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The emergence of "fifty-fifty" probability judgements in a conditional Savage world

  • Alexander Zimper

This paper models the empirical phenomenon of persistent “…fifty-…fifty ”probability judgements within a dynamic non-additive Savage framework. To this purpose I construct a model of Bayesian learning such that an agent’s probability judgement is characterized as the solution to a Choquet expected utility maximization problem with respect to a conditional neo-additive capacity. Only for the non-generic case in which this capacity degenerates to an additive probability measure, the agent’s probability judgement coincides with the familiar estimate of a Bayesian statistician who minimizes a quadratic (squared error) loss function with respect to an additive posterior distribution. In contrast, for the generic case in which the capacity is non-additive, the agent’s probability judgements converge through Bayesian learning to the unique fuzzy probability measure that assigns a 0:5 probability to any uncertain event.

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File URL: http://www.econrsa.org/node/314
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Paper provided by Economic Research Southern Africa in its series Working Papers with number 291.

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Length: 23 pages
Date of creation: 2012
Date of revision:
Handle: RePEc:rza:wpaper:291
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  1. Cesaltina Pacheco Pires, 2002. "A Rule For Updating Ambiguous Beliefs," Theory and Decision, Springer, vol. 53(2), pages 137-152, September.
  2. Cohen, M. & Gilboa, I. & Jaffray, J.Y. & Schmeidler, D., 2000. "An experimental study of updating ambiguous beliefs," Risk, Decision and Policy, Cambridge University Press, vol. 5(02), pages 123-133, June.
  3. Gilboa Itzhak & Schmeidler David, 1993. "Updating Ambiguous Beliefs," Journal of Economic Theory, Elsevier, vol. 59(1), pages 33-49, February.
  4. Siniscalchi, Marciano, 2011. "Dynamic choice under ambiguity," Theoretical Economics, Econometric Society, vol. 6(3), September.
  5. Itzhak Gilboa, 1987. "Expected Utility with Purely Subjective Non-Additive Probabilities," Post-Print hal-00756291, HAL.
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  8. Amos Tversky & Daniel Kahneman, 1979. "Prospect Theory: An Analysis of Decision under Risk," Levine's Working Paper Archive 7656, David K. Levine.
  9. Jurgen Eichberger & Simon Grant & David Kelsey, 2006. "Updating Choquet Beliefs," Discussion Papers 0607, Exeter University, Department of Economics.
  10. Michael D. Hurd, 2009. "Subjective Probabilities in Household Surveys," Annual Review of Economics, Annual Reviews, vol. 1(1), pages 543-564, 05.
  11. Colin F. Camerer, 2007. "Neuroeconomics: Using Neuroscience to Make Economic Predictions," Economic Journal, Royal Economic Society, vol. 117(519), pages C26-C42, 03.
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  13. Kleinjans, Kristin J. & van Soest, Arthur, 2010. "Nonresponse and Focal Point Answers to Subjective Probability Questions," IZA Discussion Papers 5272, Institute for the Study of Labor (IZA).
  14. Sarin, Rakesh K & Wakker, Peter, 1992. "A Simple Axiomatization of Nonadditive Expected Utility," Econometrica, Econometric Society, vol. 60(6), pages 1255-72, November.
  15. Marcello Basili & Alain Chateauneuf, 2011. "Extreme events and entropy: A multiple quantile utility model," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00685405, HAL.
  16. Wakker, Peter & Tversky, Amos, 1993. "An Axiomatization of Cumulative Prospect Theory," Journal of Risk and Uncertainty, Springer, vol. 7(2), pages 147-75, October.
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