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

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  • Alexander Zimper

    ()
    (Department of Economics, University of Pretoria)

Abstract

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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Bibliographic Info

Paper provided by University of Pretoria, Department of Economics in its series Working Papers with number 201221.

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Length: 22 pages
Date of creation: May 2012
Date of revision:
Handle: RePEc:pre:wpaper:201221

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Keywords: Non-additive measures; Learning; Decision analysis; Economics;

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  1. Eichberger, Jurgen & Grant, Simon & Kelsey, David, 2007. "Updating Choquet beliefs," Journal of Mathematical Economics, Elsevier, vol. 43(7-8), pages 888-899, September.
  2. Marciano Siniscalchi, 2006. "Dynamic Choice Under Ambiguity," Discussion Papers 1430, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  3. Michael D. Hurd, 2009. "Subjective Probabilities in Household Surveys," Annual Review of Economics, Annual Reviews, vol. 1(1), pages 543-564, 05.
  4. Itzhak Gilboa & David Schmeidler, 1991. "Updating Ambiguous Beliefs," Discussion Papers 924, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  5. Cesaltina Pacheco Pires, 2002. "A Rule For Updating Ambiguous Beliefs," Theory and Decision, Springer, vol. 53(2), pages 137-152, September.
  6. Kahneman, Daniel & Tversky, Amos, 1979. "Prospect Theory: An Analysis of Decision under Risk," Econometrica, Econometric Society, vol. 47(2), pages 263-91, March.
  7. Sarin, Rakesh K & Wakker, Peter, 1992. "A Simple Axiomatization of Nonadditive Expected Utility," Econometrica, Econometric Society, vol. 60(6), pages 1255-72, November.
  8. 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).
  9. Wakker, Peter & Tversky, Amos, 1993. " An Axiomatization of Cumulative Prospect Theory," Journal of Risk and Uncertainty, Springer, vol. 7(2), pages 147-75, October.
  10. Chateauneuf, Alain & Eichberger, J├╝rgen & Grant, Simon, 2003. "Choice under Uncertainty with the Best and Worst in Mind: Neo-additive Capacities," Sonderforschungsbereich 504 Publications 03-10, Sonderforschungsbereich 504, Universit├Ąt Mannheim;Sonderforschungsbereich 504, University of Mannheim.
  11. Colin F. Camerer, 2007. "Neuroeconomics: Using Neuroscience to Make Economic Predictions," Economic Journal, Royal Economic Society, vol. 117(519), pages C26-C42, 03.
  12. David Schmeidler, 1989. "Subjective Probability and Expected Utility without Additivity," Levine's Working Paper Archive 7662, David K. Levine.
  13. 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.
  14. Gilboa, Itzhak, 1987. "Expected utility with purely subjective non-additive probabilities," Journal of Mathematical Economics, Elsevier, vol. 16(1), pages 65-88, February.
  15. Manski, Charles F. & Molinari, Francesca, 2010. "Rounding Probabilistic Expectations in Surveys," Journal of Business & Economic Statistics, American Statistical Association, vol. 28(2), pages 219-231.
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