The Talmud On Transitivity
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).
|Date of creation:||23 Jun 2008|
|Date of revision:||04 Sep 2009|
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- 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 434-434.
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- 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.
- John C. Harsanyi, 1955. "Cardinal Welfare, Individualistic Ethics, and Interpersonal Comparisons of Utility," Journal of Political Economy, University of Chicago Press, vol. 63, pages 309-309.
- 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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