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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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Suggested Citation

  • Walter Bossert & Yves Sprumont & Kotaro Suzumura, 2006. "Rationalizability of choice functions on general domains without full transitivity," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 27(3), pages 435-458, December.
    • Handle: RePEc:spr:sochwe:v:27:y:2006:i:3:p:435-458
    DOI: 10.1007/s00355-006-0132-0
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Walter Bossert & Yves Sprumont & Kotaro Suzumura, 2005. "Maximal-Element Rationalizability," Theory and Decision, Springer, vol. 58(4), pages 325-350, June.
    2. Christopher Tyson, 2013. "Behavioral implications of shortlisting procedures," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 41(4), pages 941-963, October.
    3. S. Chaudhari & S. Desai, 2014. "Transitive and acyclic rationality indicators of fuzzy choice functions on base domain," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 42(2), pages 341-365, February.
    4. Christopher Tyson, 2015. "Satisficing behavior with a secondary criterion," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 44(3), pages 639-661, March.
    5. BOSSERT, Walter & SUZUMURA, Kotaro, 2006. "Non-Deteriorating Choice without Full Transitivity," Cahiers de recherche 2006-13, Universite de Montreal, Departement de sciences economiques.
    6. BOSSERT, Walter, 2006. "Consistent Relations," Cahiers de recherche 2006-03, Universite de Montreal, Departement de sciences economiques.
    7. BOSSERT, Walter & SPRUMONT, Yves & SUZUMURA, Kotaro, 2002. "Consistent Rationalizability," Cahiers de recherche 2002-12, Universite de Montreal, Departement de sciences economiques.
      • Bossert, Walter & Sprumont, Yves & Suzumura, Kotaro & 鈴村, 興太郎, 2002. "Consistent Rationalizability," Discussion Paper 82, Center for Intergenerational Studies, Institute of Economic Research, Hitotsubashi University.
    8. BOSSERT, Walter & SUZUMURA, Kotaro, 2005. "Rational Choice on Arbitrary Domains: A Comprehensive Treatment," Cahiers de recherche 17-2005, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    9. Christopher J. Tyson, 2018. "Rationalizability of menu preferences," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 65(4), pages 917-934, June.
    10. Somdeb Lahiri, 2015. "Rationality in a general model of choice," Journal of Economic and Financial Studies (JEFS), LAR Center Press, vol. 3(5), pages 43-52, October.
    11. Christopher Tyson, 2013. "Behavioral implications of shortlisting procedures," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 41(4), pages 941-963, October.
    12. Vicki Knoblauch, 2020. "Von Neumann–Morgenstern stable set rationalization of choice functions," Theory and Decision, Springer, vol. 89(3), pages 369-381, October.
    13. Walter Bossert & Kotaro Suzumura, 2011. "Rationality, external norms, and the epistemic value of menus," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 37(4), pages 729-741, October.
    14. BOSSERT, Walter & SUZUMURA, Kotaro, 2007. "Social Norms and Rationality of Choice," Cahiers de recherche 08-2007, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    15. BOSSERT, Walter & SUZUMURA, Kotaro, 2005. "Domain Closedness Conditions and Rational Choice," Cahiers de recherche 27-2005, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    16. Santosh Desai & Rupali Potdar, 2016. "Full Rationality of Fuzzy Choice Functions on Base Domain Through Indicators," New Mathematics and Natural Computation (NMNC), World Scientific Publishing Co. Pte. Ltd., vol. 12(03), pages 175-189, November.
    17. Alva, Samson, 2018. "WARP and combinatorial choice," Journal of Economic Theory, Elsevier, vol. 173(C), pages 320-333.

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    More about this item

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General

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