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Rationalizability of choice functions on general domains without full transitivity

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  • Walter Bossert

    ()

  • Yves Sprumont

    ()

  • Kotaro Suzumura

    ()

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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Bibliographic Info

Article provided by Springer in its journal Social Choice and Welfare.

Volume (Year): 27 (2006)
Issue (Month): 3 (December)
Pages: 435-458

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Handle: RePEc:spr:sochwe:v:27:y:2006:i:3:p:435-458

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References

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  1. Herzberger, Hans G, 1973. "Ordinal Preference and Rational Choice," Econometrica, Econometric Society, Econometric Society, vol. 41(2), pages 187-237, March.
  2. Amartya Sen, 1996. "Maximization and the Act of Choice," Harvard Institute of Economic Research Working Papers 1766, Harvard - Institute of Economic Research.
  3. Sen, Amartya K, 1971. "Choice Functions and Revealed Preference," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 38(115), pages 307-17, July.
  4. Suzumura, Kotaro, 1977. "Houthakker's axiom in the theory of rational choice," Journal of Economic Theory, Elsevier, vol. 14(2), pages 284-290, April.
  5. Bossert, W., 1995. "Choices, Consequences, and Rationality," Working Papers 9501, University of Waterloo, Department of Economics.
  6. Suzumura, Kotaro, 1976. "Rational Choice and Revealed Preference," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 43(1), pages 149-58, February.
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Citations

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Cited by:
  1. BOSSERT, Walter & SUZUMURA, Kotaro, 2005. "Rational Choice on Arbitrary Domains: A Comprehensive Treatment," Cahiers de recherche, Centre interuniversitaire de recherche en économie quantitative, CIREQ 17-2005, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  2. Walter Bossert & Yves Sprumont & Kotaro Suzumura, 2005. "Maximal-Element Rationalizability," Theory and Decision, Springer, vol. 58(4), pages 325-350, 06.
  3. BOSSERT, Walter, 2006. "Consistent Relations," Cahiers de recherche, Centre interuniversitaire de recherche en économie quantitative, CIREQ 03-2006, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  4. BOSSERT, Walter & SUZUMURA, Kotaro, 2007. "Social Norms and Rationality of Choice," Cahiers de recherche, Centre interuniversitaire de recherche en économie quantitative, CIREQ 08-2007, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  5. Christopher J. Tyson, 2014. "Satisficing Behavior with a Secondary Criterion," Working Papers 725, Queen Mary, University of London, School of Economics and Finance.
  6. Walter Bossert & Kotaro Suzumura, 2011. "Rationality, external norms, and the epistemic value of menus," Social Choice and Welfare, Springer, Springer, vol. 37(4), pages 729-741, October.
  7. Lahiri, Somdeb, 2008. "Rationality in a general model of choice," MPRA Paper 10860, University Library of Munich, Germany.
  8. BOSSERT, Walter & SUZUMURA, Kotaro, 2005. "Domain Closedness Conditions and Rational Choice," Cahiers de recherche, Universite de Montreal, Departement de sciences economiques 2005-21, Universite de Montreal, Departement de sciences economiques.
  9. Christopher J. Tyson, 2012. "Behavioral Implications of Shortlisting Procedures," Working Papers 697, Queen Mary, University of London, School of Economics and Finance.
  10. Bossert, Walter & Sprumont, Yves & Suzumura, Kotaro, 2002. "Consistent Rationalizability," Discussion Paper, Center for Intergenerational Studies, Institute of Economic Research, Hitotsubashi University 82, Center for Intergenerational Studies, Institute of Economic Research, Hitotsubashi University.
  11. BOSSERT, Walter & SUZUMURA, Kotaro, 2006. "Non-Deteriorating Choice without Full Transitivity," Cahiers de recherche, Centre interuniversitaire de recherche en économie quantitative, CIREQ 10-2006, Centre interuniversitaire de recherche en économie quantitative, CIREQ.

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