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Subjective Probability without Monotonicity: Or How Machina's Mom May Also Be Probabilistically Sophisticated

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  • Grant, Simon

Abstract

If an agent's preferences over subjectively uncertain acts are consistent with him having a subjective probability distribution over the states of nature, then those preferences can induce consistent preferences over 'objectively' risky lotteries. Such 'probabilistically sophisticated' behavior allows us to treat decision making under uncertainty as though it is under risk. This paper first characterizes exactly what probabilistic sophistication entails for an agent's beliefs about the likelihood of states of nature. Secondly, it presents characterizations of probabilistically sophisticated individuals whose induced lottery preferences obey neither the independence axiom nor a monotonicity property that is shown to share some of the nature of independence. Copyright 1995 by The Econometric Society.

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Bibliographic Info

Article provided by Econometric Society in its journal Econometrica.

Volume (Year): 63 (1995)
Issue (Month): 1 (January)
Pages: 159-89

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Handle: RePEc:ecm:emetrp:v:63:y:1995:i:1:p:159-89

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Cited by:
  1. : Constantinos Antoniou & : Glenn W. Harrison & : Morten I. Lau & : Daniel Read, 2013. "Subjective Bayesian Beliefs," Working Papers wpn13-02, Warwick Business School, Finance Group.
  2. Simon Grant & Atsushi Kajii & Ben Polak, 1999. "Decomposable Choice Under Uncertainty," Cowles Foundation Discussion Papers 1207, Cowles Foundation for Research in Economics, Yale University.
  3. FLEURBAEY, Marc & ZUBER, Stéphane, 2011. "Inequality aversion and separability in social risk evaluation," CORE Discussion Papers 2011023, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  4. Massimo Marinacci, 2002. "Probabilistic Sophistication and Multiple Priors," Econometrica, Econometric Society, vol. 70(2), pages 755-764, March.
  5. Chew, Soo Hong & Sagi, Jacob S., 2012. "An inequality measure for stochastic allocations," Journal of Economic Theory, Elsevier, vol. 147(4), pages 1517-1544.
  6. Klaus Nehring, 2006. "Decision-Making in the Context of Imprecise Probabilistic Beliefs," Economics Working Papers 0034, Institute for Advanced Study, School of Social Science.
  7. Simon Grant & Atsushi Kajii, 2005. "Probabilistically Sophisticated Multiple Priors," KIER Working Papers 608, Kyoto University, Institute of Economic Research.
  8. J. Michelle Brock & Andreas Lange & Erkut Y. Ozbay, 2013. "Dictating the Risk: Experimental Evidence on Giving in Risky Environments," American Economic Review, American Economic Association, vol. 103(1), pages 415-37, February.
  9. Edi Karni, 2005. "A New Approach to Modeling Decision-Making under Uncertainty and Defining Subjective Probabilities," Economics Working Paper Archive 519, The Johns Hopkins University,Department of Economics.
  10. Marc Fleurbaey, 2009. "Assessing risky social situations," LSE Research Online Documents on Economics 27006, London School of Economics and Political Science, LSE Library.
  11. Cerreia-Vioglio, Simone & Maccheroni, Fabio & Marinacci, Massimo & Montrucchio, Luigi, 2012. "Probabilistic sophistication, second order stochastic dominance and uncertainty aversion," Journal of Mathematical Economics, Elsevier, vol. 48(5), pages 271-283.
  12. Marc Fleurbaey & Stéphane Zuber, 2013. "Inequality aversion and separability in social risk evaluation," Economic Theory, Springer, vol. 54(3), pages 675-692, November.
  13. Skiadas, Costis, 1997. "Subjective Probability under Additive Aggregation of Conditional Preferences," Journal of Economic Theory, Elsevier, vol. 76(2), pages 242-271, October.

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