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A formulation, which is different from Guttman's is presented. The two formulations are both called the optimal scaling approach, and are proven to provide identical scale values. The proposed formulation has at least two advantages over Guttman's. Namely, (i) the former serves to clarify close relations of the optimal scaling approach to those of Slater and the vector model of preferential choice, and (ii) in addition to the stimulus scale values, it provides scores for the subjects, which indicate the degrees of response consistency (transitivity), relative to the optimum solution. The method is assumption-free and capable of multidimensional analysis.

Optimal scaling of paired comparison and rank order data: An alternative to Guttman's formulation