A theory of relative judgment

This paper is concerned with the scaling method of “ratio estimation.” The simple theory that equates reported ratio judgments to ratios of psychological magnitudes is first considered, then two close relatives of this theory are formulated, each of which places weaker constraints on the structure of the data. Structural conditions are stated that express the relations that must hold among observed ratio judgments for each of the models. The models proposed are “cumulative” in the sense that the second is a weakened version of the first, and the third a weakened version of the second. A special feature of the models is that they may be tested entirely in terms of observables, avoiding the necessity of scale construction prior to testing. Tests were carried out on data from 9 published studies. The strongest model, typically used in scale construction using ratio estimation data, was generally inadequate, showing large systematic errors. However, the weakest version generally passed the tests of internal consistency, and the model equation provided a basis for constructing ratio scales utilizing bias parameters.