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.

[1]  Louis Narens,et al.  A theory of ratio magnitude estimation , 1996 .

[2]  R. Luce,et al.  On the possible psychophysical laws. , 1959, Psychological review.

[3]  G. Myles.  Journal of Economic Theory: J.-M. Grandmont, 1992, Transformations of the commodity space, behavioural heterogeneity, and the aggregation problem 57, 1-35 , 1993 .

[4]  R. Luce,et al.  Technical note on the joint receipt of quantities of a single good , 2003 .

[5]  R. Luce,et al.  When Four Distinct Ways to Measure Utility Are the Same , 1996 .

[6]  C. T. Ng,et al.  Functional equations arising in a theory of rank dependence and homogeneous joint receipts , 2003 .

[7]  W. Ellermeier,et al.  Empirical evaluation of axioms fundamental to Stevens’s ratio-scaling approach: I. Loudness production , 2000, Perception & psychophysics.

[8]  R. Duncan Luce,et al.  Rank- and sign-dependent linear utility models for binary gambles , 1991 .

[9]  Jaap Van Brakel,et al.  Foundations of measurement , 1983 .

[10]  S. S. Stevens,et al.  Psychophysics: Introduction to Its Perceptual, Neural and Social Prospects , 1975 .

[11]  P. Fishburn,et al.  Rank- and sign-dependent linear utility models for finite first-order gambles , 1991 .

[12]  R. Duncan Luce,et al.  On the possible psychophysical laws revisited: remarks on cross-modal matching , 1990 .

[13]  R. Luce.  Utility of Gains and Losses: Measurement-Theoretical and Experimental Approaches , 2000 .

[14]  Louis Narens,et al.  Classification of concatenation measurement structures according to scale type , 1985 .

[15]  J. Aczél,et al.  Lectures on Functional Equations and Their Applications , 1968 .

[16]  D. Prelec.  The Probability Weighting Function , 1998 .

[17]  R. Luce,et al.  Reduction Invariance and Prelec's Weighting Functions. , 2001, Journal of mathematical psychology.