The dimensional representation and the metric structure of similarity data

Abstract A set of ordinal assumptions, formulated in terms of a given multidimensional stimulus set, is shown to yield essentially unique additive difference measurement of dissimilarity, or psychological distance. According to this model, dissimilarity judgments between multidimensional objects are regarded as composed of two independent processes: an intradimensional subtractive process, and an interdimensional additive process. Although the additive difference measurement model generalizes traditional metric models, the conditions under which it satisfies the metric axims impose severe restrictions on the measurement scales. The implications of the results for the representation of similarity data by metric and/or dimensional models are discussed.