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The New Palgrave Dictionary of Economics pp 8618–8632Cite as

Palgrave Macmillan

Measurement, Theory of

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Abstract

Physical measurement, as embodied in dimensional analysis, consists of interlocked, qualitative, ordered structures. Analogous approaches to behavioural science are outlined for sensory scaling such as loudness, utility of uncertain alternatives, and qualitative foundations of probability. In many cases, they are an ordered structure with a binary operation for combining elements and a Cartesian product where each factor affects the ordering of the attribute. Axioms sufficient for measurement – for the existence of a homomorphism onto the positive real numbers – are mentioned, and their uniqueness (scale type – for example, ratio, interval, ordinal) is formulated qualitatively in terms of the structure’s symmetries (or automorphisms).

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Bibliography

  • Aczél, J. 1966. Lectures on functional equations and their applications. New York/London: Academic Press.

    Google Scholar 

  • Aczél, J. 1987. A short course on functional equations: Based upon recent applications to the social and behavioral sciences. Dordrecht: Reidel.

    Book  Google Scholar 

  • Alimov, N.G. 1950. On ordered semigroups. Izvestia Akademii Nauk SSSR, Serija Mat. 14: 569–576.

    Google Scholar 

  • Allais, M., and O. Hagen. 1979. Expected utility hypotheses and the allais paradox. Dordrecht: Reidel.

    Book  Google Scholar 

  • Alper, T.M. 1987. A classification of all order-preserving homeomorphism groups that satisfy uniqueness. Journal of Mathematical Psychology 31: 135–154.

    Article  Google Scholar 

  • Anderson, N.H. 1981. Foundations of information integration theory. New York: Academic.

    Google Scholar 

  • Barberà, S., P. Hammond and C. Seidl 1998, 2004. Handbook of utility theory, vol. I: Principles; vol. II: Extensions. Boston: Kluwer.

    Google Scholar 

  • Bell, D. 1982. Regret in decision making under uncertainty. Operations Research 30: 961–981.

    Article  Google Scholar 

  • Birnbaum, M.H. 2007. Tests of branch splitting and branch-splitting independence in Allais paradoxes with positive and mixed consequences. Organizational Behavior and Human Decision Processes 102: 154–173.

    Article  Google Scholar 

  • Choquet, G. 1953. Theory of capacities. Annals Institut Fourier 5: 131–295.

    Article  Google Scholar 

  • Cohen, M., and L. Narens. 1979. Fundamental unit structures: A theory of ratio scalability. Journal of Mathematical Psychology 20: 193–232.

    Article  Google Scholar 

  • Ellermeier, W., and G. Faulhammer. 2000. Empirical evaluation of axioms fundamental to Stevens’s ratio-scaling approach: I. Loudness production. Perception and Psychophysics 62: 1505–1511.

    Article  Google Scholar 

  • Fine, T. 1973. Theories of probability. New York: Academic.

    Google Scholar 

  • Fishbum, P.C. 1985. Nontransitive preference theory and the preference reversal phenomenon. International Review of Economics and Business 32: 39–50.

    Google Scholar 

  • Fishburn, P.C. 1970. Utility theory for decision making. New York: Wiley.

    Book  Google Scholar 

  • Fishburn, P.C. 1982. Nontransitive measurable utility. Journal of Mathematical Psychology 26: 31–67.

    Article  Google Scholar 

  • Grether, D.M., and C.R. Plott. 1979. Economic theory of choice and the preference reversal phenomenon. American Economic Review 69: 623–638.

    Google Scholar 

  • Kahneman, D., and A. Tversky. 1979. Prospect theory: An analysis of decision under risk. Econometrica 47: 263–291.

    Article  Google Scholar 

  • Kolmogorov, A. 1933. Grundbegriffe der Wahrscheinlichkeitsrechnung, 1946. New York: Chelsea.

    Book  Google Scholar 

  • Luce, R.D. 2000. Utility of gains and losses: Measurement-theoretical and experimental approaches. Mahwah: Erlbaum. Errata: see Luce’s web page at http://www.socsci.uci.edu.

  • Luce, R.D. 2002. A psychophysical theory of intensity proportions, joint presentations, and matches. Psychological Review 109: 520–532.

    Article  Google Scholar 

  • Luce, R.D. 2004. Symmetric and asymmetric matching of joint presentations. Psychological Review 111: 446–454.

    Article  Google Scholar 

  • Luce, R.D., and A.A.J. Marley. 2000. On elements of chance. Theory and Decision 49: 97–126.

    Article  Google Scholar 

  • Luce, R.D., and L. Narens. 1985. Classification of concatenation measurement structures according to scale type. Journal of Mathematical Psychology 29: 1–72.

    Article  Google Scholar 

  • Luce, R.D., and R. Steingrimsson. 2006. Global psychophysical judgments of intensity: Summary of a theory and experiments. In Measurement and representations of sensations, ed. H. Colonious and E. Dzharfov. Mahwah: Lawrence Erlbaum Associates.

    Google Scholar 

  • Luce, R.D., D.H. Krantz, P. Suppes and A. Tversky 1990. Foundations of measurement, vol. 3. New York: Academic. Repr. New York: Dover, 2007.

    Google Scholar 

  • Luce, R.D., C.T. Ng, J. Aczél, and A.A.J. Marley. 2008a. Utility of gambling I: Entropy-modified linear weighted utility. Economic Theory 36: 1–33.

    Article  Google Scholar 

  • Luce, R.D., C.T. Ng, J. Aczél, and A.A.J. Marley. 2008b. Utility of gambling II: Risk, paradoxes, data. Economic Theory 36: 165–187.

