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Axiomatization of stochastic models for choice under uncertainty

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  • Dagsvik, John K.

Abstract

This paper develops a theory of probabilistic models for risky choices. This theory can be viewed as an extension of the expected utility theory. One probabilistic version of the Archimedean Axiom and two versions of the Independence Axiom are proposed. In addition, additional axioms are proposed of which one is Luce's Independence from Irrelevant Alternatives (IIA). It is demonstrated that different combinations of the axioms yield different characterizations of the probabilities for choosing the respective risky prospects. Particular dimensional invariance axioms are postulated for the case with monetary rewards. It is demonstrated that when probabilistic versions of the Archimedean and the Independence Axioms are combined with Dimensional Invariance axioms explicit functional forms of the utility function follow. It is also proved that a random utility representation exists in the particular case when IIA holds for choice among lotteries. An interesting feature of the models developed is that they allow for violations of the expected utility theory known as the common consequence effect and the common ratio effect.

Suggested Citation

  • Dagsvik, John K., 2008. "Axiomatization of stochastic models for choice under uncertainty," Mathematical Social Sciences, Elsevier, vol. 55(3), pages 341-370, May.
  • Handle: RePEc:eee:matsoc:v:55:y:2008:i:3:p:341-370
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    1. Fishburn, Peter C, 1978. "A Probabilistic Expected Utility Theory of Risky Binary Choices," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 19(3), pages 633-646, October.
    2. Dagsvik, John k: & Strøm, Steinar, 2003. "A Stochastic Model for the Utility of Income," Memorandum 32/2003, Oslo University, Department of Economics.
    3. Loomes, Graham & Sugden, Robert, 1998. "Testing Different Stochastic Specifications of Risky Choice," Economica, London School of Economics and Political Science, vol. 65(260), pages 581-598, November.
    4. John K. Dagsvik, 2005. "Choice under Uncertainty and Bounded Rationality," Discussion Papers 409, Statistics Norway, Research Department.
    5. McFadden, Daniel L., 1984. "Econometric analysis of qualitative response models," Handbook of Econometrics,in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 2, chapter 24, pages 1395-1457 Elsevier.
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    7. Faruk Gul & Wolfgang Pesendorfer, 2006. "Random Expected Utility," Econometrica, Econometric Society, vol. 74(1), pages 121-146, January.
    8. Hey, John D & Orme, Chris, 1994. "Investigating Generalizations of Expected Utility Theory Using Experimental Data," Econometrica, Econometric Society, vol. 62(6), pages 1291-1326, November.
    9. Loomes, Graham & Sugden, Robert, 1995. "Incorporating a stochastic element into decision theories," European Economic Review, Elsevier, vol. 39(3-4), pages 641-648, April.
    10. Harless, David W & Camerer, Colin F, 1994. "The Predictive Utility of Generalized Expected Utility Theories," Econometrica, Econometric Society, vol. 62(6), pages 1251-1289, November.
    11. Carbone, Enrica, 1997. "Investigation of stochastic preference theory using experimental data," Economics Letters, Elsevier, vol. 57(3), pages 305-311, December.
    12. Hey, John D., 1995. "Experimental investigations of errors in decision making under risk," European Economic Review, Elsevier, vol. 39(3-4), pages 633-640, April.
    13. L. Thurstone, 2010. "Psychophysical Analysis," Levine's Working Paper Archive 458, David K. Levine.
    14. Dagsvik, John K. & Strom, Steinar & Jia, Zhiyang, 2006. "Utility of income as a random function: Behavioral characterization and empirical evidence," Mathematical Social Sciences, Elsevier, vol. 51(1), pages 23-57, January.
    15. Chris Starmer, 2000. "Developments in Non-expected Utility Theory: The Hunt for a Descriptive Theory of Choice under Risk," Journal of Economic Literature, American Economic Association, vol. 38(2), pages 332-382, June.
    16. Karni, Edi & Schmeidler, David, 1991. "Utility theory with uncertainty," Handbook of Mathematical Economics,in: W. Hildenbrand & H. Sonnenschein (ed.), Handbook of Mathematical Economics, edition 1, volume 4, chapter 33, pages 1763-1831 Elsevier.
    17. Gerard Debreu, 1957. "Stochastic Choice and Cardinal Utility," Cowles Foundation Discussion Papers 39, Cowles Foundation for Research in Economics, Yale University.
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    Citations

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    Cited by:

    1. Dagsvik, John K., 2015. "Stochastic models for risky choices: A comparison of different axiomatizations," Journal of Mathematical Economics, Elsevier, vol. 60(C), pages 81-88.
    2. Matthew Ryan, 2017. "Random Binary Choices that Satisfy Stochastic Betweenness," Working Papers 2017-01, Auckland University of Technology, Department of Economics.
    3. Matthew Ryan, 2015. "A Strict Stochastic Utility Theorem," Economics Bulletin, AccessEcon, vol. 35(4), pages 2664-2672.
    4. Matthew Ryan, 2015. "Binary Choice Probabilities on Mixture Sets," Working Papers 2015-01, Auckland University of Technology, Department of Economics.
    5. repec:eee:mateco:v:70:y:2017:i:c:p:176-184 is not listed on IDEAS
    6. Dagsvik, John K, 2017. "Invariance Axioms and Functional Form Restrictions in Structural Models," Memorandum 08/2017, Oslo University, Department of Economics.
    7. repec:spr:joecth:v:65:y:2018:i:3:d:10.1007_s00199-017-1033-4 is not listed on IDEAS
    8. John Dagsvik & Stine Røine Hoff, 2011. "Justification of functional form assumptions in structural models: applications and testing of qualitative measurement axioms," Theory and Decision, Springer, vol. 70(2), pages 215-254, February.
    9. repec:eee:matsoc:v:91:y:2018:i:c:p:85-95 is not listed on IDEAS
    10. Cadogan, Godfrey, 2010. "Asymptotic Theory Of Stochastic Choice Functionals For Prospects With Embedded Comotonic Probability Measures," MPRA Paper 22380, University Library of Munich, Germany.

    More about this item

    JEL classification:

    • C25 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions; Probabilities
    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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