A psychophysical theory of intensity proportions, joint presentations, and matches

Empirically testable assumptions relate 3 psychophysical primitives: presentations of pairs of physical intensities (e.g., pure tones of the same frequency and phase to the 2 ears or 2 successive tones to both ears); a respondent's ordering of such signal pairs by perceived intensity (e.g., loudness); and judgments about 2 pairs of stimuli being related as some proportion (numerical factor, as in magnitude production). Explicit behavioral assumptions lead to 2 families of psychophysical functions, one corresponding to unbiased joint presentations and the other to biased ones. Under an invariance assumption, the psychophysical functions in the unbiased case are approximate power functions, and those in the biased case are exact power functions. A number of testable predictions are made. The mathematics involved draws from publications in utility theory and mathematics but with a reinterpretation of the primitives.