Rationalizability of choice functions on general domains without full transitivity
The rationalizability of a choice function by means of a transitive relation has been analyzed thoroughly in the literature. However, not much seems to be known when transitivity is weakened to quasi-transitivity or acyclicity. We describe the logical relationships between the different notions of rationalizability involving, for example, the transitivity, quasi-transitivity, or acyclicity of the rationalizing relation. Furthermore, we discuss sufficient conditions and necessary conditions for rational choice on arbitrary domains. Transitive, quasi-transitive, and acyclical rationalizability are fully characterized for domains that contain all singletons and all two-element subsets of the universal set.
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Volume (Year): 27 (2006)
Issue (Month): 3 (December)
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References listed on IDEAS
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- Suzumura, Kotaro, 1977. "Houthakker's axiom in the theory of rational choice," Journal of Economic Theory, Elsevier, vol. 14(2), pages 284-290, April.
- Herzberger, Hans G, 1973. "Ordinal Preference and Rational Choice," Econometrica, Econometric Society, vol. 41(2), pages 187-237, March.
- Amartya Sen, 1996.
"Maximization and the Act of Choice,"
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1766, Harvard - Institute of Economic Research.
- Kotaro Suzumura, 1976. "Rational Choice and Revealed Preference," Review of Economic Studies, Oxford University Press, vol. 43(1), pages 149-158.
- Amartya K. Sen, 1971. "Choice Functions and Revealed Preference," Review of Economic Studies, Oxford University Press, vol. 38(3), pages 307-317.
- Bossert, W., 1995. "Choices, Consequences, and Rationality," Working Papers 9501, University of Waterloo, Department of Economics.
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