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Vector-Adjusted Expected Utility

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  • Marciano Siniscalchi

Abstract

This paper proposes a representation of (possibly) probabilistically unsophisticated preferences whereby (1) beliefs are jointly represented by a finitely additive probability measure and a vector-valued measure; (2) uncertain prospects are ranked according to the difference between a baseline expected utility evaluation and an adjustment term; and (3) the latter is the norm of the vector-valued expected utility of the prospect under consideration. Vector-valued measures are employed to represent the extent to which ambiguity about different events “cancels out” or “adds up”, as revealed by the decision maker’s preferences. The proposed representation, vector-adjusted expected utility (VEU), is shown to be consistent with the maxmin-expected utility model (MEU). A necessary and sufficient condition characterizing the class of VEU preferences within the MEU family of preferences is provided.

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Paper provided by IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University in its series Working Papers with number 191.

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Handle: RePEc:igi:igierp:191

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  1. Epstein, Larry G, 1999. "A Definition of Uncertainty Aversion," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 66(3), pages 579-608, July.
  2. Epstein, L.G. & Zhang, J., 1998. "Subjective Probabilities on Subjectivity Unambiguous Event," RCER Working Papers, University of Rochester - Center for Economic Research (RCER) 456, University of Rochester - Center for Economic Research (RCER).
  3. Ramon Casadesus-Masanell & Peter Klibanoff & Emre Ozdenoren, 1998. "Maximum Expected Utility over Savage Acts with a Set of Priors," Discussion Papers, Northwestern University, Center for Mathematical Studies in Economics and Management Science 1218, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  4. Mark J. Machina & David Schmeidler, 1990. "A More Robust Definition of Subjective Probability," Discussion Paper Serie A, University of Bonn, Germany 306, University of Bonn, Germany.
  5. Casadesus-Masanell, Ramon & Klibanoff, Peter & Ozdenoren, Emre, 2000. "Maxmin Expected Utility over Savage Acts with a Set of Priors," Journal of Economic Theory, Elsevier, Elsevier, vol. 92(1), pages 35-65, May.
  6. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
  7. Ghirardato, Paolo & Klibanoff, Peter & Marinacci, Massimo, 1998. "Additivity with multiple priors," Journal of Mathematical Economics, Elsevier, vol. 30(4), pages 405-420, November.
  8. Ghirardato, Paolo & Marinacci, Massimo, 2002. "Ambiguity Made Precise: A Comparative Foundation," Journal of Economic Theory, Elsevier, Elsevier, vol. 102(2), pages 251-289, February.
  9. Mark J. Machina & David Schmeidler, 1994. "Bayes Without Bernoulli: Simple Conditions for Probabilistically Sophisticated Choice," Discussion Papers, Northwestern University, Center for Mathematical Studies in Economics and Management Science 1088, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  10. Itzhak Gilboa & David Schmeidler, 1991. "Updating Ambiguous Beliefs," Discussion Papers, Northwestern University, Center for Mathematical Studies in Economics and Management Science 924, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  11. Lars Peter Hansen & Thomas J. Sargent & Thomas D. Tallarini Jr., 1997. "Robust Permanent Income and Pricing," Levine's Working Paper Archive 596, David K. Levine.
  12. F J Anscombe & R J Aumann, 2000. "A Definition of Subjective Probability," Levine's Working Paper Archive 7591, David K. Levine.
  13. David Schmeidler, 1989. "Subjective Probability and Expected Utility without Additivity," Levine's Working Paper Archive 7662, David K. Levine.
  14. Daniel Ellsberg, 2000. "Risk, Ambiguity and the Savage Axioms," Levine's Working Paper Archive 7605, David K. Levine.
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Cited by:
  1. Erio Castagnoli & Fabio Maccheroni & Massimo Marinacci, 2002. "Insurance Premia Consistent with the Market," ICER Working Papers - Applied Mathematics Series, ICER - International Centre for Economic Research 24-2002, ICER - International Centre for Economic Research.
  2. Siniscalchi, Marciano, 2006. "A behavioral characterization of plausible priors," Journal of Economic Theory, Elsevier, Elsevier, vol. 128(1), pages 91-135, May.

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