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Incomplete preferences on conditional random quantities: Representability by conditional previsions

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  • Vantaggi, Barbara
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    Abstract

    We study "partial" preference relations, defined on an arbitrary set of conditional bounded random quantities: we provide a condition of rationality (interpretable in terms of betting scheme) characterizing preference relations representable by a conditional expectation. Moreover, we study the problem of extending a rational preference relation.

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    Bibliographic Info

    Article provided by Elsevier in its journal Mathematical Social Sciences.

    Volume (Year): 60 (2010)
    Issue (Month): 2 (September)
    Pages: 104-112

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    Handle: RePEc:eee:matsoc:v:60:y:2010:i:2:p:104-112

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    Web page: http://www.elsevier.com/locate/inca/505565

    Related research

    Keywords: Preference relations Completeness Fair price Rationality Conditional expectation Book-making principle;

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    1. Rumbos, Beatriz, 2001. "Representing subjective orderings of random variables: an extension," Journal of Mathematical Economics, Elsevier, vol. 36(1), pages 31-43, September.
    2. Bruno Girotto & Silvano Holzer, 2003. "Representing complete and incomplete subjective linear preferences on random numbers," Decisions in Economics and Finance, Springer, vol. 26(2), pages 129-144, November.
    3. Paolo Ghirardato, 2002. "Revisiting Savage in a conditional world," Economic Theory, Springer, vol. 20(1), pages 83-92.
    4. Andrea Capotorti & Giulianella Coletti & Barbara Vantaggi, 2008. "Preferences Representable by a Lower Expectation: Some Characterizations," Theory and Decision, Springer, vol. 64(2), pages 119-146, March.
    5. Vind, Karl, 2000. "von Neumann Morgenstern preferences," Journal of Mathematical Economics, Elsevier, vol. 33(1), pages 109-122, February.
    6. Dubra, Juan & Maccheroni, Fabio & Ok, Efe A., 2004. "Expected utility theory without the completeness axiom," Journal of Economic Theory, Elsevier, vol. 115(1), pages 118-133, March.
    7. Chateauneuf, Alain, 1985. "On the existence of a probability measure compatible with a total preorder on a Boolean algebra," Journal of Mathematical Economics, Elsevier, vol. 14(1), pages 43-52, February.
    8. Kelsey, David & Yalcin, Erkan, 2007. "The arbitrage pricing theorem with incomplete preferences," Mathematical Social Sciences, Elsevier, vol. 54(1), pages 90-105, July.
    9. Giulianella Coletti & Barbara Vantaggi, 2006. "Representability of Ordinal Relations on a Set of Conditional Events," Theory and Decision, Springer, vol. 60(2), pages 137-174, 05.
    10. Diecidue, Enrico & Wakker, Peter P., 2002. "Dutch books: avoiding strategic and dynamic complications, and a comonotonic extension," Mathematical Social Sciences, Elsevier, vol. 43(2), pages 135-149, March.
    11. Klaus Nehring, 2000. "A Theory of Rational Choice under Ignorance," Theory and Decision, Springer, vol. 48(3), pages 205-240, May.
    12. Arlegi, Ricardo & Nieto, Jorge, 2001. "Incomplete preferences and the preference for flexibility," Mathematical Social Sciences, Elsevier, vol. 41(2), pages 151-165, March.
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