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Objective and Subjective Rationality in a Multiple Prior Model

  • Itzhak Gilboa
  • Fabio Maccheroni
  • Massimo Marinacci
  • David Schmeidler

A decision maker is characterized by two binary relations. The first reflects decisions that are rational in an “objective” sense: the decision maker can convince others that she is right in making them. The second relation models decisions that are rational in a “subjective” sense: the decision maker cannot be convinced that she is wrong in making them. We impose axioms on these relations that allow a joint representation by a single set of prior probabilities. It is “objectively rational” to choose f in the presence of g if and only if the expected utility of f is at least as high as that of g given each and every prior in the set. It is “subjectively rational” to choose f rather than g if and only if the minimal expected utility of f (relative to all priors in the set) is at least as high as that of g.

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Paper provided by Collegio Carlo Alberto in its series Carlo Alberto Notebooks with number 73.

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Length: 40 pages
Date of creation: 2008
Date of revision: 2008
Handle: RePEc:cca:wpaper:73
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  1. Efe A. Ok & Pietro Ortoleva & Gil Riella, 2012. "Incomplete Preferences Under Uncertainty: Indecisiveness in Beliefs versus Tastes," Econometrica, Econometric Society, vol. 80(4), pages 1791-1808, 07.
  2. Eric Danan & Anthony Ziegelmeyer, 2006. "Are preferences complete? An experimental measurement of indecisiveness under risk," Papers on Strategic Interaction 2006-01, Max Planck Institute of Economics, Strategic Interaction Group.
  3. Manel Baucells & Lloyd S. Shapley, 2000. "Multiperson Utility," Econometric Society World Congress 2000 Contributed Papers 0078, Econometric Society.
  4. Mandler, Michael, 2005. "Incomplete preferences and rational intransitivity of choice," Games and Economic Behavior, Elsevier, vol. 50(2), pages 255-277, February.
  5. Gajdos, T. & Hayashi, T. & Tallon, J.-M. & Vergnaud, J.-C., 2008. "Attitude toward imprecise information," Journal of Economic Theory, Elsevier, vol. 140(1), pages 27-65, May.
  6. Danan, Eric, 2008. "Revealed preference and indifferent selection," Mathematical Social Sciences, Elsevier, vol. 55(1), pages 24-37, January.
  7. Evren, Özgür & Ok, Efe A., 2011. "On the multi-utility representation of preference relations," Journal of Mathematical Economics, Elsevier, vol. 47(4-5), pages 554-563.
  8. Juan Dubra & Fabio Maacheroni & Efe A. Ok, 2001. "Expected Utility Theory without the Completeness Axiom," Cowles Foundation Discussion Papers 1294, Cowles Foundation for Research in Economics, Yale University.
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