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A General Update Rule for Convex Capacities

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  • Mayumi Horie

    ()
    (Institute of Economic Research, Kyoto University)

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    Abstract

    A characterization of a general update rule for convex capacities, the G-updating rule, is investigated. We introduce a consistency property which bridges between unconditional and conditional preferences, and deduce an update rule for unconditional capacities. The axiomatic basis for the G-updating rule is established through consistent counterfactual acts, which take the form of trinary acts expressed in terms of G, an ordered tripartition of global states.

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    File URL: http://www.kier.kyoto-u.ac.jp/DP/DP644.pdf
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    Bibliographic Info

    Paper provided by Kyoto University, Institute of Economic Research in its series KIER Working Papers with number 644.

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    Length: 14pages
    Date of creation: Nov 2007
    Date of revision:
    Handle: RePEc:kyo:wpaper:644

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    Keywords: ambiguous belief; Bayes' rule; update rule; convex capacity; Choquet ex- pected utility; conditional preference;

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    1. repec:ebl:ecbull:v:4:y:2006:i:19:p:1-6 is not listed on IDEAS
    2. Jurgen Eichberger & Simon Grant & David Kelsey, 2006. "Updating Choquet Beliefs," Discussion Papers 0607, Exeter University, Department of Economics.
    3. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-87, May.
    4. Paolo Ghirardato & Massimo Marinacci, 2000. "Risk, Ambiguity and the Separation of Utility and Beliefs," Econometric Society World Congress 2000 Contributed Papers 1143, Econometric Society.
    5. Gilboa Itzhak & Schmeidler David, 1993. "Updating Ambiguous Beliefs," Journal of Economic Theory, Elsevier, vol. 59(1), pages 33-49, February.
    6. 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.
    7. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    8. Tapking, Jens, 2004. "Axioms for preferences revealing subjective uncertainty and uncertainty aversion," Journal of Mathematical Economics, Elsevier, vol. 40(7), pages 771-797, November.
    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.
    10. Ramon Casadesus-Masanell & Peter Klibanoff & Emre Ozdenoren, 1998. "Maximum Expected Utility over Savage Acts with a Set of Priors," Discussion Papers 1218, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    11. Daniel Ellsberg, 2000. "Risk, Ambiguity and the Savage Axioms," Levine's Working Paper Archive 7605, David K. Levine.
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