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A Subjective Spin on Roulette Wheels

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Author Info
Paolo Ghirardato
Fabio Maccheroni
Massimo Marinacci
Marciano Siniscalchi

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Abstract

We provide a simple behavioral definition of 'subjective mixture' of acts for a large class of (not necessarily expected-utility) preferences. Subjective mixtures enjoy the same algebraic properties as the 'objective mixtures' used to great advantage in the decision setting introduced by Anscombe and Aumann (1963). This makes it possible to formulate mixture-space axioms in a fully subjective setting. For illustration, we present simple subjective axiomatizations of some models of choice under uncertainty, including Bewley's model of choice with incomplete preferences (2002). Copyright The Econometric Society 2003.

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Article provided by Econometric Society in its journal Econometrica.

Volume (Year): 71 (2003)
Issue (Month): 6 (November)
Pages: 1897-1908
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Handle: RePEc:ecm:emetrp:v:71:y:2003:i:6:p:1897-1908

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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April. [Downloadable!] (restricted)
  2. Paolo Ghirardato & Massimo Marinacci, 2000. "Risk, Ambiguity and the Separation of Utility and Beliefs," Econometric Society World Congress 2000 Contributed Papers 1143, Econometric Society. [Downloadable!]
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  3. Nakamura, Yutaka, 1990. "Subjective expected utility with non-additive probabilities on finite state spaces," Journal of Economic Theory, Elsevier, vol. 51(2), pages 346-366, August. [Downloadable!] (restricted)
  4. Mark Machina, 2004. "Almost-objective uncertainty," Economic Theory, Springer, vol. 24(1), pages 1-54, 07. [Downloadable!] (restricted)
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  5. Gilboa, Itzhak, 1987. "Expected utility with purely subjective non-additive probabilities," Journal of Mathematical Economics, Elsevier, vol. 16(1), pages 65-88, February. [Downloadable!] (restricted)
  6. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-87, May. [Downloadable!] (restricted)
  7. Ghirardato, Paolo & Marinacci, Massimo, 2002. "Ambiguity Made Precise: A Comparative Foundation," Journal of Economic Theory, Elsevier, vol. 102(2), pages 251-289, February. [Downloadable!] (restricted)
  8. Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 323-343, December. [Downloadable!] (restricted)
  9. Casadesus-Masanell, Ramon & Klibanoff, Peter & Ozdenoren, Emre, 2000. "Maxmin Expected Utility over Savage Acts with a Set of Priors," Journal of Economic Theory, Elsevier, vol. 92(1), pages 35-65, May. [Downloadable!] (restricted)
  10. Casadesus-Masanell, Ramon & Klibanoff, Peter & Ozdenoren, Emre, 2000. "Maxmin expected utility through statewise combinations," Economics Letters, Elsevier, vol. 66(1), pages 49-54, January. [Downloadable!] (restricted)
  11. Truman F. Bewley, 1986. "Knightian Decision Theory: Part 1," Cowles Foundation Discussion Papers 807, Cowles Foundation, Yale University. [Downloadable!]
  12. Hong Chew Soo & Karni Edi, 1994. "Choquet Expected Utility with a Finite State Space: Commutativity and Act-Independence," Journal of Economic Theory, Elsevier, vol. 62(2), pages 469-479, April. [Downloadable!] (restricted)
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(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Ghirardato, Paolo & Katz, Jonathan N., 2000. "Indecision Theory: Explaining Selective Abstention in Multiple Elections," Working Papers 1106, California Institute of Technology, Division of the Humanities and Social Sciences. [Downloadable!]
  2. Thibault Gajdos & Jean-Marc Tallon & Jean-Christophe Vergnaud, 2002. "Decision Making with Imprecise Probabilistic Information," ICER Working Papers - Applied Mathematics Series 18-2003, ICER - International Centre for Economic Research, revised May 2003. [Downloadable!]
    Other versions:
  3. Antonio Lijoi & Igor Prünster & Stephen G. Walker, 2004. "Contributions to the understanding of Bayesian consistency," ICER Working Papers - Applied Mathematics Series 13-2004, ICER - International Centre for Economic Research. [Downloadable!]
