Allais, Ellsberg, and Preferences for Hedging
We study the relation between ambiguity aversion and the Allais paradox. To this end, we introduce a novel de nition of hedging which applies to objective lotteries as well as to uncertain acts, and we use it to de ne a novel axiom that captures a preference for hedging which generalizes the one of Schmeidler (1989). We argue how this generalized axiom captures both aversion to ambiguity, and attraction towards certainty for objective lotteries. We show that this axiom, together with other standard ones, is equivalent to to two representations both of which generalize the MaxMin Expected Utility model of Gilboa and Schmeidler (1989). In both, the agent reacts to ambiguity using multiple priors, but does not use expected utility to evaluate objective lotteries. In our rst representation, the agent treats objective lotteries as `ambiguous objects,' and use a set of priors to evaluate them. In the second, equivalent representation, lotteries are evaluated by distorting probabilities as in the RankDependent Utility model, but using the worst from a set of such distortions. Finally, we show how a preference for hedging is not sucient to guarantee an Ellsberglike behavior if the agent violate expected utility for objective lotteries. We then provide an axiom that guarantees that this is the case, and nd an associated representation in which the agent rst maps acts to an objective lottery using the worst of the priors in a set; then evaluates this lottery using the worst distortion from a set of concave RankDependent Utility functionals.
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Date of creation:  2012 
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Handle:  RePEc:bro:econwp:20122 
Contact details of provider:  Postal: Department of Economics, Brown University, Providence, RI 02912

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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
 Ghirardato, Paolo & Maccheroni, Fabio & Marinacci, Massimo & Siniscalchi, Marciano, 2001.
"A Subjective Spin on Roulette Wheels,"
Working Papers
1127, California Institute of Technology, Division of the Humanities and Social Sciences.
 Paolo Ghirardato & Fabio Maccheroni & Massimo Marinacci & Marciano Siniscalchi, 2003. "A Subjective Spin on Roulette Wheels," Econometrica, Econometric Society, vol. 71(6), pages 18971908, November.
 Paolo Ghirardato & Fabio Maccheroni & Massimo Marinacci & Marciano Siniscalchi, 2001. "A subjective spin on roulette wheels," ICER Working Papers  Applied Mathematics Series 172001, ICER  International Centre for Economic Research, revised Aug 2001.
 Mohammed Abdellaoui & Laetitia Placido & Aurélien Baillon & P.P. Wakker, 2011. "The Rich Domain of Uncertainty: Source Functions and Their Experimental Implementation," Université Paris1 PanthéonSorbonne (PostPrint and Working Papers) hal00609214, HAL.
 Fabio Maccheroni & Massimo Marinacci & Aldo Rustichini, 2006.
"Ambiguity Aversion, Robustness, and the Variational Representation of Preferences,"
Econometrica,
Econometric Society, vol. 74(6), pages 14471498, November.
 Fabio Maccheroni & Massimo Marinacci & Aldo Rustichini, 2004. "Ambiguity Aversion, Robustness, and the Variational Representation of Preferences," Carlo Alberto Notebooks 12, Collegio Carlo Alberto, revised 2006.
 CerreiaVioglio, S. & Maccheroni, F. & Marinacci, M. & Montrucchio, L., 2011.
"Uncertainty averse preferences,"
Journal of Economic Theory,
Elsevier, vol. 146(4), pages 12751330, July.
 Simone CerreiaVioglio & Fabio Maccheroni & Massimo Marinacci & Luigi Montrucchio, 2008. "Uncertainty Averse Preferences," Carlo Alberto Notebooks 77, Collegio Carlo Alberto.
 Wakker, Peter P, 2001. "Testing and Characterizing Properties of Nonadditive Measures through Violations of the SureThing Principle," Econometrica, Econometric Society, vol. 69(4), pages 103959, July.
 Enrico Diecidue & Ulrich Schmidt & Horst Zank, 2008.
"Parametric Weighting Functions,"
Kiel Working Papers
1395, Kiel Institute for the World Economy.
 Diecidue, Enrico & Schmidt, Ulrich & Zank, Horst, 2009. "Parametric weighting functions," Journal of Economic Theory, Elsevier, vol. 144(3), pages 11021118, May.
 Diecidue, Enrico & Schmidt, Ulrich & Zank, Horst, 2008. "Parametric weighting functions," Kiel Working Papers 1395, Kiel Institute for the World Economy (IfW).
 Zank, Horst & Schmidt, Ulrich & Diecidue, Enrico, 2007. "Parametric Weighting Functions," Economics Working Papers 2007,01, ChristianAlbrechtsUniversity of Kiel, Department of Economics.
 Enrico Diecidue & Ulrich Schmidt & Horst Zank, 2006. "Parametric Weighting Functions," The School of Economics Discussion Paper Series 0622, Economics, The University of Manchester.
 Nakamura Y., 1996.
"Rank dependent utility for arbitrary consequnce spaces,"
Mathematical Social Sciences,
Elsevier, vol. 31(1), pages 5454, February.
