Some extensions of Luce's measures of risk

Theory and Decision volume 22, pages125–141(1987)Cite this article

Abstract

In this paper we extend measures of risk proposed by Luce. A new exponential model of risk is developed that may be empirically more acceptable than the log model of Luce.

Expectation principle is often employed in the construction of measures of risk. Empirical studies, however, suggest that this principle may not be valid. We suggest a generalization of the expectation principle and show as examples how two measures of Luce can be modified to incorporate this generalized expectation principle.

Finally, the gambles with gains only are perceived by some subjets to have no risk at all. A new concept of riskiness that is based on the choice between two gambles is defined.

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References

  1. Aczél, J.: 1966, Lectures on Functional Equations and Their Applications, Academic Press, New York.

    Google Scholar 

  2. Coombs, C. H. and Bowen, J. N.: 1971, ‘A Test of VE-Theories of Risk and the Effect of the Central Limit Theorem’, Acta Psychologica 35, 15–28.

    Google Scholar 

  3. Coombs, C. H. and Huang, L. C.: 1970a, ‘Polynomial Psychophysics of Risk’, Journal of Mathematical Psychology 7, 317–338.

    Google Scholar 

  4. Coombs, C. H. and Huang, L. C.: 1970b, ‘Test of a Portfolio Theory of Risk Preference’, Journal of Experimental Psychology 85, 23–29.

    Google Scholar 

  5. Coombs, C. H. and Lehner, P. E.: 1981a, ‘An Evaluation of Two Alternative Models for a Theory of Risk: Part I’, Journal of Experimental Psychology, Human Perception and Performance 7, 1110–1123.

    Google Scholar 

  6. Coombs, C. H. and Lehner, P. E.: 1981, ‘Evaluation of Two Alternative Models for a Theory of Risk: Part II. The Bilinear Model and its Conjoint Analysis’, University of Michigan.

  7. Fishburn, P. C.: 1982, ‘Foundations of Risk Measurement. II: Effects of Gains on Risk’, Journal of Mathematical Psychology 25, 226–242.

    Google Scholar 

  8. Fishburn, P. C.: 1982, ‘Foundations of Risk Measurement. I: Risk as Probable Loss’, Management Science 30, 396–406.

    Google Scholar 

  9. Krantz, D. H., Luce, R. D., Suppes, P., and Tversky, A.: 1971, Foundations of Measurement, I, Academic Press, New York.

    Google Scholar 

  10. Luce, R. D.: 1980, ‘Several Possible Measures of Risk’, Theory and Decision 12, 217–228, Correction, 13 (1981), 381.

    Google Scholar 

  11. Machina, M.: 1982, ‘Expected Utility' Analysis without the Independence Axiom’, Econometrica 50, 277–323.

    Google Scholar 

  12. Pollatsek, A. and Tversky, A.: 1970, ‘A Theory of Risk’, Journal of Mathematical Psychology 7, 540–553.

    Google Scholar 

  13. von Neumann, J. and Morgenstern, O.: 1947, Theory of Games and Economic Behavior, 2nd ed., Princeton University Press, Princeton, N.J.

    Google Scholar 

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Affiliations

  1. Graduate School of Management, University of California Los Angeles, 90024, Los Angeles, CA, USA

    Rakesh K. Sarin

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  1. Rakesh K. Sarin
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Sarin, R.K. Some extensions of Luce's measures of risk. Theor Decis 22, 125–141 (1987). https://doi.org/10.1007/BF00126387

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Keywords

  • Empirical Study
  • Exponential Model
  • Generalize Expectation
  • Expectation Principle