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Rationality of Belief Or: Why Savage's axioms are neither necessary nor sufficient for rationality, Second Version

Author

Listed:
  • Itzhak Gilboa

    () (Eitan Berglas School of Economics, Tel Aviv University and HEC, Paris)

  • Andrew Postlewaite

    () (Department of Economics, University of Pennsylvania)

  • David Schmeidler

    () (Tel-Aviv University and Ohio State University)

Abstract

Economic theory reduces the concept of rationality to internal consistency. As far as beliefs are concerned, rationality is equated with having a prior belief over a “Grand State Space”, describing all possible sources of uncertainties. We argue that this notion is too weak in some senses and too strong in others. It is too weak because it does not distinguish between rational and irrational beliefs. Relatedly, the Bayesian approach, when applied to the Grand State Space, is inherently incapable of describing the formation of prior beliefs. On the other hand, this notion of rationality is too strong because there are many situations in which there is not sufficient information for an individual to generate a Bayesian prior. It follows that the Bayesian approach is neither sufficient not necessary for the rationality of beliefs.

Suggested Citation

  • Itzhak Gilboa & Andrew Postlewaite & David Schmeidler, 2004. "Rationality of Belief Or: Why Savage's axioms are neither necessary nor sufficient for rationality, Second Version," PIER Working Paper Archive 08-043, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 03 Dec 2008.
  • Handle: RePEc:pen:papers:08-043
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    References listed on IDEAS

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    1. Machina Mark J. & Schmeidler David, 1995. "Bayes without Bernoulli: Simple Conditions for Probabilistically Sophisticated Choice," Journal of Economic Theory, Elsevier, vol. 67(1), pages 106-128, October.
    2. Faruk Gul & Wolfgang Pesendorfer, 2005. "The Case for Mindless Economics," Levine's Working Paper Archive 784828000000000581, David K. Levine.
    3. Nishimura, Kiyohiko G. & Ozaki, Hiroyuki, 2004. "Search and Knightian uncertainty," Journal of Economic Theory, Elsevier, vol. 119(2), pages 299-333, December.
    4. Epstein Larry G. & Wang Tan, 1995. "Uncertainty, Risk-Neutral Measures and Security Price Booms and Crashes," Journal of Economic Theory, Elsevier, vol. 67(1), pages 40-82, October.
    5. Lawrence Blume & Adam Brandenburger & Eddie Dekel, 2014. "Lexicographic Probabilities and Choice Under Uncertainty," World Scientific Book Chapters,in: The Language of Game Theory Putting Epistemics into the Mathematics of Games, chapter 6, pages 137-160 World Scientific Publishing Co. Pte. Ltd..
    6. Epstein, Larry G. & Schneider, Martin, 2003. "Recursive multiple-priors," Journal of Economic Theory, Elsevier, vol. 113(1), pages 1-31, November.
    7. Paolo Ghirardato, 2002. "Revisiting Savage in a conditional world," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), pages 83-92.
    8. In-Koo Cho & David M. Kreps, 1987. "Signaling Games and Stable Equilibria," The Quarterly Journal of Economics, Oxford University Press, vol. 102(2), pages 179-221.
    9. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    10. Enriqueta Aragones & Itzhak Gilboa & Andrew Postlewaite & David Schmeidler, 2005. "Fact-Free Learning," American Economic Review, American Economic Association, pages 1355-1368.
    11. Machina, Mark J & Schmeidler, David, 1992. "A More Robust Definition of Subjective Probability," Econometrica, Econometric Society, vol. 60(4), pages 745-780, July.
    12. Hansen, Lars Peter & Sargent, Thomas J., 2003. "Robust control of forward-looking models," Journal of Monetary Economics, Elsevier, pages 581-604.
    13. Mukerji, Sujoy, 1998. "Ambiguity Aversion and Incompleteness of Contractual Form," American Economic Review, American Economic Association, pages 1207-1231.
    14. Daniel Ellsberg, 1961. "Risk, Ambiguity, and the Savage Axioms," The Quarterly Journal of Economics, Oxford University Press, vol. 75(4), pages 643-669.
    15. Epstein, Larry G. & Miao, Jianjun, 2003. "A two-person dynamic equilibrium under ambiguity," Journal of Economic Dynamics and Control, Elsevier, vol. 27(7), pages 1253-1288, May.
    16. Mailath George J. & Okuno-Fujiwara Masahiro & Postlewaite Andrew, 1993. "Belief-Based Refinements in Signalling Games," Journal of Economic Theory, Elsevier, vol. 60(2), pages 241-276, August.
    17. Dow, James & Werlang, Sergio Ribeiro da Costa, 1992. "Uncertainty Aversion, Risk Aversion, and the Optimal Choice of Portfolio," Econometrica, Econometric Society, vol. 60(1), pages 197-204, January.
    18. Kahneman, Daniel & Tversky, Amos, 1979. "Prospect Theory: An Analysis of Decision under Risk," Econometrica, Econometric Society, pages 263-291.
    19. Epstein, Larry G & Wang, Tan, 1994. "Intertemporal Asset Pricing Under Knightian Uncertainty," Econometrica, Econometric Society, vol. 62(2), pages 283-322, March.
    20. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-587, May.
    21. Lars Peter Hansen & Thomas J. Sargent, 2001. "Acknowledging Misspecification in Macroeconomic Theory," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 4(3), pages 519-535, July.
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    Cited by:

    1. Tigran Melkonyan & Mark Pingle, 2010. "Ambiguity, pessimism, and rational religious choice," Theory and Decision, Springer, pages 417-438.
    2. Jayant V Ganguli & Scott Condie, 2008. "Ambiguity and rational expectations equilibria," 2008 Meeting Papers 719, Society for Economic Dynamics.
    3. Scott Condie & Jayant V. Ganguli, 2011. "Ambiguity and Rational Expectations Equilibria," Review of Economic Studies, Oxford University Press, vol. 78(3), pages 821-845.

    More about this item

    Keywords

    Decision making; Bayesian; Behavioral Economics;

    JEL classification:

    • B4 - Schools of Economic Thought and Methodology - - Economic Methodology
    • D8 - Microeconomics - - Information, Knowledge, and Uncertainty

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