In the present study we investigated judgments of similarity between pairs of objects that differed on two dimensions. We were concerned with the question that was raised by Attneave (1950): How does the overall judgment of similarity depend upon differences on the dimensional components?Since 1950, two alternative answers have been proposed. Both answers assume that [udgments of similarity can be represented by a "spatial model." The assumption of a spatial model emphasizes the perceived difference or dissimilarity between two objects rather than the perceived similarity. The perceived dissimilarity (or the complement of the judged similarity) is treated as if it has the properties of a distance metric. The additional assumption is made that the set of psychological distances between all pairs of specified objects can be embedded within an n-dimensional coordinate space. The question of which spatial model is appropriate, then, is the question of what is the form of the space in which the psychological' distances can be embedded. And this question, in turn, reduces to one about the nature of the function which relates perceived distance to perceived differences on the component dimensions. Attneave (1950) proposed the answer, on the basis of his research, that the appropriate spatial model was of a non-Euclidean form-a form which has subsequently become known as the "city block" model. According to this answer, the perceived distance between two objects can be represented as the sum of the perceived differences on the component dimensions.Torgerson (1952), following the earlier suggestion of Richardson (1938), concluded that the Euclidean space was appropriate, at least for his data. In the Euclidean model the perceived distance between two objects is related to the component differences by means of the Pythagorean theorem.These conclusions about the appropriate spatial model are based on two different types of evidence or approaches-the approach of multidimensional scaling and the approach of multidimensional psychophysics. In the scaling approach, the investigator assumes he knows the appropriate spatial model. So far this approach has restricted itself to the Euclidean model. Assuming a Euclidean space, the investigator treats the obtained judgments as distances in an n-dimensional space, and he extracts a number of dimensions sufficient to reproduce adequately the original distances. The appropriateness of the model is determined by how well these dimensions reproduce the original distances. The decision as to whether the "goodness of fit" to the model is adequate is "absolute," in that no comparison is made with a specified alternative model. If the amount of variance accounted for exceeds an arbitrary value -a value which is rarely specified in advance and for which there is no consensual standard-then the Euclidean metric is declared appropriate. In the psychophysical approach the investigator assumes he knows the component dimensions. He then attempts to directly decide which combinatorial rule or spati...