Betting on Machina’s reflection example: an experiment on ambiguity
- 249 Downloads
- 19 Citations
Abstract
In a recent article, Machina (Am Econ Rev forthcoming, 2008) suggested choice problems in the spirit of Ellsberg (Q J Econ 75:643–669, 1961), which challenge tail-separability, an implication of Choquet expected utility (CEU), to a similar extent as the Ellsberg paradox challenged the sure-thing principle implied by subjective expected utility (SEU). We have tested choice behavior for bets on one of Machina’s choice problems, the reflection example. Our results indicate that tail-separability is violated by a large majority of subjects (over 70% of the sample). These empirical findings complement the theoretical analysis of Machina (Am Econ Rev forthcoming, 2008) and, together, they confirm the need for new approaches in the analysis of ambiguity for decision making.
Keywords
Ambiguity Choquet expected utility Experimental economicsJEL Classification
C90 D81Preview
Unable to display preview. Download preview PDF.
References
- Abdellaoui M., Vossmann F., Weber M. (2005) Choice-based elicitation and decomposition of decision weights for gains and losses under uncertainty. Management Science 51(9): 1384–1399CrossRefGoogle Scholar
- Baillon, A., L’Haridon, O., & Placido, L. (2008). Risk, ambiguity, and the rank-dependence axioms: A comment. Working Paper, HEC-Paris School of Management.Google Scholar
- Birnbaum M. (2008) New paradoxes of risky decision making. Psychological Review 115: 463–501CrossRefGoogle Scholar
- Camerer C., Ho T.H. (1994) Violations of the betweenness axiom and nonlinearity in probability. Journal of Risk and Uncertainty 8(2): 167–196CrossRefGoogle Scholar
- Camerer C., Weber M. (1992) Recent developments in modeling preferences: Uncertainty and ambiguity. Journal of Risk and Uncertainty 5: 325–370CrossRefGoogle Scholar
- Chew H.S., Wakker P. (1996) The comonotonic sure-thing principle. Journal of Risk and Uncertainty 12(1): 5–27CrossRefGoogle Scholar
- Conlisk J. (1989) Three variants on the allais example. American Economic Review 79(3): 392–407Google Scholar
- Diecidue E., Wakker P. (2001) On the intuition of rank-dependent utility. Journal of Risk and Uncertainty 23(3): 281–298CrossRefGoogle Scholar
- Diecidue E., Wakker P., Zeelenberg M. (2007) Eliciting decision weights by adapting de finetti’s betting-odds method to prospect theory. Journal of Risk and Uncertainty 34(3): 179–199CrossRefGoogle Scholar
- Ellsberg D. (1961) Risk, ambiguity and the savage axioms. Quarterly Journal of Economics 75: 643–669CrossRefGoogle Scholar
- Fennema H., Wakker P. (1996) A test of rank-dependent utility in the context of ambiguity. Journal of Risk and Uncertainty 13(1): 19–35CrossRefGoogle Scholar
- Fox C., Tversky A. (1995) Ambiguity aversion and comparative ignorance. The Quarterly Journal of Economics 110(3): 585–603CrossRefGoogle Scholar
- Frisch D., Baron J. (1988) Ambiguity and rationality. Journal of Behavioral Decision Making 1: 149–157CrossRefGoogle Scholar
- Gilboa I. (1987) Expected utility with purely subjective non-additive probabilities. Journal of Mathematical Economics 16(1): 65–88CrossRefGoogle Scholar
- Gilboa I., Schmeidler D. (1989) Maxmin expected utility with non-unique prior. Journal of Mathematical Economics 18(2): 141–153CrossRefGoogle Scholar
- Halevy Y. (2007) Ellsberg revisited: An experimental study. Econometrica 75(2): 503–536CrossRefGoogle Scholar
- Harrison G., Lau M., Rutström E. (2007a) Estimating risk attitudes in Denmark: A field experiment. Scandinavian Journal of Economics 109(2): 341–368CrossRefGoogle Scholar
- Harrison G., List J., Towe C. (2007b) Naturally occurring preferences and exogenous laboratory experiments: A case study of risk aversion. Econometrica 75(2): 433–458CrossRefGoogle Scholar
- Hey, J., Lolito, G., & Maffioletti, A. (2007). Choquet ok? Discussion Paper, University of York.Google Scholar
- Kahneman D., Tversky A. (1979) Prospect theory: An analysis of decision under risk. Econometrica 47: 263–291CrossRefGoogle Scholar
- L’Haridon O., Placido L. (2008) An allais paradox for generalized expected utility theories?. Economic Bulletin 4(19): 1–6Google Scholar
- Luce R., Marley A. (2005) Ranked additive utility representations of gambles: Old and new axiomatizations. Journal of Risk and Uncertainty 30: 21–62CrossRefGoogle Scholar
- Machina, M. (2008). Risk, ambiguity, and the rank-dependence axioms. American Economic Review, forthcoming.Google Scholar
- McCrimmon, K., & Larsson, S. (1979). Utility theory: Axioms versus paradoxes. In M. Allais, & O. Hagen (Eds.), Expected utility hypotheses and the Allais paradox (pp. 27–145). D. Reidel.Google Scholar
- Mukerji, S., & Tallon, J. M. (2004). An overview of economic applications of David Schmeidler’s models of decision making under uncertainty. In I. Gilboa (Ed.), Uncertainty in economic theory: A collection of essays in honor of David Schmeidler’s 65th birthday. Routledge Publishers.Google Scholar
- Quiggin J. (1982) A theory of anticipated utility. Journal of Economic Behavior & Organization 3(4): 323–343CrossRefGoogle Scholar
- Sarin R., Wakker P. (1992) A simple axiomatization of nonadditive expected utility. Econometrica 60(6): 1255–1272CrossRefGoogle Scholar
- Savage, L. (1954). The foundations of statistics (2nd ed., Vol. 1972). Wiley, New York: Dover Publications.Google Scholar
- Schmeidler D. (1989) Subjective probability and expected utility without additivity. Econometrica 57: 571–587CrossRefGoogle Scholar
- Siniscalchi, M. (2008). Vector expected utility and attitudes toward variation. Discussion papers, Northwestern University, Center for Mathematical Studies in Economics and Management Science.Google Scholar
- Slovic P., Tversky A. (1974) Who accepts Savage’s axiom?. Behavioral Science 19: 368–373CrossRefGoogle Scholar
- Tversky A., Kahneman D. (1992) Advances in prospect theory: Cumulative representation of uncertainty. Journal of Risk and Uncertainty 5: 297–323CrossRefGoogle Scholar
- Wakker P., Tversky A. (1993) An axiomatization of cumulative prospect theory. Journal of Risk and Uncertainty 7(2): 147–175CrossRefGoogle Scholar
- Wu G. (1994) An empirical test of ordinal independence. Journal of Risk and Uncertainty 9: 39–60CrossRefGoogle Scholar
- Wu G., Gonzalez R. (1999a) Nonlinear decision weights in choice under uncertainty. Management Science 45(1): 74–85CrossRefGoogle Scholar
- Wu, G., & Gonzalez, R. (1999b). Dominance violations and event spitting in decision under uncertainty. Unpublished Manuscript.Google Scholar