal models for each of these judgments should be validated by predicting one kind of judgment from knowledge of another kind of judgment. The present report proposes two different, though related, systems of formal models for similarity, commonality and magnitude ratio judgments. One, called E-model, interprets the judgments in terms of set- and vector-representations, and connections between them; the other, called R-model, interprets the judgments in terms of set- and distance-representations and their connections. The results are slightly in favor of the E-model. In a subsequent paper, the authors will report the results of multidimensional analyses for the same data, which slightly favor the R-model.