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The Talmud On Transitivity

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  • 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).

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Bibliographic Info

Paper provided by Boston College Department of Economics in its series Boston College Working Papers in Economics with number 687.

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Length: 24 pages
Date of creation: 23 Jun 2008
Date of revision: 04 Sep 2009
Handle: RePEc:boc:bocoec:687

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Keywords: transitivity; Talmud;

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  1. Gil Kalai & Ariel Rubinstein & Ran Spiegler, 2001. "Rationalizing Choice Functions by Multiple Rationales," Discussion Paper Series dp278, The Center for the Study of Rationality, Hebrew University, Jerusalem.
  2. Sugden, Robert, 1985. "Why Be Consistent? A Critical Analysis of Consistency Requirements in Choice Theory," Economica, London School of Economics and Political Science, vol. 52(206), pages 167-83, May.
  3. 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, pages 434.
  4. John C. Harsanyi, 1955. "Cardinal Welfare, Individualistic Ethics, and Interpersonal Comparisons of Utility," Journal of Political Economy, University of Chicago Press, vol. 63, pages 309.
  5. Aumann, Robert J. & Maschler, Michael, 1985. "Game theoretic analysis of a bankruptcy problem from the Talmud," Journal of Economic Theory, Elsevier, vol. 36(2), pages 195-213, August.
  6. Sugden Robert, 1993. "An Axiomatic Foundation for Regret Theory," Journal of Economic Theory, Elsevier, vol. 60(1), pages 159-180, June.
  7. 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.
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