Axiomatization of stochastic models for choice under uncertainty
AbstractThis 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.
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Bibliographic InfoArticle provided by Elsevier in its journal Mathematical Social Sciences.
Volume (Year): 55 (2008)
Issue (Month): 3 (May)
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Web page: http://www.elsevier.com/locate/inca/505565
Other versions of this item:
- John K. Dagsvik, 2006. "Axiomatization of Stochastic Models for Choice under Uncertainty," Discussion Papers 465, Research Department of Statistics Norway.
- C25 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions
- D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory
- D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Harless, David W & Camerer, Colin F, 1994. "The Predictive Utility of Generalized Expected Utility Theories," Econometrica, Econometric Society, vol. 62(6), pages 1251-89, November.
- Loomes, Graham & Sugden, Robert, 1998. "Testing Different Stochastic Specifications of Risky Choice," Economica, London School of Economics and Political Science, vol. 65(260), pages 581-98, November.
- 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.
- Dagsvik, John k: & Strøm, Steinar, 2003.
"A Stochastic Model for the Utility of Income,"
32/2003, Oslo University, Department of Economics.
- L. Thurstone, 2010. "Psychophysical Analysis," Levine's Working Paper Archive 458, David K. Levine.
- 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 633-46, October.
- Gerard Debreu, 1957. "Stochastic Choice and Cardinal Utility," Cowles Foundation Discussion Papers 39, Cowles Foundation for Research in Economics, Yale University.
- Iverson, G. & Falmagne, J. -C., 1985. "Statistical issues in measurement," Mathematical Social Sciences, Elsevier, vol. 10(2), pages 131-153, October.
- Carbone, Enrica, 1997. "Investigation of stochastic preference theory using experimental data," Economics Letters, Elsevier, vol. 57(3), pages 305-311, December.
- 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.
- John K. Dagsvik, 2005. "Choice under Uncertainty and Bounded Rationality," Discussion Papers 409, Research Department of Statistics Norway.
- F. Gul & W. Pesendorfer, 2002.
"Random Expected Utility,"
Princeton Economic Theory Working Papers
497768e9b9fc18361ac0810b3, David K. Levine.
- 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.
- 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.
- Loomes, Graham & Sugden, Robert, 1995. "Incorporating a stochastic element into decision theories," European Economic Review, Elsevier, vol. 39(3-4), pages 641-648, April.
- John K. Dagsvik & Steinar Strøm & Zhiyang Jia, 2005.
"Utility of Income as a Random Function. Behavioral Characterization and Empirical Evidence,"
431, Research Department of Statistics Norway.
- 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.
- 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.
- Cadogan, Godfrey, 2010. "Asymptotic Theory Of Stochastic Choice Functionals For Prospects With Embedded Comotonic Probability Measures," MPRA Paper 22380, University Library of Munich, Germany.
- 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.
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