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Allais Paradoxes Can be Reversed by Presenting Choices in Canonical Split Form

  • Michael H. Birnbaum
  • Ulrich Schmidt

This paper tests Birnbaum’s (2004) theory that the constant consequence paradoxes of Allais are due to violations of coalescing, the assumption that when two branches lead to the same consequence, they can be combined by adding their probabilities. Rank dependent utility and cumulative prospect theory imply that the Allais paradoxes are due to violations of restricted branch independence, a weaker form of Savage’s sure thing axiom. This paper will analyze separately whether erroneous random response variation might be responsible for these two effects. When errors are factored out, violations of restricted branch independence also remain significant and opposite from the direction of Allais paradoxes, suggesting that models such as CPT that attribute Allais paradoxes to violations of restricted branch independence should be rejected

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File URL: https://www.ifw-members.ifw-kiel.de/publications/allais-paradoxes-can-be-reversed-by-presenting-choices-in-canonical-split-form/kwp_1615.pdf
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Paper provided by Kiel Institute for the World Economy in its series Kiel Working Papers with number 1615.

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Length: 28 pages
Date of creation: Mar 2010
Date of revision:
Handle: RePEc:kie:kieliw:1615
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  1. Ulrich Schmidt & Tibor Neugebauer, 2007. "Testing expected utility in the presence of errors," Economic Journal, Royal Economic Society, vol. 117(518), pages 470-485, 03.
  2. Birnbaum, Michael H. & Schmidt, Ulrich, 2008. "An experimental investigation of violations of transitivity in choice under uncertainty," Kiel Working Papers 1396, Kiel Institute for the World Economy (IfW).
  3. Luce, R Duncan & Fishburn, Peter C, 1991. "Rank- and Sign-Dependent Linear Utility Models for Finite First-Order Gambles," Journal of Risk and Uncertainty, Springer, vol. 4(1), pages 29-59, January.
  4. Blavatskyy, Pavlo R., 2006. "Violations of betweenness or random errors?," Economics Letters, Elsevier, vol. 91(1), pages 34-38, April.
  5. Luce, R. Duncan, 1991. "Rank- and sign-dependent linear utility models for binary gambles," Journal of Economic Theory, Elsevier, vol. 53(1), pages 75-100, February.
  6. Humphrey, Steven J, 1995. "Regret Aversion or Event-Splitting Effects? More Evidence under Risk and Uncertainty," Journal of Risk and Uncertainty, Springer, vol. 11(3), pages 263-74, December.
  7. Michael H. Birnbaum & Jeffrey P. Bahra, 2007. "Gain-Loss Separability and Coalescing in Risky Decision Making," Management Science, INFORMS, vol. 53(6), pages 1016-1028, June.
  8. Mark J Machina, 1982. ""Expected Utility" Analysis without the Independence Axiom," Levine's Working Paper Archive 7650, David K. Levine.
  9. Birnbaum, Michael H & Navarrete, Juan B, 1998. "Testing Descriptive Utility Theories: Violations of Stochastic Dominance and Cumulative Independence," Journal of Risk and Uncertainty, Springer, vol. 17(1), pages 49-78, October.
  10. Ulrich Schmidt & John D. Hey, 2004. "Are Preference Reversals Errors? An Experimental Investigation," Journal of Risk and Uncertainty, Springer, vol. 29(3), pages 207-218, December.
  11. Butler, David & Loomes, Graham, 2011. "Imprecision as an account of violations of independence and betweenness," Journal of Economic Behavior & Organization, Elsevier, vol. 80(3), pages 511-522.
  12. Amos Tversky & Daniel Kahneman, 1979. "Prospect Theory: An Analysis of Decision under Risk," Levine's Working Paper Archive 7656, David K. Levine.
  13. Camerer, Colin F, 1989. "An Experimental Test of Several Generalized Utility Theories," Journal of Risk and Uncertainty, Springer, vol. 2(1), pages 61-104, April.
  14. Wakker, Peter & Tversky, Amos, 1993. "An Axiomatization of Cumulative Prospect Theory," Journal of Risk and Uncertainty, Springer, vol. 7(2), pages 147-75, October.
  15. 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.
  16. 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.
  17. Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 323-343, December.
  18. Birnbaum, Michael H., 2004. "Tests of rank-dependent utility and cumulative prospect theory in gambles represented by natural frequencies: Effects of format, event framing, and branch splitting," Organizational Behavior and Human Decision Processes, Elsevier, vol. 95(1), pages 40-65, September.
  19. David J. Butler & Graham C. Loomes, 2007. "Imprecision as an Account of the Preference Reversal Phenomenon," American Economic Review, American Economic Association, vol. 97(1), pages 277-297, March.
  20. 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.
  21. Starmer, Chris & Sugden, Robert, 1993. "Testing for Juxtaposition and Event-Splitting Effects," Journal of Risk and Uncertainty, Springer, vol. 6(3), pages 235-54, June.
  22. 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.
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