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Utility Theory of General Lotteries

Author

Listed:
  • Danilov, V.

    (Central Economics and Mathematics Institute, Russian Academy of Sciences, Moscow, Russia)

Abstract

Generalizing the notions of roulette lotteries, horse lotteries, and quantum lotteries, we introduce maximally general notion of lottery. It uses the theory of ordered vector spaces. Under appropriate conditions on preference relation between lotteries (generalizing the conditions considered by von Neumann, Savage, Aumann and Anscombe) we give a formula for the utility of lotteries. Its ingredients are a utility function of prizes and a belief functional giving probability of events. Inthe second part of paper we discuss the issue about updating of beliefs under receiving additional information. We give a formula for the updated belief (which generates Bayes rule and von Neumann-Luders projection postulate), suppose that the ordered vector space is the real part of C*-algebra.

Suggested Citation

  • Danilov, V., 2016. "Utility Theory of General Lotteries," Journal of the New Economic Association, New Economic Association, vol. 32(4), pages 12-29.
    • Handle: RePEc:nea:journl:y:2016:i:32:p:12-29
    as

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    References listed on IDEAS

    as
    1. Segal, Uzi, 1990. "Two-Stage Lotteries without the Reduction Axiom," Econometrica, Econometric Society, vol. 58(2), pages 349-377, March.
    2. V. Danilov & A. Lambert-Mogiliansky, 2010. "Expected utility theory under non-classical uncertainty," Theory and Decision, Springer, vol. 68(1), pages 25-47, February.
    3. Jacob Gyntelberg & Frank Hansen, 2004. "Expected Utility Theory with “Small Worlds”," FRU Working Papers 2004/04, University of Copenhagen. Department of Economics. Finance Research Unit.
    4. V. I. Danilov & A. Lambert-Mogiliansky & V. Vergopoulos, 2018. "Dynamic consistency of expected utility under non-classical (quantum) uncertainty," Theory and Decision, Springer, vol. 84(4), pages 645-670, June.
    5. Paolo Ghirardato, 2002. "Revisiting Savage in a conditional world," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 20(1), pages 83-92.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    utility function; probability; measurement; ordered vector space; updating; C *-algebra;
    All these keywords.

    JEL classification:

    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • D84 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Expectations; Speculations

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