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Probabilistic Sophistication, Second Order Stochastic Dominance, and Uncertainty Aversion

  • Simone Cerreia-Vioglio
  • Fabio Maccheroni
  • Massimo Marinacci
  • Luigi Montrucchio

We study the interplay of probabilistic sophistication, second order stochastic dominance, and uncertainty aversion, three fundamental notions in choice under uncertainty. In particular, our main result, Theorem 2, characterizes uncertainty averse preferences that satisfy second order stochastic dominance, as well as uncertainty averse preferences that are probabilistically sophisticated.

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Paper provided by Collegio Carlo Alberto in its series Carlo Alberto Notebooks with number 174.

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Length: 22 pages
Date of creation: 2010
Date of revision:
Handle: RePEc:cca:wpaper:174
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  1. Alain Chateauneuf & José Heleno Faro, 2009. "Ambiguity through confidence functions," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00634651, HAL.
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  4. Mark J. Machina & David Schmeidler, 1990. "A More Robust Definition of Subjective Probability," Discussion Paper Serie A 306, University of Bonn, Germany.
  5. Mark J. Machina & David Schmeidler, 1994. "Bayes Without Bernoulli: Simple Conditions for Probabilistically Sophisticated Choice," Discussion Papers 1088, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
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  9. David Schmeidler, 1989. "Subjective Probability and Expected Utility without Additivity," Levine's Working Paper Archive 7662, David K. Levine.
  10. Simone Cerreia-Vioglio & Fabio Maccheroni & Massimo Marinacci & Luigi Montrucchio, 2008. "Complete Monotone Quasiconcave Duality," Carlo Alberto Notebooks 80, Collegio Carlo Alberto.
  11. Grant, Simon, 1995. "Subjective Probability without Monotonicity: Or How Machina's Mom May Also Be Probabilistically Sophisticated," Econometrica, Econometric Society, vol. 63(1), pages 159-89, January.
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  14. Simone Cerreia-Vioglio & Fabio Maccheroni & Massimo Marinacci & Luigi Montrucchio, 2008. "Uncertainty Averse Preferences," Carlo Alberto Notebooks 77, Collegio Carlo Alberto.
  15. Kopylov, Igor, 2007. "Subjective probabilities on "small" domains," Journal of Economic Theory, Elsevier, vol. 133(1), pages 236-265, March.
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  17. Tomasz Strzalecki, . "Probabilistic Sophistication and Variational Preferences," Working Paper 8337, Harvard University OpenScholar.
  18. Wakker, Peter, 1993. "Clarification of some mathematical misunderstandings about Savage's foundations of statistics, 1954," Mathematical Social Sciences, Elsevier, vol. 25(2), pages 199-202, February.
  19. Fabio Maccheroni & Massimo Marinacci & Aldo Rustichini, 2006. "Ambiguity Aversion, Robustness, and the Variational Representation of Preferences," Econometrica, Econometric Society, vol. 74(6), pages 1447-1498, November.
  20. Aharon Ben-Tal & Marc Teboulle, 1986. "Expected Utility, Penalty Functions, and Duality in Stochastic Nonlinear Programming," Management Science, INFORMS, vol. 32(11), pages 1445-1466, November.
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  22. Simone Cerreia-Vioglio & Paolo Ghirardato & Fabio Maccheroni & Massimo Marinacci & Marciano Siniscalchi, 2011. "Rational preferences under ambiguity," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 48(2), pages 341-375, October.
  23. William Neilson, 2010. "A simplified axiomatic approach to ambiguity aversion," Journal of Risk and Uncertainty, Springer, vol. 41(2), pages 113-124, October.
  24. Sujoy Mukerji & Peter Klibanoff, 2002. "A Smooth Model of Decision,Making Under Ambiguity," Economics Series Working Papers 113, University of Oxford, Department of Economics.
  25. Chew, Soo Hong & Sagi, Jacob S., 2008. "Small worlds: Modeling attitudes toward sources of uncertainty," Journal of Economic Theory, Elsevier, vol. 139(1), pages 1-24, March.
  26. Massimo Marinacci, 2002. "Probabilistic Sophistication and Multiple Priors," Econometrica, Econometric Society, vol. 70(2), pages 755-764, March.
  27. Ghirardato, Paolo & Marinacci, Massimo, 2002. "Ambiguity Made Precise: A Comparative Foundation," Journal of Economic Theory, Elsevier, vol. 102(2), pages 251-289, February.
  28. Ghirardato, Paolo & Maccheroni, Fabio & Marinacci, Massimo, 2004. "Differentiating ambiguity and ambiguity attitude," Journal of Economic Theory, Elsevier, vol. 118(2), pages 133-173, October.
  29. Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 323-343, December.
  30. Grant, Simon & Polak, Ben, 2006. "Bayesian beliefs with stochastic monotonicity: An extension of Machina and Schmeidler," Journal of Economic Theory, Elsevier, vol. 130(1), pages 264-282, September.
  31. Chew Soo Hong & Jacob S. Sagi, 2006. "Event Exchangeability: Probabilistic Sophistication Without Continuity or Monotonicity," Econometrica, Econometric Society, vol. 74(3), pages 771-786, 05.
  32. Simon Grant & Ben Polak & Tomasz Strzalecki, 2010. "Second-Order Expected Utility," Working Paper 8340, Harvard University OpenScholar.
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