Axiomatization of stochastic models for choice under uncertainty
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.
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
References listed on IDEAS
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.:
- 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.
- John K. Dagsvik & Steinar Strøm & Zhiyang Jia, 2003.
"A Stochastic Model for the Utility of Income,"
358, Statistics Norway, Research Department.
- 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.
- John K. Dagsvik, 2005. "Choice under Uncertainty and Bounded Rationality," Discussion Papers 409, Statistics Norway, Research Department.
- 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.
- 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.
- Loomes, Graham & Sugden, Robert, 1995. "Incorporating a stochastic element into decision theories," European Economic Review, Elsevier, vol. 39(3-4), pages 641-648, April.
- 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.
- Carbone, Enrica, 1997. "Investigation of stochastic preference theory using experimental data," Economics Letters, Elsevier, vol. 57(3), pages 305-311, December.
- 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.
- Faruk Gul & Wolfgang Pesendorfer, 2006.
"Random Expected Utility,"
Econometric Society, vol. 74(1), pages 121-146, 01.
- 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.
- John K. Dagsvik & Steinar Strøm & Zhiyang Jia, 2005. "Utility of Income as a Random Function. Behavioral Characterization and Empirical Evidence," Discussion Papers 431, Statistics Norway, Research Department.
- 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.
- 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.
- L. Thurstone, 2010. "Psychophysical Analysis," Levine's Working Paper Archive 458, David K. Levine.
- 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.
When requesting a correction, please mention this item's handle: RePEc:eee:matsoc:v:55:y:2008:i:3:p:341-370. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu)
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.