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Measurement analogies: comparisons of behavioral and physical measures*

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Abstract

Two examples of behavioral measurement are explored—utility theory and a global psychophysical theory of intensity—that closely parallel the foundations of classical physical measurement in several ways. First, the qualitative attribute in question can be manipulated in two independent ways. Second, each method of manipulation is axiomatized and each leads to a measure of the attribute that, because they are order preserving, must be strictly monotonically related. Third, a law-like constraint, somewhat akin to the distribution property underlying, e.g., mass measurement, links the two types of manipulation. Fourth, given the numerical measures that result from each manipulation, the linking law between them can be recast as a functional equation that establishes the connection between the two measures of the same attribute. Fifth, a major difference from most physical measurement is that the resulting measures are themselves mathematical functions of underlying physical variables—of money and probability in the utility case and of physical intensity and numerical proportions in the psychophysical case. Axiomatizing these functions, although still problematic, appears to lead to interesting results and to limit the degrees of freedom in the representations.

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  1. Social Science Plaza, University of California, Irvine, CA, 92697-5100, USA

    R. Duncan Luce

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Correspondence to R. Duncan Luce.

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This article is derived from two of my talks: a keynote address presented at the annual meeting of the Psychometric Society in Pacific Grove, CA, June 14–17, 2004, and the other at the sessions in honor of Jean-Claude Falmagne’s 70th birth year at the meeting in Gent, Belgium, September 2–5, 2004, of the European Mathematical Psychology Group that he founded some 31 years ago. The work described here was supported, in part, by National Science Foundation grant SES-0136431 to the University of California, Irvine, and, in part, by the University. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors(s) and do not necessarily reflect the views of the National Science Foundation. I appreciate the detailed and useful comments of my collaborators A. J. Marley and Ragnar Steingrimsson on earlier versions of the manuscript, as well as those of three referees, one of whom, Ehtibar Dzhafarov, provided very useful comments and criticisms.

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Luce, R.D. Measurement analogies: comparisons of behavioral and physical measures*. Psychometrika 70, 227–251 (2005). https://doi.org/10.1007/s11336-004-1248-8

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