 Nakamura, Yutaka, 1995. "Rank dependent utility for arbitrary consequence spaces," Mathematical Social Sciences, Elsevier, vol. 29(2), pages 103129, April.
 Ramon CasadesusMasanell & Peter Klibanoff & Emre Ozdenoren, 1998. "Maximum Expected Utility over Savage Acts with a Set of Priors," Discussion Papers 1218, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
 Tversky, Amos & Kahneman, Daniel, 1992. "Advances in Prospect Theory: Cumulative Representation of Uncertainty," Journal of Risk and Uncertainty, Springer, vol. 5(4), pages 297323, October.
 Simone CerreiaVioglio & Paolo Ghirardato & Fabio Maccheroni & Massimo Marinacci & Marciano Siniscalchi, 2011.
"Rational preferences under ambiguity,"
Economic Theory,
Springer;Society for the Advancement of Economic Theory (SAET), vol. 48(2), pages 341375, October.
 Simone CerreiaVioglio & Paolo Ghirardato & Fabio Maccheroni & Massimo Marinacci & Marciano Siniscalchi, 2010. "Rational Preferences under Ambiguity," Carlo Alberto Notebooks 169, Collegio Carlo Alberto.
 Mark J. Machina & David Schmeidler, 1994.
"Bayes Without Bernoulli: Simple Conditions for Probabilistically Sophisticated Choice,"
Discussion Papers
1088, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
 Machina Mark J. & Schmeidler David, 1995. "Bayes without Bernoulli: Simple Conditions for Probabilistically Sophisticated Choice," Journal of Economic Theory, Elsevier, vol. 67(1), pages 106128, October.
 Vincent Feltkamp & Yoram Halevy, 1999.
" A Bayesian Approach To Uncertainty Aversion,"
Working Papers. Serie AD
199914, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
 Yoram Halevy & Vincent Feltkamp, 2005. "A Bayesian Approach to Uncertainty Aversion," Review of Economic Studies, Oxford University Press, vol. 72(2), pages 449466.
 Yoram Halevy & Vincent Feltkamp, . "A Bayesian Approach to Uncentainty Aversion," Penn CARESS Working Papers f17f3e2c6ad93e4b53fd58fc9, Penn Economics Department.
 Yoram Halevy & Vincent Feltkamp, . "A Bayesian Approach to Uncentainty Aversion," CARESS Working Papres 9903, University of Pennsylvania Center for Analytic Research and Economics in the Social Sciences.
 Feltkamp, Vincent & Halevy, Yoram, 2004. "A Bayesian Approach to Uncertainty Aversion," Microeconomics.ca working papers halevy040213074837, Vancouver School of Economics, revised 25 Feb 2014.
 Vincent Feltkamp & Yoram Halevy, 2000. "A Bayesian Approach to Uncertainty Aversion," Econometric Society World Congress 2000 Contributed Papers 1125, Econometric Society.
 Safra, Zvi & Segal, Uzi, 1998. "Constant Risk Aversion," Journal of Economic Theory, Elsevier, vol. 83(1), pages 1942, November.
 Uzi Segal, 1989.
"TwoStage Lotteries Without the Reduction Axiom,"
UCLA Economics Working Papers
552, UCLA Department of Economics.
 Segal, Uzi, 1990. "TwoStage Lotteries without the Reduction Axiom," Econometrica, Econometric Society, vol. 58(2), pages 34977, March.
 Uzi Segal, 2000. "Two Stage Lotteries Without the Reduction Axiom," Levine's Working Paper Archive 7599, David K. Levine.
 Uzi Segal, 1985.
"The Ellsberg Paradox and Risk Aversion: An Anticipated Utility Approach,"
UCLA Economics Working Papers
362, UCLA Department of Economics.
 Segal, Uzi, 1987. "The Ellsberg Paradox and Risk Aversion: An Anticipated Utility Approach," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 28(1), pages 175202, February.
 David Schmeidler, 1989.
"Subjective Probability and Expected Utility without Additivity,"
Levine's Working Paper Archive
7662, David K. Levine.
 Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 57187, May.
 Chateauneuf, Alain, 1999. "Comonotonicity axioms and rankdependent expected utility theory for arbitrary consequences," Journal of Mathematical Economics, Elsevier, vol. 32(1), pages 2145, August.
 Mark J. Machina & David Schmeidler, 1990.
"A More Robust Definition of Subjective Probability,"
Discussion Paper Serie A
306, University of Bonn, Germany.
 Machina, Mark J & Schmeidler, David, 1992. "A More Robust Definition of Subjective Probability," Econometrica, Econometric Society, vol. 60(4), pages 74580, July.
 Machina,Mark & Schmeidler,David, 1991. "A more robust definition of subjective probability," Discussion Paper Serie A 365, University of Bonn, Germany.
 Gilboa, Itzhak & Schmeidler, David, 1989.
"Maxmin expected utility with nonunique prior,"
Journal of Mathematical Economics,
Elsevier, vol. 18(2), pages 141153, April.
 Itzhak Gilboa & David Schmeidler, 1989. "Maxmin Expected Utility with NonUnique Prior," PostPrint hal00753237, HAL.
