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Attitude toward imprecise information

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Author Info
Thibault Gajdos () (Centre d'Economie de la Sorbonne)
Takashi Hayashi () (University of Texas)
Jean-Marc Tallon () (Centre d'Economie de la Sorbonne)
Jean-Christophe Vergnaud () (Centre d'Economie de la Sorbonne)

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Abstract

This paper presents an axiomatic model of decision making which incorporates objective but imprecise information. We axiomatize a decision criterion of the multiple priors (or maxmin expected utility) type. The model achieves two primary objectives. First, it explains how subjective belief varies with information. Second, it identifies an explicit attitude toward imprecision that underlies usual hedging axioms. Information is assumed to take the form of a probability-possibility set, that is, a set P of probability measures on the state space. The decision maker is told that the true probability law lies in P. She is assumed to rank pairs of the form (P,f) where P is a probability-possibility set and f is an act mapping states into outcomes. The representation result delivers multiple-priors utility at each probability-possibility set. There is a mapping that gives for each probability-possibility set the subjective set of priors. This allows both subjective expected utility when the subjective set of priors is reduced to a singleton and the other extreme where the decision maker takes the worst case scenario in the entire probability-possibility set. We show that the relation “more averse to imprecision” is characterized by inclusion of the sets of priors, irrespective of the utility functions that capture risk attitude. We characterize, under extra axioms, a more precise functional form, in which the subjective set of priors is obtained by (i) solving for the “mean value” of the probability-possibility set and (ii) shrinking the probability-possibility set toward the mean value to a degree determined by preference.

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Publisher Info
Paper provided by Université Panthéon-Sorbonne (Paris 1) in its series Cahiers de la Maison des Sciences Economiques with number v06081.

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Length: 38 pages
Date of creation: Jul 2006
Date of revision:
Handle: RePEc:mse:wpsorb:v06081

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Related research
Keywords: Imprecise information; imprecision aversion; multiple priors; Steiner point.;

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Find related papers by JEL classification:
D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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References listed on IDEAS
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.:
  1. Epstein, Larry G & Wang, Tan, 1994. "Intertemporal Asset Pricing Under Knightian Uncertainty," Econometrica, Econometric Society, vol. 62(2), pages 283-322, March. [Downloadable!] (restricted)
  2. Wojciech Olszewski, 2007. "Preferences Over Sets of Lotteries," Review of Economic Studies, Blackwell Publishing, vol. 74(2), pages 567-595, 04. [Downloadable!] (restricted)
  3. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April. [Downloadable!] (restricted)
  4. Sujoy Mukerji & Peter Klibanoff, 2002. "A Smooth Model of DecisionMaking Under Ambiguity," Economics Series Working Papers 113, University of Oxford, Department of Economics. [Downloadable!]
    Other versions:
  5. Tapking, Jens, 2004. "Axioms for preferences revealing subjective uncertainty and uncertainty aversion," Journal of Mathematical Economics, Elsevier, vol. 40(7), pages 771-797, November. [Downloadable!] (restricted)
  6. Fabio Maccheroni & Massimo Marinacci & Aldo Rustichini, 2006. "Ambiguity Aversion, Robustness, and the Variational Representation of Preferences," Econometrica, Econometric Society, vol. 74(6), pages 1447-1498, November. [Downloadable!] (restricted)
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  7. Raphaël Giraud, 2006. "Objective Imprecise Probabilistic Information, Second Order Beliefs and Ambiguity Aversion: an Axiomatization," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00102346_v1, HAL. [Downloadable!]
  8. Sujoy Mukerji & Jean-Marc Tallon, 2001. "Ambiguity Aversion and Incompleteness of Financial Markets," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00174539_v1, HAL. [Downloadable!]
    Other versions:
  9. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-87, May. [Downloadable!] (restricted)
  10. Gajdos, Thibault & Tallon, Jean-Marc & Vergnaud, Jean-Christophe, 2004. "Decision making with imprecise probabilistic information," Journal of Mathematical Economics, Elsevier, vol. 40(6), pages 647-681, September. [Downloadable!] (restricted)
    Other versions:
  11. Epstein, Larry G, 1999. "A Definition of Uncertainty Aversion," Review of Economic Studies, Blackwell Publishing, vol. 66(3), pages 579-608, July. [Downloadable!] (restricted)
  12. Ghirardato, Paolo & Marinacci, M., 1997. "Ambiguity Made Precise: A Comparative Foundation and Some Implications," Working Papers 1026, California Institute of Technology, Division of the Humanities and Social Sciences. [Downloadable!]
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Cited by:
(explanations, 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.)

  1. Jürgen Eichberger & Ani Guerdjikova, 2008. "Multiple Priors as Similarity Weighted Frequencies," Working Papers 0470, University of Heidelberg, Department of Economics, revised Jul 2008. [Downloadable!]
  2. Hill, Brian, 2009. "Confidence and ambiguity," Les Cahiers de Recherche 914, HEC Paris. [Downloadable!]
  3. Eichberger, Jürgen & Guerdjikova, Ani, 2008. "Multiple Priors as Similarity Weighted Frequencies," Sonderforschungsbereich 504 Publications 08-07, Sonderforschungsbereich 504, Universität Mannheim & Sonderforschungsbereich 504, University of Mannheim. [Downloadable!]
  4. Marie-Louise Vierø, 2009. "Exactly what happens after the Anscombe–Aumann race?," Economic Theory, Springer, vol. 41(2), pages 175-212, November. [Downloadable!] (restricted)
  5. Thibault Gajdos & Feriel Kandil, 2008. "The ignorant observer," Social Choice and Welfare, Springer, vol. 31(2), pages 193-232, August. [Downloadable!] (restricted)
    Other versions:
  6. Marie-Louise Vierø, 2006. "Exactly What Happens After the Anscombe-Aumann Race? Representing Preferences in Vague Environments," Working Papers 1094, Queen's University, Department of Economics. [Downloadable!]
  7. Itzhak Gilboa, 2009. "Questions in Decision Theory," Levine's Working Paper Archive 814577000000000335, David K. Levine. [Downloadable!]
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