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Large Compound Lotteries

Author

Listed:
  • Zvi Safra

    (Warwick Business School)

  • Uzi Segal

    (Boston College)

Abstract

Extending preferences over simple lotteries to compound (two-stage) lotteries can be done using two different methods: (1) using the Re- duction of compound lotteries axiom, under which probabilities of the two stages are multiplied; (2) using the compound independence ax- iom, under which each second-stage lottery is replaced by its certainty equivalent. Except for expected utility preferences, the rankings in- duced by the two methods are always in disagreement and deciding on which method to use is not straightforward. Moreover, sometimes each of the two methods may seem to violate some kind of first order stochastic dominance. In this paper we demonstrate that, under some conditions, the disagreement disappears in the limit and that for (al- most) any pair of compound lotteries, the two methods agree if the lotteries are replicated sufficiently many times.

Suggested Citation

  • Zvi Safra & Uzi Segal, 2021. "Large Compound Lotteries," Boston College Working Papers in Economics 1057, Boston College Department of Economics, revised 01 Aug 2023.
    • Handle: RePEc:boc:bocoec:1057
    as

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    References listed on IDEAS

    as
    1. McClennen,Edward F., 1990. "Rationality and Dynamic Choice," Cambridge Books, Cambridge University Press, number 9780521360470, January.
    2. Segal, Uzi, 1990. "Two-Stage Lotteries without the Reduction Axiom," Econometrica, Econometric Society, vol. 58(2), pages 349-377, March.
    3. Gul, Faruk, 1991. "A Theory of Disappointment Aversion," Econometrica, Econometric Society, vol. 59(3), pages 667-686, May.
    4. Chew, Soo Hong, 1983. "A Generalization of the Quasilinear Mean with Applications to the Measurement of Income Inequality and Decision Theory Resolving the Allais Paradox," Econometrica, Econometric Society, vol. 51(4), pages 1065-1092, July.
    5. Ben Gillen & Erik Snowberg & Leeat Yariv, 2019. "Experimenting with Measurement Error: Techniques with Applications to the Caltech Cohort Study," Journal of Political Economy, University of Chicago Press, vol. 127(4), pages 1826-1863.
    6. Chateauneuf, Alain & Cohen, Michele, 1994. "Risk Seeking with Diminishing Marginal Utility in a Non-expected Utility Model," Journal of Risk and Uncertainty, Springer, vol. 9(1), pages 77-91, July.
    7. Daniel Kahneman & Amos Tversky, 2013. "Prospect Theory: An Analysis of Decision Under Risk," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 6, pages 99-127, World Scientific Publishing Co. Pte. Ltd..
    8. Tversky, Amos & Kahneman, Daniel, 1992. "Advances in Prospect Theory: Cumulative Representation of Uncertainty," Journal of Risk and Uncertainty, Springer, vol. 5(4), pages 297-323, October.
    9. Safra, Zvi & Segal, Uzi, 2022. "A lot of ambiguity," Journal of Economic Theory, Elsevier, vol. 200(C).
    10. Yoram Halevy, 2007. "Ellsberg Revisited: An Experimental Study," Econometrica, Econometric Society, vol. 75(2), pages 503-536, March.
    11. Hong, Chew Soo & Karni, Edi & Safra, Zvi, 1987. "Risk aversion in the theory of expected utility with rank dependent probabilities," Journal of Economic Theory, Elsevier, vol. 42(2), pages 370-381, August.
    12. Machina, Mark J, 1989. "Dynamic Consistency and Non-expected Utility Models of Choice under Uncertainty," Journal of Economic Literature, American Economic Association, vol. 27(4), pages 1622-1668, December.
    13. Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 323-343, December.
    14. Kreps, David M & Porteus, Evan L, 1978. "Temporal Resolution of Uncertainty and Dynamic Choice Theory," Econometrica, Econometric Society, vol. 46(1), pages 185-200, January.
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    More about this item

    Keywords

    Reduction of compound lotteries axiom; compound independence axiom; duplicated lotteries;
    All these keywords.

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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