    Article  Google Scholar 

  • MacCrimmon, K.R. 1967. Descriptive and normative implications of the decision theory postulates. In Risk and uncertainty, ed. K. Borch and J. Mossin. New York: Macmillan.

    Google Scholar 

  • Marley, A.A.J., and R.D. Luce. 2005. Independence properties vis-à-vis several utility representations. Theory and Decision 58: 77–143.

    Article  Google Scholar 

  • Meginniss, J.R. 1976. A new class of symmetric utility rules for gambles, subjective marginal probability functions, and a generalized Bayes’ rule. Proceedings of the American statistical association, business and economic statistics section, 471–6.

    Google Scholar 

  • Michell, J. 1990. An introduction to the logic of psychological measurement. Hillsdale: Lawrence Erlbaum Associates.

    Google Scholar 

  • Michell, J. 1999. Measurement in psychology: Critical history of a methodological concept. Cambridge: Cambridge University Press.

    Book  Google Scholar 

  • Myung, J.I., G. Karabatsos, and G.J. Iverson. 2005. A Bayesian approach to testing decision making axioms. Journal of Mathematical Psychology 49: 205–225.

    Article  Google Scholar 

  • Narens, L. 1981a. A general theory of ratio scalability with remarks about the measurement-theoretic concept of meaningfulness. Theory and Decision 13: 1–70.

    Article  Google Scholar 

  • Narens, L. 1981b. On the scales of measurement. Journal of Mathematical Psychology 24: 249–275.

    Article  Google Scholar 

  • Narens, L. 1985. Abstract measurement theory. Cambridge, MA: MIT Press.

    Google Scholar 

  • Narens, L. 1996. A theory of ratio magnitude estimation. Journal of Mathematical Psychology 40: 109–129.

    Article  Google Scholar 

  • Narens, L. 2002. Theories of meaningfulness. Mahwah: Lawrence Erlbaum Associates.

    Google Scholar 

  • Narens, L. 2007. Introduction to the theories of measurement and meaningfulness and the use of invariance in science. Mahwah: Lawrence Erlbaum Associates.

    Google Scholar 

  • Narens, L. 2008. Theories of probability: An examination of logical and qualitative foundations. London: World Scientific.

    Google Scholar 

  • Pfanzagl, J. 1968. Theory of measurement. New York: Wiley. 2nd edn, Vienna: Physica, 1971.

    Google Scholar 

  • Quiggin, J. 1993. Generalized expected utility theory: The rank-dependent model. Boston: Kluwer.

    Book  Google Scholar 

  • Roberts, F.S. 1979. Measurement theory. Reading: Addison-Wesley.

    Google Scholar 

  • Roberts, F.S., and R.D. Luce. 1968. Axiomatic thermodynamics and extensive measurement. Synthese 18: 311–326.

    Article  Google Scholar 

  • Savage, L.J. 1954. The foundations of probability. New York: Wiley.

    Google Scholar 

  • Steingrimsson, R., and R.D. Luce. 2005a. Evaluating a model of global psychophysical judgments I: Behavioral properties of summations and productions. Journal of Mathematical Psychology 49: 290–306.

    Article  Google Scholar 

  • Steingrimsson, R., and R.D. Luce. 2005b. Evaluating a model of global psychophysical judgments II: Behavioral properties linking summations and productions. Journal of Mathematical Psychology 49: 308–319.

    Article  Google Scholar 

  • Steingrimsson, R., and R.D. Luce. 2006. Empirical Evaluation of a model of global psychophysical judgments III: A form for the psychophysical and perceptual filtering. Journal of Mathematical Psychology 50: 15–29.

    Article  Google Scholar 

  • Steingrimsson, R., and R.D. Luce. 2007. Empirical Evaluation of a model of global psychophysical judgments IV: Forms for the weighting function. Journal of Mathematical Psychology 51: 29–44.

    Article  Google Scholar 

  • Stevens, S.S. 1946. On the theory of scales of measurement. Science 103: 677–680.

    Article  Google Scholar 

  • Suppes, P. 2002. Representation and invariance of scientific structures. Stanford: CSLI publications.

    Google Scholar 

  • Suppes, P., Krantz, D.H., Luce, R.D. and Tversky, A. 1989. Foundations of measurement, vol. 2. New York: Academic. Repr. New York: Dover, 2007.

    Google Scholar 

  • Tversky, A., and D. Kahneman. 1992. Advances in prospect theory: Cumulative representation of uncertainty. Journal of Risk and Uncertainty 5: 297–323.

    Article  Google Scholar 

  • von Neumann, J. 1995. Mathematical foundations of quantum mechanics. Princeton: Princeton University Press.

    Google Scholar 

  • Zimmer, K. 2005. Examining the validity of numerical ratios in loudness fractionation. Perception & Psychophysics 67: 569–579.

    Article  Google Scholar 

  • Krantz, D.H., R.D. Luce, P. Suppes and A. Tversky 1971. Foundations of measurement, vol. 1. New York: Academic. Repr. New York: Dover, 2007.

    Google Scholar 

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  1. http://link.springer.com/referencework/10.1057/978-1-349-95121-5

    R. Duncan Luce & Louis Narens

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  1. R. Duncan Luce
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  2. Louis Narens
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Luce, R.D., Narens, L. (2018). Measurement, Theory of. In: The New Palgrave Dictionary of Economics. Palgrave Macmillan, London. https://doi.org/10.1057/978-1-349-95189-5_1220

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