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The Talmud On Transitivity

Author

Listed:
  • Shlomo Naeh

    (Hebrew University)

  • Uzi Segal

    (Boston College)

Abstract

Transitivity is a fundamental axiom in Economics that appears in consumer theory, decision under uncertainty, and social choice theory. While the appeal of transitivity is obvious, observed choices sometimes contradict it. This paper shows that treatments of violations of transitivity al- ready appear in the rabbinic literature, starting with the Mishnah and the Talmud (1st–5th c CE). This literature offers several solutions that are similar to those used in the modern economic literature, as well as some other solutions that may be adopted in modern situations. We analyze several examples. One where nontransitive relations are acceptable; one where a violation of transitivity leads to problems with extended choice functions; and a third where a nontransitive cycle is deliberately created (to enhance justice).

Suggested Citation

  • Shlomo Naeh & Uzi Segal, 2008. "The Talmud On Transitivity," Boston College Working Papers in Economics 687, Boston College Department of Economics, revised 04 Sep 2009.
    • Handle: RePEc:boc:bocoec:687
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    References listed on IDEAS

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    1. Gil Kalai & Ariel Rubinstein & Ran Spiegler, 2002. "Rationalizing Choice Functions By Multiple Rationales," Econometrica, Econometric Society, vol. 70(6), pages 2481-2488, November.
    2. Robert J. Aumann, 2025. "Game-Theoretic Analysis of a Bankruptcy Problem from the Talmud," World Scientific Book Chapters, in: SELECTED CONTRIBUTIONS TO GAME THEORY, chapter 9, pages 219-242, World Scientific Publishing Co. Pte. Ltd..
    3. Sugden Robert, 1993. "An Axiomatic Foundation for Regret Theory," Journal of Economic Theory, Elsevier, vol. 60(1), pages 159-180, June.
    4. John C. Harsanyi, 1953. "Cardinal Utility in Welfare Economics and in the Theory of Risk-taking," Journal of Political Economy, University of Chicago Press, vol. 61(5), pages 434-434.
    5. John C. Harsanyi, 1955. "Cardinal Welfare, Individualistic Ethics, and Interpersonal Comparisons of Utility," Journal of Political Economy, University of Chicago Press, vol. 63(4), pages 309-309.
    6. Loomes, Graham & Sugden, Robert, 1987. "Some implications of a more general form of regret theory," Journal of Economic Theory, Elsevier, vol. 41(2), pages 270-287, April.
    7. Fishburn, Peter C & LaValle, Irving H, 1988. "Context-Dependent Choice with Nonlinear and Nontransitive Preferences," Econometrica, Econometric Society, vol. 56(5), pages 1221-1239, September.
    8. repec:bla:econom:v:52:y:1985:i:206:p:167-83 is not listed on IDEAS
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    Cited by:

    1. Peter Baumann, 2022. "Rational intransitive preferences," Politics, Philosophy & Economics, , vol. 21(1), pages 3-28, February.

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    Keywords

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    JEL classification:

    • B21 - Schools of Economic Thought and Methodology - - History of Economic Thought since 1925 - - - Microeconomics
    • K40 - Law and Economics - - Legal Procedure, the Legal System, and Illegal Behavior - - - General

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