Skip to main content

From Indices to Mappings: The Representational Approach to Measurement

  • Chapter
Frontiers of Mathematical Psychology

Part of the book series: Recent Research in Psychology ((PSYCHOLOGY))

Abstract

I am pleased to be able to offer this essay on measurement in honor of Clyde Coombs. It was Coombs, more than anyone else, who saw the relevance of qualitative measurement structures to behavioral science theory and data, and who inspired his students to test axioms by carefully designed experiments. Though I was not his student, my work benefitted for many years from his encouragement, and from his intense joy in the struggle to understand.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  • Bock, R. D. & Jones, L. V. (1968). The measurement and prediction of judgment and choice. San Francisco: Holden-Day.

    Google Scholar 

  • Briggs, L. K & Krantz, D. H. (1990). Judging the strength of designated evidence. Unpublished manuscript.

    Google Scholar 

  • Cicerone, C. M., Krantz, D. H. & Larimer, J. (1975). Opponent process additivity—III: Effect of moderate chromatic adaptation. Vision Research, 15, 1125–1135.

    Article  PubMed  Google Scholar 

  • Coombs, C. H. (1950). Psychological scaling without a unit of measurement. Psychological Review, 57, 145–158.

    Article  PubMed  Google Scholar 

  • Debreu, G. (1960). Topological methods in cardinal utility theory. In K J. Arrow, S. Karlin & P. Suppes (Eds.), Mathematical methods in the social sciences, 1959. Stanford: Stanford Univ. Press. Pp. 16–26.

    Google Scholar 

  • Dempster, A. (1967). Upper and lower probabilities induced by a multivalued mapping. Annals of Mathematical Statistics, 38, 325–339.

    Article  Google Scholar 

  • Donnell, M. L. (1977). Individual red/green and yellow/blue opponent-isocancellation functions: Their measurement and prediction. Ph.D. dissertation, University of Michigan. Ann Arbor: University Microfilms.

    Google Scholar 

  • Ejimo, Y. & Takahashi, S. (1984). Bezold-Bruecke hue shift and nonlinearity in opponent-color process. Vision Research, 24, 1897–1904.

    Article  Google Scholar 

  • Hering, E. (1878). Zur Lehre vom Lichtsinne. Vienna: C. Gerold’s Sohn.

    Google Scholar 

  • Hering, E. (1920). Grundzuege der Lehre vom Lichtsinn. Berlin: Springer. English translation by L. M. Hurvich & D. Jameson (1964), Outlines of a Theory of the Light Sense, Cambridge, Mass.: Harvard Univ. Press.

    Google Scholar 

  • Hicks, J. (1939). Value and capital. Oxford: Clarendon Press.

    Google Scholar 

  • Hurvich, L. M. & Jameson, D. (1951a). The binocular fusion of yellow in relation to color theories. Science, 114, 199–202.

    Article  PubMed  Google Scholar 

  • Hurvich, L. M. & Jameson, D. (1951b). A psychophysical study of white. I. Neutral adaptation. Journal of the Optical Society of America, 41, 521–527.

    Article  PubMed  Google Scholar 

  • Hurvich, L. M. & Jameson, D. (1955). Some quantitative aspects of an opponent-colors theory. II. Brightness, saturation, and hue in normal and dichromatic vision. Journal of the Optical Society of America, 45, 602–616.

    Article  PubMed  Google Scholar 

  • Hurvich, L. M. & Jameson, D. (1957). An opponent-process theory of color vision. Psychological Review, 64, 384–404.

    Article  PubMed  Google Scholar 

  • Jameson, D. & Hurvich, L. M. (1955). Some quantitative aspects of an opponent-colors theory. I. Chromatic responses and spectral saturation. Journal of the Optical Society of America, 45, 546–552.

    Article  Google Scholar 

  • Jameson, D. & Hurvich, L. M. (1961). Opponent chromatic induction: Experimental evaluation and theoretical account. Journal of the Optical Society of America, 51, 46–53.