 Diecidue, E. & Wakker, P.P., 2000.
"On the Intuition of RankDependent Utility,"
Discussion Paper
200074, Tilburg University, Center for Economic Research.
 Diecidue, Enrico & Wakker, Peter P, 2001. "On the Intuition of RankDependent Utility," Journal of Risk and Uncertainty, Springer, vol. 23(3), pages 28198, November.
 Mohammed Abdellaoui & Aurelien Baillon & Laetitia Placido & Peter P. Wakker, 2011.
"The Rich Domain of Uncertainty: Source Functions and Their Experimental Implementation,"
American Economic Review,
American Economic Association, vol. 101(2), pages 695723, April.
 Peter Klibanoff & Massimo Marinacci & Sujoy Mukerji, 2005.
"A Smooth Model of Decision Making under Ambiguity,"
Econometrica,
Econometric Society, vol. 73(6), pages 18491892, November.
 Peter Klibanoff & Massimo Marinacci & Sujoy Mukerji, 2002. "A smooth model of decision making under ambiguity," ICER Working Papers  Applied Mathematics Series 112003, ICER  International Centre for Economic Research, revised Apr 2003.
 Sujoy Mukerji & Peter Klibanoff, 2002. "A Smooth Model of Decision,Making Under Ambiguity," Economics Series Working Papers 113, University of Oxford, Department of Economics.
 Barry Sopher & Mattison Narramore, 2000. "Stochastic Choice and Consistency in Decision Making Under Uncertainty: An Experimental Study," Departmental Working Papers 199626, Rutgers University, Department of Economics.
 Mohammed Abdellaoui & Olivier l’Haridon & Horst Zank, 2009. "Separating Curvature and Elevation: A Parametric Weighting Function," The School of Economics Discussion Paper Series 0901, Economics, The University of Manchester.
 Chris Starmer, 2000. "Developments in Nonexpected Utility Theory: The Hunt for a Descriptive Theory of Choice under Risk," Journal of Economic Literature, American Economic Association, vol. 38(2), pages 332382, June.
 Mohammed Abdellaoui, 2002. "A Genuine RankDependent Generalization of the Von NeumannMorgenstern Expected Utility Theorem," Econometrica, Econometric Society, vol. 70(2), pages 717736, March.
 Sopher & Narramore, 2000. "Stochastic Choice and Consistency in Decision Making Under Risk: An Experimental Study," Theory and Decision, Springer, vol. 48(4), pages 323349, June.
 Hong Chew Soo & Karni Edi, 1994. "Choquet Expected Utility with a Finite State Space: Commutativity and ActIndependence," Journal of Economic Theory, Elsevier, vol. 62(2), pages 469479, April.
 Dillenberger, David, 2008. "Preferences for OneShot Resolution of Uncertainty and AllaisType Behavior," MPRA Paper 8342, University Library of Munich, Germany.
 repec:hal:journl:halshs00177057 is not listed on IDEAS
 Massimo Marinacci & Fabio Maccheroni & Alain Chateauneuf & JeanMarc Tallon, 2003.
"Monotone Continuous Multiple Priors,"
ICER Working Papers  Applied Mathematics Series
302003, ICER  International Centre for Economic Research.
 Alain Chateauneuf & Fabio Maccheroni & Massimo Marinacci & JeanMarc Tallon, 2005. "Monotone continuous multiple priors," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 26(4), pages 973982, November.
 Alain Chateauneuf & Fabio Macheronni & Massimo Marinacci & JeanMarc Tallon, 2005. "Monotone continuous multiple priors," Université Paris1 PanthéonSorbonne (PostPrint and Working Papers) halshs00177057, HAL.
 Fabio Maccheroni, 2002. "Maxmin under risk," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 19(4), pages 823831.
 Larry G. Epstein, 1999. "A Definition of Uncertainty Aversion," Review of Economic Studies, Oxford University Press, vol. 66(3), pages 579608.
 Halevy, Yoram, 2005.
"Ellsberg Revisited: an Experimental Study,"
Microeconomics.ca working papers
halevy050726115113, Vancouver School of Economics, revised 25 Feb 2014.
 Yoram Halevy, 2007. "Ellsberg Revisited: An Experimental Study," Econometrica, Econometric Society, vol. 75(2), pages 503536, 03.
 Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 323343, December.
 Gul, Faruk, 1991. "A Theory of Disappointment Aversion," Econometrica, Econometric Society, vol. 59(3), pages 66786, May.
 Itzhak Gilboa & Massimo Marinacci, 2011. "Ambiguity and the Bayesian Paradigm," Working Papers 379, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
 Paolo Ghirardato & Marciano Siniscalchi, 2010. "A more robust definition of multiple priors," Carlo Alberto Notebooks 144, Collegio Carlo Alberto.
 Efe A. Ok & Pietro Ortoleva & Gil Riella, 2012. "Incomplete Preferences Under Uncertainty: Indecisiveness in Beliefs versus Tastes," Econometrica, Econometric Society, vol. 80(4), pages 17911808, 07.
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