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.
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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): 1384–1399
Baillon, A., L’Haridon, O., & Placido, L. (2008). Risk, ambiguity, and the rank-dependence axioms: A comment. Working Paper, HEC-Paris School of Management.
Birnbaum M. (2008) New paradoxes of risky decision making. Psychological Review 115: 463–501
Camerer C., Ho T.H. (1994) Violations of the betweenness axiom and nonlinearity in probability. Journal of Risk and Uncertainty 8(2): 167–196
Camerer C., Weber M. (1992) Recent developments in modeling preferences: Uncertainty and ambiguity. Journal of Risk and Uncertainty 5: 325–370
Chew H.S., Wakker P. (1996) The comonotonic sure-thing principle. Journal of Risk and Uncertainty 12(1): 5–27
Conlisk J. (1989) Three variants on the allais example. American Economic Review 79(3): 392–407
Diecidue E., Wakker P. (2001) On the intuition of rank-dependent utility. Journal of Risk and Uncertainty 23(3): 281–298
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): 179–199
Ellsberg D. (1961) Risk, ambiguity and the savage axioms. Quarterly Journal of Economics 75: 643–669
Fennema H., Wakker P. (1996) A test of rank-dependent utility in the context of ambiguity. Journal of Risk and Uncertainty 13(1): 19–35
Fox C., Tversky A. (1995) Ambiguity aversion and comparative ignorance. The Quarterly Journal of Economics 110(3): 585–603
Frisch D., Baron J. (1988) Ambiguity and rationality. Journal of Behavioral Decision Making 1: 149–157
Gilboa I. (1987) Expected utility with purely subjective non-additive probabilities. Journal of Mathematical Economics 16(1): 65–88
Gilboa I., Schmeidler D. (1989) Maxmin expected utility with non-unique prior. Journal of Mathematical Economics 18(2): 141–153
Halevy Y. (2007) Ellsberg revisited: An experimental study. Econometrica 75(2): 503–536
Harrison G., Lau M., Rutström E. (2007a) Estimating risk attitudes in Denmark: A field experiment. Scandinavian Journal of Economics 109(2): 341–368
Harrison G., List J., Towe C. (2007b) Naturally occurring preferences and exogenous laboratory experiments: A case study of risk aversion. Econometrica 75(2): 433–458
Hey, J., Lolito, G., & Maffioletti, A. (2007). Choquet ok? Discussion Paper, University of York.
Kahneman D., Tversky A. (1979) Prospect theory: An analysis of decision under risk. Econometrica 47: 263–291
L’Haridon O., Placido L. (2008) An allais paradox for generalized expected utility theories?. Economic Bulletin 4(19): 1–6
Luce R., Marley A. (2005) Ranked additive utility representations of gambles: Old and new axiomatizations. Journal of Risk and Uncertainty 30: 21–62
Machina, M. (2008). Risk, ambiguity, and the rank-dependence axioms. American Economic Review, forthcoming.
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.
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.
Quiggin J. (1982) A theory of anticipated utility. Journal of Economic Behavior & Organization 3(4): 323–343
Sarin R., Wakker P. (1992) A simple axiomatization of nonadditive expected utility. Econometrica 60(6): 1255–1272
Savage, L. (1954). The foundations of statistics (2nd ed., Vol. 1972). Wiley, New York: Dover Publications.
Schmeidler D. (1989) Subjective probability and expected utility without additivity. Econometrica 57: 571–587
Siniscalchi, M. (2008). Vector expected utility and attitudes toward variation. Discussion papers, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
Slovic P., Tversky A. (1974) Who accepts Savage’s axiom?. Behavioral Science 19: 368–373
Tversky A., Kahneman D. (1992) Advances in prospect theory: Cumulative representation of uncertainty. Journal of Risk and Uncertainty 5: 297–323
Wakker P., Tversky A. (1993) An axiomatization of cumulative prospect theory. Journal of Risk and Uncertainty 7(2): 147–175
Wu G. (1994) An empirical test of ordinal independence. Journal of Risk and Uncertainty 9: 39–60
Wu G., Gonzalez R. (1999a) Nonlinear decision weights in choice under uncertainty. Management Science 45(1): 74–85
Wu, G., & Gonzalez, R. (1999b). Dominance violations and event spitting in decision under uncertainty. Unpublished Manuscript.
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L’Haridon, O., Placido, L. Betting on Machina’s reflection example: an experiment on ambiguity. Theory Decis 69, 375–393 (2010). https://doi.org/10.1007/s11238-008-9128-9
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DOI: https://doi.org/10.1007/s11238-008-9128-9