    Article  PubMed  Google Scholar 

  • Judd, D. B. (1951). Basic correlates of the visual stimulus. In S. S. Stevens (Ed.), Handbook of Experimental Psychology, New York: Wiley. Pp. 811–867.

    Google Scholar 

  • Kahneman, D. & Tversky, A. (1972). Subjective probability: A judgment of representativeness. Cognitive Psychology, 3, 430–454.

    Article  Google Scholar 

  • Krantz, D. H. (1968). A theory of context effects based on cross-context matching. Journal of Mathematical Psychology, 5, 1–48.

    Article  Google Scholar 

  • Krantz, D. H. (1975a). Color measurement and color theory: I. Representation theorem for Grassmann structures. Journal of Mathematical Psychology, 12, 283–303.

    Article  Google Scholar 

  • Krantz, D. H. (1975b). Color measurement and color theory: II. Opponent-colors theory. Journal of Mathematical Psychology, 12, 304–327.

    Article  Google Scholar 

  • Krantz, D. H. & Briggs, L. K. (1990). Judgments of frequency and evidence strength. Unpublished manuscript.

    Google Scholar 

  • Krantz, D. H., Luce, R. D., Suppes P. & Tversky, A. (1971). Foundations of measurement. Vol. 1. Additive and polynomial representations. New York: Academic Press.

    Google Scholar 

  • Krantz, D. H. & Miller, G. F. (1990). Judging the strength of likelihood evidence. Unpublished manuscript.

    Google Scholar 

  • Krantz, D. H. & Miyamoto, J. (1990). Foundations of the theory of evidence: Separable support structures. Unpublished manuscript.

    Google Scholar 

  • Krantz, D. H., Ray, B. & Briggs, L. K (1990). Foundations of the theory of evidence: The role of schemata. Unpublished manuscript.

    Google Scholar 

  • Krantz, D. H. & Tversky, A. (1971). Conjoint-measurement analysis of composition rules in psychology. Psychological Review, 78, 151–169.

    Article  Google Scholar 

  • Larimer, J., Krantz, D. H. & Cicerone, C. M. (1974). Opponent process additivity—I: Red/green equilibria. Vision Research, 14 1127–1140.

    Article  PubMed  Google Scholar 

  • Larimer, J., Krantz, D. H. & Cicerone, C. M. (1975). Opponent-process additivity—II: Yellow/blue equilibria and nonlinear models. Vision Research, 15, 723–731.

    Article  PubMed  Google Scholar 

  • Luce, R. D. & Cohen, M. (1983). Factorizable automorphisms in solvable conjoint structures. Journal of Pure and Applied Algebra, 27, 225–261.

    Article  Google Scholar 

  • Luce, R. D., Krantz, D. H., Suppes, P. & Tversky, A. (1990). Foundations of measurement. Vol. III. Representation, axiomatization, and invariance. New York: Academic Press.

    Google Scholar 

  • Luce, R. D. & Tukey, J. W. (1964). Simultaneous conjoint measurement: A new form of fundamental measurement. Journal of Mathematical Psychology, 1, 1–27.

    Article  Google Scholar 

  • Moeller, J. R. (1976). Measuring the red/green quality of lights: A study relating the Jameson and Hurvich red/green cancellation valence to direct magnitude estimation of greenness. Ph.D. dissertation, University of Michigan. Ann Arbor: University Microfilms.

    Google Scholar 

  • Narens, L. & Luce, R. D. (1976). The algebra of measurement. Journal of Pure and Applied Algebra, 8, 197–233.

    Article  Google Scholar 

  • Purdy, D. M. (1931). Spectral hue as a function of intensity. American Journal of Psychology, 43, 541–559.

    Article  Google Scholar 

  • Ray, B. & Krantz, D. H. (1990). Foundations of the theory of evidence: Resolving conflicts among schemata. Unpublished manuscript.

