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Rationalizability of Choice Functions on General Domains Without Full Transitivity

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  • Bossert, Walter
  • Sprumont, Yves
  • Suzumura, Kotaro

Abstract

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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File URL: http://hermes-ir.lib.hit-u.ac.jp/rs/bitstream/10086/14474/1/pie_dp28.pdf
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Bibliographic Info

Paper provided by Center for Intergenerational Studies, Institute of Economic Research, Hitotsubashi University in its series Discussion Paper with number 28.

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Length: 29 p.
Date of creation: May 2001
Date of revision:
Handle: RePEc:hit:piedp1:28

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Keywords: Rational Choice; Quasi-Transitivity; Acyclicity; Base Domains;

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References

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  1. Amartya Sen, 1996. "Maximization and the Act of Choice," Harvard Institute of Economic Research Working Papers 1766, Harvard - Institute of Economic Research.
  2. Sen, Amartya K, 1971. "Choice Functions and Revealed Preference," Review of Economic Studies, Wiley Blackwell, vol. 38(115), pages 307-17, July.
  3. Suzumura, Kotaro, 1977. "Houthakker's axiom in the theory of rational choice," Journal of Economic Theory, Elsevier, vol. 14(2), pages 284-290, April.
  4. Herzberger, Hans G, 1973. "Ordinal Preference and Rational Choice," Econometrica, Econometric Society, vol. 41(2), pages 187-237, March.
  5. Suzumura, Kotaro, 1976. "Rational Choice and Revealed Preference," Review of Economic Studies, Wiley Blackwell, vol. 43(1), pages 149-58, February.
  6. Bossert, W., 1995. "Choices, Consequences, and Rationality," Working Papers 9501, University of Waterloo, Department of Economics.
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Cited by:
  1. BOSSERT, Walter & SUZUMURA, Kotaro, 2005. "Rational Choice on Arbitrary Domains: A Comprehensive Treatment," Cahiers de recherche 2005-13, Universite de Montreal, Departement de sciences economiques.
  2. BOSSERT, Walter & SPRUMONT, Yves & SUZUMURA, Kotaro, 2002. "Consistent Rationalizability," Cahiers de recherche 2002-12, Universite de Montreal, Departement de sciences economiques.
  3. Bossert, Walter & Suzumura, Kotaro, 2007. "Social Norms and Rationality of Choice," Cahiers de recherche 2007-07, Universite de Montreal, Departement de sciences economiques.
  4. BOSSERT, Walter & SUZUMURA, Kotaro, 2005. "Domain Closedness Conditions and Rational Choice," Cahiers de recherche 27-2005, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  5. BOSSERT, Walter & SPRUMONT, Yves & SUZUMURA, Kotaro, 2002. "Maximal-Element Rationalizability," Cahiers de recherche 2002-16, Universite de Montreal, Departement de sciences economiques.
  6. BOSSERT, Walter & SUZUMURA, Kotaro, 2006. "Non-Deteriorating Choice without Full Transitivity," Cahiers de recherche 10-2006, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  7. Walter Bossert & Kotaro Suzumura, 2011. "Rationality, external norms, and the epistemic value of menus," Social Choice and Welfare, Springer, vol. 37(4), pages 729-741, October.
  8. Lahiri, Somdeb, 2008. "Rationality in a general model of choice," MPRA Paper 10860, University Library of Munich, Germany.
  9. BOSSERT, Walter, 2006. "Consistent Relations," Cahiers de recherche 2006-03, Universite de Montreal, Departement de sciences economiques.
  10. Christopher Tyson, 2013. "Behavioral implications of shortlisting procedures," Social Choice and Welfare, Springer, vol. 41(4), pages 941-963, October.

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