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Bayesian Updating for General Maxmin Expected Utility Preferences

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  • Marciano Siniscalchi

Abstract

A characterization of “generalized Bayesian updating” in a maxmin expected utility setting is provided. The key axioms are consequentialism and constant-act dynamic consistency. The latter requires that, if an arbitrary act f is preferred (inferior) to a constant act y conditional upon E, and if f dominates (is dominated by) y pointwise on the complementary event Ec, then f is unconditionally preferred (inferior) to y. The result provides a basis for a model of dynamic choice that accommodates arbitrary unconditional maxmin EU preferences, and allows for deviations from full dynamic consistency related to ambiguity. Standard Expected Utility (EU) preferences are separable across events. In a static setting, the notion of separability is formalized by Savage’s Postulate P2 (the “Sure-Thing Principle”). In a dynamic framework, separability corresponds to dynamic consistency: if the decision maker would prefer some course of action to another if she learned that some event has obtained, and also if she learned that the same event has not obtained, then she should prefer it even prior to learning whether or not the event in question has obtained. As is well-known, P2 and dynamic consistency are closely related (see e.g. Ghirardato, 2001). In a static setting, Ellsberg (1961) demonstrates that separability may fail if the decision maker perceives some ambiguity in the relative likelihood of events. Thus, in a dynamic setting, it is at least plausible to expect some tension between ambiguity and dynamic consistency. Recent experimental evidence (Cohen et al., 2000) based on a dynamic version of the single-urn Ellsberg example seems to indicate that ambiguity may indeed lead to violations of dynamic consistency.

Suggested Citation

  • 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.
  • Handle: RePEc:nwu:cmsems:1366
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    References listed on IDEAS

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    6. Paolo Ghirardato & Fabio Maccheroni & Massimo Marinacci & Marciano Siniscalchi, 2003. "A Subjective Spin on Roulette Wheels," Econometrica, Econometric Society, vol. 71(6), pages 1897-1908, November.
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    Cited by:

    1. Siniscalchi, Marciano, 2011. "Dynamic choice under ambiguity," Theoretical Economics, Econometric Society, vol. 6(3), September.
    2. Chambers, Robert G. & Melkonyan, Tigran, 2009. "Smoothing preference kinks with information," Mathematical Social Sciences, Elsevier, vol. 58(2), pages 173-189, September.
    3. A. Ludwig & A. Zimper, 2013. "A parsimonious model of subjective life expectancy," Theory and Decision, Springer, vol. 75(4), pages 519-541, October.
    4. Zimper, Alexander, 2009. "Half empty, half full and why we can agree to disagree forever," Journal of Economic Behavior & Organization, Elsevier, vol. 71(2), pages 283-299, August.
    5. Alexander Zimper & Alexander Ludwig, 2007. "Attitude polarization," MEA discussion paper series 07155, Munich Center for the Economics of Aging (MEA) at the Max Planck Institute for Social Law and Social Policy.
    6. Paolo Ghirardato & Fabio Maccheroni & Massimo Marinacci, 2002. "Ambiguity from the Differential Viewpoint," ICER Working Papers - Applied Mathematics Series 17-2002, ICER - International Centre for Economic Research.
    7. Siniscalchi, Marciano, 2006. "A behavioral characterization of plausible priors," Journal of Economic Theory, Elsevier, vol. 128(1), pages 91-135, May.
    8. Faro, José Heleno & Lefort, Jean Philippe, 2013. "Dynamic Objective and Subjective Rationality," Insper Working Papers wpe_312, Insper Working Paper, Insper Instituto de Ensino e Pesquisa.

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