  4. Ghirardato, Paolo & Maccheroni, Fabio & Marinacci, Massimo, 2002. "Ambiguity from the Differential Viewpoint," Working Papers 1130, California Institute of Technology, Division of the Humanities and Social Sciences. [Downloadable!]
    Other versions:
  5. Marciano Siniscalchi, 2003. "A Behavioral Characterization of Plausible Priors," Discussion Papers 1365, Northwestern University, Center for Mathematical Studies in Economics and Management Science. [Downloadable!]
    Other versions:
  6. Antonio Lijoi & Igor Prünster & Stephen G. Walker, 2004. "On consistency of nonparametric normal mixtures for Bayesian density estimation," ICER Working Papers - Applied Mathematics Series 23-2004, ICER - International Centre for Economic Research. [Downloadable!]
  7. Chateauneuf, Alain & Eichberger, Jürgen & Grant, Simon, 2003. "Choice under Uncertainty with the Best and Worst in Mind: Neo-additive Capacities," Sonderforschungsbereich 504 Publications 03-10, Sonderforschungsbereich 504, Universität Mannheim & Sonderforschungsbereich 504, University of Mannheim. [Downloadable!]
  8. Jerome Renault & Sergio Scarlatti & Marco Scarsini, 2003. "A folk theorem for minority games," ICER Working Papers - Applied Mathematics Series 10-2003, ICER - International Centre for Economic Research. [Downloadable!]
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  9. Antonio Lijoi & Igor Prünster & Stephen G. Walker, 2004. "On rates of convergence for posterior distributions in infinite–dimensional models," ICER Working Papers - Applied Mathematics Series 24-2004, ICER - International Centre for Economic Research. [Downloadable!]
  10. Fabio Maccheroni & William H. Ruckle, 2001. "BV as a dual space," ICER Working Papers - Applied Mathematics Series 29-2001, ICER - International Centre for Economic Research. [Downloadable!]
  11. Thibault Gajdos & Eric Maurin, 2002. "Unequal uncertainties and uncertain inequalities: an axiomatic approach," ICER Working Papers - Applied Mathematics Series 15-2003, ICER - International Centre for Economic Research, revised Mar 2003. [Downloadable!]
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  12. Grant, Simon & Chateauneuf, A. & Eichberger, J., 2002. "Choice under Uncertainty with the Best and Worst in Mind: Neo-additive Capacities," Working Papers 2002-10, Rice University, Department of Economics. [Downloadable!]
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  13. Erio Castagnoli & Fabio Maccheroni & Massimo Marinacci, 2002. "Insurance Premia Consistent with the Market," ICER Working Papers - Applied Mathematics Series 24-2002, ICER - International Centre for Economic Research. [Downloadable!]
    Other versions:
  14. Luca Rigotti & Chris Shannon, 2001. "Uncertainty and Risk in Financial Markets," Department of Economics, Working Paper Series 1000, Department of Economics, Institute for Business and Economic Research, UC Berkeley. [Downloadable!]
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  15. Massimo Marinacci & Paolo Ghirardato, 2001. "Risk, ambiguity, and the separation of utility and beliefs," ICER Working Papers - Applied Mathematics Series 21-2001, ICER - International Centre for Economic Research. [Downloadable!]
    Other versions:
  16. Alfred Müller & Marco Scarsini, 2003. "Archimedean Copulae and Positive Dependence," ICER Working Papers - Applied Mathematics Series 25-2003, ICER - International Centre for Economic Research. [Downloadable!]
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  17. Salvatore Modica & Marco Scarsini, 2003. "The convexity-cone approach to comparative risk and downside risk," ICER Working Papers - Applied Mathematics Series 01-2003, ICER - International Centre for Economic Research. [Downloadable!]
  18. Marciano Siniscalchi, 2001. "Bayesian Updating for General Maxmin Expected Utility Preferences," Discussion Papers 1366, Northwestern University, Center for Mathematical Studies in Economics and Management Science. [Downloadable!]
  19. Taizhong Hu & Alfred Müller & Marco Scarsini, 2002. "Some Counterexamples in Positive Dependence," ICER Working Papers - Applied Mathematics Series 28-2003, ICER - International Centre for Economic Research, revised Jul 2003. [Downloadable!]
  20. Enrico Diecidue & Fabio Maccheroni, 2002. "Coherence without Additivity," ICER Working Papers - Applied Mathematics Series 10-2002, ICER - International Centre for Economic Research. [Downloadable!]
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