Abstract
This paper discusses Jean-Yves Jaffray’s ideas on ambiguity and the views underlying his ideas. His models, developed 20 years ago, provide the most tractable separation of risk attitudes, ambiguity attitudes, and ambiguity beliefs available in the literature today.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Anscombe F. J., Aumann R. J. (1963) A definition of subjective probability. Annals of Mathematical Statistics 34: 199–205
Chateauneuf A., Jaffray J.-Y. (1989) Some characterizations of lower probabilities and other monotone capacities through the use of Möbius inversion. Mathematical Social Sciences 17: 263–283
Cohen M., Jaffray J.-Y. (1980) Rational behavior under complete ignorance. Econometrica 48: 1281–1299
Dempster A. P. (1967) Upper and lower probabilities induced by a multivalued mapping. Annals of Mathematical Statistics 38: 325–339
Denoeux T. (2008) Conjunctive and disjunctive combination of belief functions induced by non distinct bodies of evidence. Artificial Intelligence 172: 234–264
Eichberger, J., Grant, S., Kelsey, D., & Koshevoy, G. A. (2009). The alpha-meu model: A comment, mimeo.
Gajdos, T. (2008). Zoom, La Lettre du CES, no. 3, University of Paris I, 1–2 December 2008.
Gajdos T., Hayashi T., Tallon J.-M., Vergnaud J.-C. (2008) Attitude towards imprecise information. Journal of Economic Theory 140: 27–65
Ghirardato P. (2001) Coping with ignorance: unforeseen contingencies and non-additive uncertainty. Economic Theory 17: 247–276
Ghirardato P., Maccheroni F., Marinacci M. (2004) Differentiating ambiguity and ambiguity attitude. Journal of Economic Theory 118: 133–173
Gilboa I. (1987) Expected utility with purely subjective non-additive probabilities. Journal of Mathematical Economics 16: 65–88
Gilboa I., Schmeidler D. (1989) Maxmin expected utility with a non-unique prior. Journal of Mathematical Economics 18: 141–153
Jaffray J.-Y. (1989a) Linear utility theory for belief functions. Operations Research Letters 8: 107–112
Jaffray J.-Y. (1989b) Généralisation du Critère de l’Utilité Espérée aux Choix dans l’Incertain Régulier. RAIRO-RO/Operations Research 23: 237–267
Jaffray J.-Y. (1991) Linear utility theory and belief functions: A discussion. In: Chikan A. (eds) Progress in decision, utility and risk theory. Kluwer, Dordrecht
Jaffray J.-Y. (1992) Bayesian updating and belief functions. IEEE Transactions on Systems, Man, and Cybernetics 22: 1144–1152
Jaffray J.-Y. (1994) Dynamic decision making with belief functions. In: Yager R. R., Fedrizzi M., Kacprzyk J. (eds) Advances in the Dempster–Shafer theory of evidence. Wiley, New York, pp 331–352
Jaffray, J.-Y., & Meglena, J. (2010). How to deal with partially analyzed acts? Theory and Decision (this issue).
Jaffray J.-Y., Philippe F. (1997) On the existence of subjective upper and lower probabilities. Mathematics of Operations Research 22: 165–185
Jaffray J.-Y., Said T. (1994) Optimal hypothesis testing with a vague prior. In: Rios S. (eds) Decision theory and decision analysis: Trends and challenges. Kluwer, Dordrecht, The Netherlands, pp 207–223
Jaffray J.-Y., Wakker P. P. (1993) Decision making with belief functions: Compatibility and incompatibility with the sure-thing principle. Journal of Risk and Uncertainty 7: 255–271
Keeney, R. L., & Raiffa, H. (1976). Decisions with multiple objectives. New York: Wiley. (Cambridge, UK: Cambridge University Press, 2nd edn, 1993).
Luce R. D., Raiffa H. (1957) Games and decisions. Wiley, New York
Machina M. J. (1989) Dynamic consistency and non-expected utility models of choice under uncertainty. Journal of Economic Literature 27: 1622–1688
Milnor J. (1954) Games against nature. In: Thrall R. M., Coombs C. H., Davis R. L. (eds) Decision processes. Wiley, New York, pp 49–59
Philippe F., Debs G., Jaffray J.-Y. (1999) Decision making with monotone lower probabilities of infinite order. Mathematics of Operations Research 24: 767–784
Savage, L. J. (1954). The foundations of statistics. New York: Wiley. (New York: Dover Publications, 2nd edn, 1972)
Schmeidler D. (1989) Subjective probability and expected utility without additivity. Econometrica 57: 571–587
Shafer G. (1976) A mathematical theory of evidence. Princeton University Press, Princeton, NJ
Tversky A., Kahneman D. (1992) Advances in prospect theory: Cumulative representation of uncertainty. Journal of Risk and Uncertainty 5: 297–323
Open Access
This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Wakker, P.P. Jaffray’s ideas on ambiguity. Theory Decis 71, 11–22 (2011). https://doi.org/10.1007/s11238-010-9209-4
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11238-010-9209-4