IDEAS home Printed from
MyIDEAS: Login to save this paper or follow this series

Chance Theory: A Separation of Riskless and Risky Utility

  • Ulrich Schmidt
  • Horst Zank

We present a preference foundation for Chance Theory (CT), a model of decision making under uncertainty where the evaluation of an act depends distinctively on its lowest outcome. This outcome is evaluated with the riskless value function u and the potential increments over it are evaluated by subjective expected utility with a risky utility function u. In contrast to earlier approaches with models that aimed at separating riskless and risky utility, CT does not violate basic rationality principles like first-order stochastic dominance or transitivity. Decision makers with CT-preferences always prefer the expected value of a lottery to the latter, so they are weakly risk averse. Besides explaining behavioral irregularities like the expected utility paradoxes of Allais and Rabin, CT also separates risk attitude in the strong sense from attitude towards wealth. Risk attitude is completely determined by the curvature of vuand is independent of the value function v. Conversely, attitude towards wealth is reflected solely through the curvature of v without imposing constraints on u

(This abstract was borrowed from another version of this item.)

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.

File URL:
Download Restriction: no

Paper provided by Economics, The University of Manchester in its series The School of Economics Discussion Paper Series with number 1324.

in new window

Date of creation: 2013
Date of revision:
Handle: RePEc:man:sespap:1324
Contact details of provider: Postal: Manchester M13 9PL
Phone: (0)161 275 4868
Fax: (0)161 275 4812
Web page:

More information through EDIRC

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.:

as in new window
  1. Kahneman, Daniel & Tversky, Amos, 1979. "Prospect Theory: An Analysis of Decision under Risk," Econometrica, Econometric Society, vol. 47(2), pages 263-91, March.
  2. George Wu & John List & Uri Gneezy, 2006. "The uncertainty effect: When a risky prospect is valued less than its worst possible outcome," Framed Field Experiments 00152, The Field Experiments Website.
  3. Enrico Diecidue & Ulrich Schmidt & Peter P. Wakker, 2004. "The Utility of Gambling Reconsidered," Journal of Risk and Uncertainty, Springer, vol. 29(3), pages 241-259, December.
  4. David Schmeidler, 1989. "Subjective Probability and Expected Utility without Additivity," Levine's Working Paper Archive 7662, David K. Levine.
  5. Matthew Rabin, 2000. "Risk Aversion and Expected-Utility Theory: A Calibration Theorem," Econometrica, Econometric Society, vol. 68(5), pages 1281-1292, September.
  6. James Andreoni & Charles Sprenger, 2012. "Risk Preferences Are Not Time Preferences," American Economic Review, American Economic Association, vol. 102(7), pages 3357-76, December.
  7. Wakker,Peter P., 2010. "Prospect Theory," Cambridge Books, Cambridge University Press, number 9780521765015, October.
  8. Simone Cerreia‐Vioglio & David Dillenberger & Pietro Ortoleva, 2015. "Cautious Expected Utility and the Certainty Effect," Econometrica, Econometric Society, vol. 83, pages 693-728, 03.
  9. Itzhak Gilboa & David Schmeidler, 1989. "Maxmin Expected Utility with Non-Unique Prior," Post-Print hal-00753237, HAL.
  10. Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, vol. 2(3), pages 225-243, September.
  11. Itzhak Gilboa, 1988. "A Combination of Expected Utility and Maxmin Decision Criteria," Post-Print hal-00753244, HAL.
  12. John W. Payne & Dan J. Laughhunn & Roy Crum, 1980. "Translation of Gambles and Aspiration Level Effects in Risky Choice Behavior," Management Science, INFORMS, vol. 26(10), pages 1039-1060, October.
  13. Dillenberger, David, 2008. "Preferences for One-Shot Resolution of Uncertainty and Allais-Type Behavior," MPRA Paper 8342, University Library of Munich, Germany.
  14. Wakker,Peter P., 2010. "Prospect Theory," Cambridge Books, Cambridge University Press, number 9780521748681.
  15. Chateauneuf, Alain & Eichberger, Jurgen & Grant, Simon, 2007. "Choice under uncertainty with the best and worst in mind: Neo-additive capacities," Journal of Economic Theory, Elsevier, vol. 137(1), pages 538-567, November.
  16. Segal, Uzi & Spivak, Avia, 1990. "First order versus second order risk aversion," Journal of Economic Theory, Elsevier, vol. 51(1), pages 111-125, June.
  17. 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.
  18. Kimball, Miles S, 1990. "Precautionary Saving in the Small and in the Large," Econometrica, Econometric Society, vol. 58(1), pages 53-73, January.
  19. Conlisk, John, 1989. "Three Variants on the Allais Example," American Economic Review, American Economic Association, vol. 79(3), pages 392-407, June.
  20. Wakker, Peter, 1993. "Additive representations on rank-ordered sets : II. The topological approach," Journal of Mathematical Economics, Elsevier, vol. 22(1), pages 1-26.
  21. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
  22. Fishburn, Peter C, 1977. "Mean-Risk Analysis with Risk Associated with Below-Target Returns," American Economic Review, American Economic Association, vol. 67(2), pages 116-26, March.
  23. 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.
  24. Craig Webb & Horst Zank, 2011. "Accounting for Optimism and Pessimism in Expected Utility," The School of Economics Discussion Paper Series 1111, Economics, The University of Manchester.
  25. Alain Chateauneuf & Jürgen Eichberger & Simon Grant, 2007. "Choice under uncertainty with the best and worst in mind: neo-additive capacities," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00271279, HAL.
  26. James S. Dyer & Rakesh K. Sarin, 1982. "Relative Risk Aversion," Management Science, INFORMS, vol. 28(8), pages 875-886, August.
  27. Peter Fishburn, 1980. "A simple model for the utility of gambling," Psychometrika, Springer, vol. 45(4), pages 435-448, December.
  28. Tversky, Amos & Kahneman, Daniel, 1992. " Advances in Prospect Theory: Cumulative Representation of Uncertainty," Journal of Risk and Uncertainty, Springer, vol. 5(4), pages 297-323, October.
  29. Gul, Faruk, 1991. "A Theory of Disappointment Aversion," Econometrica, Econometric Society, vol. 59(3), pages 667-86, May.
  30. Milton Friedman & L. J. Savage, 1948. "The Utility Analysis of Choices Involving Risk," Journal of Political Economy, University of Chicago Press, vol. 56, pages 279.
  31. James Andreoni & Charles Sprenger, 2010. "Certain and Uncertain Utility: The Allais Paradox and Five Decision Theory Phenomena," Levine's Working Paper Archive 814577000000000447, David K. Levine.
  32. Gerard Debreu, 1959. "Topological Methods in Cardinal Utility Theory," Cowles Foundation Discussion Papers 76, Cowles Foundation for Research in Economics, Yale University.
  33. Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 323-343, December.
  34. 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.
Full references (including those not matched with items on IDEAS)

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

When requesting a correction, please mention this item's handle: RePEc:man:sespap:1324. 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: (Marianne Sensier)

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.

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.