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Synthese

, Volume 187, Issue 1, pp 11–31 | Cite as

Rationality of belief or: why savage’s axioms are neither necessary nor sufficient for rationality

  • Itzhak GilboaEmail author
  • Andrew Postlewaite
  • David Schmeidler
Article

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.

Keywords

Probability Rationality Beliefs Bayesian paradigm Savage axioms 

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References

  1. Alonso I. (2005) Ambiguity in a two-country world. Mimeo, Princeton University, PrincetonGoogle Scholar
  2. Aragonès E., Gilboa I., Postlewaite A. W., Schmeidler D. (2005) Fact-free learning. American Economic Review 95: 1355–1368CrossRefGoogle Scholar
  3. Bewley T. (2002) Knightian decision theory: Part I. Decisions in Economics and Finance 25: 79–110 (Working paper, 1986)CrossRefGoogle Scholar
  4. Carnap R. (1952) The continuum of inductive methods. University of Chicago Press, ChicagoGoogle Scholar
  5. Cho I.-K., Kreps D. M. (1987) Signaling games and stable equilibria. The Quarterly Journal of Economics 102: 179–222CrossRefGoogle Scholar
  6. de Finetti B. (1937) La Prevision: Ses Lois Logiques, Ses Sources Subjectives. Annales de l’Institute Henri Poincare 7: 1–68Google Scholar
  7. Dow J., Werlang S. R. C. (1992) Uncertainty aversion, risk aversion, and the optimal choice of portfolio. Econometrica 60: 197–204CrossRefGoogle Scholar
  8. Epstein L. G., Miao J. (2003) A two-person dynamic equilibrium under ambiguity. Journal of Economic Dynamics and Control 27: 1253–1288CrossRefGoogle Scholar
  9. Epstein L. G., Schneider M. (2003) Recursive multiple priors. Journal of Economic Theory 113: 32–50CrossRefGoogle Scholar
  10. Epstein L. G., Wang T. (1994) Intertemporal asset pricing under knightian uncertainty. Econometrica 62: 283–322CrossRefGoogle Scholar
  11. Epstein L. G., Wang T. (1995) Uncertainty, risk-neutral measures and security price booms and crashes. Journal of Economic Theory 67: 40–82CrossRefGoogle Scholar
  12. Ellsberg D. (1961) Risk, ambiguity and the savage axioms. Quarterly Journal of Economics 75: 643–669CrossRefGoogle Scholar
  13. Ghirardato P. (2002) Revisiting savage in a conditional world. Economic Theory 20: 83–92CrossRefGoogle Scholar
  14. Gilboa I., Schmeidler D. (1989) Maxmin expected utility with a non-unique prior. Journal of Mathematical Economics 18: 141–153CrossRefGoogle Scholar
  15. Hájek A. (2008) Dutch book arguments. In: Paul Anand, Prasanta P., Clemens P. (eds) The Oxford handbook of rational and social choice. Oxford University Press, OxfordGoogle Scholar
  16. Hansen L. P., Sargent T. J. (2001) Acknowledging misspecification in macroeconomic theory. Review of Economic Dynamics 4: 519–535CrossRefGoogle Scholar
  17. Hansen L. P., Sargent T. J. (2003) Robust control of forward-looking models. Journal of Monetary Economics 50: 581–604CrossRefGoogle Scholar
  18. Hansen L. P., Sargent T. J. (2006) Robustness. Princeton University Press, Princeton (forthcoming)Google Scholar
  19. Jeffrey R. (2004) Subjective probability: The real thing. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  20. Kahneman D., Tversky A. (1979) Prospect theory: An analysis of decision under risk. Econometrica 47: 263–291CrossRefGoogle Scholar
  21. Knight F. H. (1921) Risk, uncertainty, and profit. Houghton Mifflin, BostonGoogle Scholar
  22. Levi I. (1980) MIT Press, CambridgeGoogle Scholar
  23. Lindley D. (1965) Introduction to probability and statistics from a Bayesian viewpoint. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  24. Machina M. J., Schmeidler D. (1992) A more robust definition of subjective probability. Econometrica 60: 745–780CrossRefGoogle Scholar
  25. Machina M.J., Schmeidler D. (1995) Bayes without bernoulli: Simple conditions for probabilistically sophisticated choice. JET 67: 106–128Google Scholar
  26. Mailath G., Masahiro O.-F., Andrew P. (1993) On belief based refinements in signaling games. Journal of Economic Theory 60: 241–276CrossRefGoogle Scholar
  27. Mas-Collel A., Michael W., Jerry G. (1995) Microeconomic theory. Oxford Press, New YorkGoogle Scholar
  28. Mukerji S. (1998) Ambiguity aversion and the incompleteness of contractual form. American Economic Review 88: 1207–1232Google Scholar
  29. Ramsey F.P. (1931) Truth and probability. In: Braithwaite R.B. (eds) The foundation of mathematics and other logical essays. Brace and Co, New York: HarcourtGoogle Scholar
  30. Rostek M. (2010) Quantile maximization in decision theory. The Review of Economic Studies 77: 339–371CrossRefGoogle Scholar
  31. Savage, L. J. (1954). The foundations of statistics. New York: John Wiley and Sons. (Second addition in 1972, Dover).Google Scholar
  32. Schmeidler D. (1989) Subjective probability and expected utility without additivity. Econometrica 57: 571–587 (Working paper, 1982)CrossRefGoogle Scholar
  33. Shafer G. (1986) Savage revisited. Statistical Science 1: 463–486CrossRefGoogle Scholar
  34. Tversky A., Kahneman D. (1974) Judgment under uncertainty: Heuristics and biases. Science 185: 1124–1131CrossRefGoogle Scholar
  35. Zajonc R. B. (1980) Feeling and thinking: Preferences need no inferences. American Psychologist 35: 151–175CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  • Itzhak Gilboa
    • 1
    • 2
    Email author
  • Andrew Postlewaite
    • 5
  • David Schmeidler
    • 1
    • 3
    • 4
  1. 1.Tel-Aviv UniversityTel-AvivIsrael
  2. 2.HECParisFrance
  3. 3.The Interdisciplinary Center (IDC)HerzliyaIsrael
  4. 4.Ohio State UniversityColumbusUSA
  5. 5.University of PennsylvaniaPhiladelphiaUSA

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