    Google Scholar 

  • Romeskie, M. & Yager, D. (1978). Psychophysical measure and theoretical analysis of dichromatic opponent-response functions. Modern Problems of Ophthalmology, 19, 212–217.

    Google Scholar 

  • Savage, L. J. (1954). The foundations of statistics. New York: Wiley

    Google Scholar 

  • Scott, D. & Suppes, P. (1958). Foundational aspects of theories of measurement. Journal of Symbolic Logic, 23, 113–128.

    Article  Google Scholar 

  • Shafer, G. (1976). A mathematical theory of evidence. Princeton: Princeton Univ. Press.

    Google Scholar 

  • Shafer, G. (1981). Two theories of probability. In P. D. Asquith & I. Hacking (Eds.), PSA, 1978, vol. 2. East Lansing, MI: Philosophy of Science Association.

    Google Scholar 

  • Shafer, G. (1982). Constructive decision theory. Unpublished manuscript.

    Google Scholar 

  • Shevell, S. K. (1978). The dual role of chromatic backgrounds in color perception. Vision Research, 18, 1649–1661.

    Article  PubMed  Google Scholar 

  • Slovic, P. & Lichtenstein, S. (1968). The relative importance of probabilities and payoffs in risk-taking. Journal of Experimental Psychology Monograph Supplement, 78 (3), part 2 (b).

    Google Scholar 

  • Slovic, P. & Lichtenstein, S. (1983). Preference reversals: A broader perspective. American Economic Review, 73, 596–605.

    Google Scholar 

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

    Article  Google Scholar 

  • Stevens, S. S. (1966). A metric for the social consensus. Science, 151, 530–541.

    Article  PubMed  Google Scholar 

  • Suppes, P., Krantz, D. H., Luce, R. D. & Tversky, A. (1989). Foundations of measurement. Vol. II. Geometrical, threshold and probabilistic representations. New York: Academic Press.

    Google Scholar 

  • Thornton, J. E. & Pugh, E. N., Jr. (1983). Relationship of opponent-colours cancellation measures to cone-antagonistic signals deduced from increment threshold data. In J. D. Mollon & L. T. Sharpe (Eds.), Colour vision: Physiology and psychophysics. New York: Academic Press.

    Google Scholar 

  • Thurstone, L. L. (1959). The measurement of values. Chicago: Univ. of Chicago Press.

    Google Scholar 

  • Tversky, A. (1969). Intransitivity of preferences. Psychological Review, 76, 31–48.

    Article  Google Scholar 

  • Tversky, A. & Kahneman, D. (1986). Rational choice and the framing of decisions. The Journal of Business, 59 (4), part 2, 251–278.

    Google Scholar 

  • Tversky, A., Slovic, D. & Kahneman, D. (1990). The causes of preference reversal. American Economic Review, 80, 204–217.

    Google Scholar 

  • von Neumann, J. & Morgenstern, O. (1947). Theory of games and economic behavior. (2nd Ed.) Princeton: Princeton Univ. Press.

    Google Scholar 

  • Werner, J. S. & Wooten, B. R. (1979). Opponent chromatic mechanisms: Relation to photopigments and hue naming. Journal of the Optical Society of America, 69, 422–434.

    Article  PubMed  Google Scholar 

  • Yager, D. & Taylor, E. (1970). Experimental measures and theoretical account of hue scaling as a function of luminance. Perception & Psychophysics, 7, 360–364.

    Article  Google Scholar 

Download references

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1991 Springer-Verlag New York Inc.

About this chapter

Cite this chapter

Krantz, D.H. (1991). From Indices to Mappings: The Representational Approach to Measurement. In: Brown, D.R., Keith Smith, J.E. (eds) Frontiers of Mathematical Psychology. Recent Research in Psychology. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-3088-5_1

Download citation

  • DOI: https://doi.org/10.1007/978-1-4612-3088-5_1

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-0-387-97451-4

  • Online ISBN: 978-1-4612-3088-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics