Abstract
Daniel Ellsberg presented in Ellsberg (The Quarterly Journal of Economics 75:643–669, 1961) various examples questioning the thesis that decision making under uncertainty can be reduced to decision making under risk. These examples constitute one of the main challenges to the received view on the foundations of decision theory offered by Leonard Savage in Savage (1972). Craig Fox and Amos Tversky have, nevertheless, offered an indirect defense of Savage. They provided in Fox and Tversky (1995) an explanation of Ellsberg’s two-color problem in terms of a psychological effect: ambiguity aversion. The ‘comparative ignorance’ hypothesis articulates how this effect works and explains why it is important to an understanding of the typical pattern of responses associated with Ellsberg’s two-color problem. In the first part of this article we challenge Fox and Tversky’s explanation. We present first an experiment that extends Ellsberg’s two-color problem where certain predictions of the comparative ignorance hypothesis are not confirmed. In addition the hypothesis seems unable to explain how the subjects resolve trade-offs between security and expected pay-off when vagueness is present. Ellsberg offered an explanation of the typical behavior elicited by his examples in terms of these trade-offs and in section three we offer a model of Ellsberg’s trade-offs. The model takes seriously the role of imprecise probabilities in explaining Ellsberg’s phenomenon. The so-called three-color problem was also considered in Fox and Tversky (1995). We argue that Fox and Tversky’s analysis of this case breaks a symmetry with their analysis of the two-color problem. We propose a unified treatment of both problems and we present a experiment that confirms our hypothesis.
Similar content being viewed by others
References
Allais M. (1953) Le comportement de l’homme rationnel devant le risque: Critique des postulats et axioms de l’ecole americaine. Econometrica 21: 503–546
Arló-Costa, H., & Helzner, J. (2007). On the explanatory power of indeterminate probabilities. In Proceedings of the 5th international symposium on imprecise probability: Theories and applications.
Chow C.C., Sarin R.K. (2001) Comparative ignorance and the Ellsberg paradox. Journal of Risk and Uncertainty 22(2): 129–139
Cohen J., Hansel M. (1959) Preferences for different combinations of chance and skill in gambling. Nature 183: 841–842
Dawes, R. (2002). Avoiding the ‘Ellsberg bag’ as avoiding a ‘stacked deck’ possibility rather than avoiding ambiguity. Manuscript, Carnegie Mellon University.
Ellsberg D. (1961) Ambiguity, and the Savage axioms. The Quarterly Journal of Economics 75: 643–669
Fox C., Tversky A. (1995) Ambiguity aversion and comparative ignorance. The Quarterly Journal of Economics 110(3): 585–603
Fox C., Weber M. (2002) Ambiguity aversion, comparative ignorance, and decision context. Organizational Behavior and Human Decision Processes 88(1): 476–498
Gärdenfors P., Sahlin N.E. (1982) Unreliable probabilities, risk taking, and decision making. Synthese 53(33): 361–386
Gilboa I., Schmeidler D. (1989) Maxmin expected utility with non-unique prior. Journal of Mathematical Economics 18(2): 141–153
Heath C., Tversky A. (1991) Preference and belief: Ambiguity and competence in choice under uncertainty. Journal of Risk and Uncertainty 4(0): 5–28
Herstein I., Milnor J. (1953) An axiomatic approach to measurable utility. Econometrica 21(2): 291–297
Howell W.C. (1971) Uncertainty from internal and external sources: A clear case of overconfidence. Journal of Experimental Psychology 89(2): 240–243
Kahneman D., Tversky A. (1979) Prospect Theory: An analysis of decision under risk. Econometrica 47: 263–291
Kreps D. (1988) Notes on the theory of choice. Westview Press, Boulder, CO
Levi I. (1974) On indeterminate probabilities. Journal of Philosophy 71: 391–418
Levi I. (1986) The paradoxes of Allais and Ellsberg. Economics and Philosophy 2: 23–53
Loomes G., Sudgen R. (1982) Regret Theory: An alternative theory of rational choice under uncertainty. The Economic Journal 92(368): 805–824
Machina M., Schmeidler D. (1992) A more robust definition of subjective probability. Econometrica 60(4): 745–780
Moore D.A. (1999) Order effects in preference judgments: Evidence for context dependence in the generation of preferences. Organization Behavior and Human Decision Processes 78(2): 146–165
Savage, L. J. (1972). The foundations of statistics. Dover Publications; 2 Revised edition (June 1, 1972).
Schmeidler D. (1989) Subjective probability and expected utility without additivity. Econometrica 57(3): 571–587
Seidenfeld T. (1988) Decision theory without independence or without ordering. Economics and Philosophy 6: 267–290
Seidenfeld T., Kadane J., Schervish M. (1989) On the shared preferences of two Bayesian decision makers. Journal of Philosophy 86: 225–244
Tversky A., Fox C. (1995) Weighing risk and uncertainty. Psychological Review 102(2): 269–283
Tversky A., Kahneman D. (1992) Advances in prospect theory: Cumulative representation of uncertainty. Journal of Risk and Uncertainty 5(4): 297–323
Wakker P., Tversky A. (1993) An axiomatization of cumulative prospect theory. Journal of Risk and Uncertainty 7(2): 147–175
Author information
Authors and Affiliations
Corresponding author
Additional information
A preliminary version of the experiment presented in Sect. 2 was first presented in the 4th International Symposium on Imprecise Probabilities and Their Applications, Pittsburgh, Pennsylvania, 2005. The experiment for the three color problem and the analysis of Ellsberg’s trade-offs was discussed in a paper presented in the Workshop on Rationality and Knowledge organized as part of European Summer School on Logic, Language and Information: ESSLLI 2006.
Rights and permissions
About this article
Cite this article
Arló-Costa, H., Helzner, J. Ambiguity aversion: the explanatory power of indeterminate probabilities. Synthese 172, 37–55 (2010). https://doi.org/10.1007/s11229-009-9475-2
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11229-009-9475-2