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Expected Utility Theory without the Completeness Axiom

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Author Info
Juan Dubra
Fabio Maacheroni (Universita Bocconi)
Efe A. Ok (New York University)

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Abstract

We study axiomatically the problem of obtaining an expected utility representation for a potentially incomplete preference relation over lotteries by means of a set of von Neumann-Morgenstern utility functions. It is shown that, when the prize space is a compact metric space, a preference relation admits such a multi-utility representation provided that it satisfies the standard axioms of expected utility theory. Moreover, the representing set of utilities is unique in a well-defined sense.

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Publisher Info
Paper provided by Cowles Foundation, Yale University in its series Cowles Foundation Discussion Papers with number 1294.

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Length: 12 pages
Date of creation: Feb 2001
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Handle: RePEc:cwl:cwldpp:1294

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Keywords: Expected utility incomplete preferences

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Find related papers by JEL classification:
D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory
D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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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.:
  1. Mandler, Michael, 2005. "Incomplete preferences and rational intransitivity of choice," Games and Economic Behavior, Elsevier, vol. 50(2), pages 255-277, February. [Downloadable!] (restricted)
  2. Lloyd S. Shapley & Manel Baucells, 1998. "Multiperson Utility," UCLA Economics Working Papers 779, UCLA Department of Economics. [Downloadable!]
  3. Majumdar, Mukul & Sen, Amartya K, 1976. "A Note on Representing Partial Orderings," Review of Economic Studies, Blackwell Publishing, vol. 43(3), pages 543-45, October. [Downloadable!] (restricted)
  4. Grandmont, Jean-Michel, 1972. "Continuity properties of a von Neumann-Morgenstern utility," Journal of Economic Theory, Elsevier, vol. 4(1), pages 45-57, February. [Downloadable!] (restricted)
  5. Fishburn, Peter C., 1975. "Separation theorems and expected utilities," Journal of Economic Theory, Elsevier, vol. 11(1), pages 16-34, August. [Downloadable!] (restricted)
  6. Vind, Karl, 2000. "von Neumann Morgenstern preferences," Journal of Mathematical Economics, Elsevier, vol. 33(1), pages 109-122, February. [Downloadable!] (restricted)
    Other versions:
  7. Juan Dubra & Efe A. Ok, 2002. "A Model of Procedural Decision Making in the Presence of Risk," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 43(4), pages 1053-1080, November. [Downloadable!] (restricted)
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(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.)

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  2. LE BRETON, Michel & PELUSO, Eugenio, 2006. "Third-Degree Stochastic Dominance and the von-Neumann-Morgenstern Independence Property," IDEI Working Papers 421, Institut d'Économie Industrielle (IDEI), Toulouse. [Downloadable!]
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  5. Thibault Gajdos & Jean-Marc Tallon & Jean-Christophe Vergnaud, 2002. "Decision Making with Imprecise Probabilistic Information," ICER Working Papers - Applied Mathematics Series 18-2003, ICER - International Centre for Economic Research, revised May 2003. [Downloadable!]
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  6. Raphaël Giraud, 2004. "Reference-dependent preferences : rationality, mechanism and welfare implications," Cahiers de la Maison des Sciences Economiques v04087, Université Panthéon-Sorbonne (Paris 1). [Downloadable!]
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  10. Bruno Girotto & Silvano Holzer, 2003. "Representing complete and incomplete subjective linear preferences on random numbers," Decisions in Economics and Finance, Springer, vol. 26(2), pages 129-144, November. [Downloadable!] (restricted)
  11. Evren Özgür, 2005. "Expected Multi-Utility Theorems with Topological Continuity Axioms," Departmental Working Papers 0502, Bilkent University, Department of Economics. [Downloadable!]
  12. Eric Danan & Anthony Ziegelmeyer, 2004. "Are preferences incomplete? An experimental study using flexible choices," Discussion Papers on Strategic Interaction 2004-23, Max Planck Institute of Economics, Strategic Interaction Group. [Downloadable!]
  13. Taizhong Hu & Alfred Müller & Marco Scarsini, 2002. "Some Counterexamples in Positive Dependence," ICER Working Papers - Applied Mathematics Series 28-2003, ICER - International Centre for Economic Research, revised Jul 2003. [Downloadable!]
  14. Michael Mandler, 2001. "Compromises Between Cardinality and Ordinality in Preference Theory and Social Choice," Cowles Foundation Discussion Papers 1322, Cowles Foundation, Yale University. [Downloadable!]
  15. Özgür Evren, 2008. "On the existence of expected multi-utility representations," Economic Theory, Springer, vol. 35(3), pages 575-592, June. [Downloadable!] (restricted)
  16. Raphaël Giraud, 2004. "Framing under risk : Endogenizing the Reference Point and Separating Cognition and Decision," Cahiers de la Maison des Sciences Economiques bla04090, Université Panthéon-Sorbonne (Paris 1). [Downloadable!]
  17. Antonio Lijoi & Igor Prünster & Stephen G. Walker, 2004. "Contributions to the understanding of Bayesian consistency," ICER Working Papers - Applied Mathematics Series 13-2004, ICER - International Centre for Economic Research. [Downloadable!]
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