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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 relationship between the different notions of rationalizability involving, for example, the transitivity, quasi-transitivity, or acyclicity of the rationalizing relation.
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  • 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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    1. Amartya Sen, 1997. "Maximization and the Act of Choice," Econometrica, Econometric Society, vol. 65(4), pages 745-780, July.
    2. Herzberger, Hans G, 1973. "Ordinal Preference and Rational Choice," Econometrica, Econometric Society, vol. 41(2), pages 187-237, March.
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    6. Bossert, W., 1995. "Choices, Consequences, and Rationality," Working Papers 9501, University of Waterloo, Department of Economics.
    7. Amartya K. Sen, 1971. "Choice Functions and Revealed Preference," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 38(3), pages 307-317.
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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. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. BOSSERT, Walter & SUZUMURA, Kotaro, 2007. "Social Norms and Rationality of Choice," Cahiers de recherche 08-2007, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    8. 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.
    9. 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.
    10. BOSSERT, Walter, 2006. "Consistent Relations," Cahiers de recherche 03-2006, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    11. 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.
    12. BOSSERT, Walter & SUZUMURA, Kotaro, 2005. "Domain Closedness Conditions and Rational Choice," Cahiers de recherche 27-2005, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    13. 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.
    14. 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.
    15. Vicki Knoblauch, 2020. "Von Neumann–Morgenstern stable set rationalization of choice functions," Theory and Decision, Springer, vol. 89(3), pages 369-381, October.
    16. Alva, Samson, 2018. "WARP and combinatorial choice," Journal of Economic Theory, Elsevier, vol. 173(C), pages 320-333.
    17. BOSSERT, Walter & SUZUMURA, Kotaro, 2006. "Non-Deteriorating Choice without Full Transitivity," Cahiers de recherche 2006-13, Universite de Montreal, Departement de sciences economiques.
    18. 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.

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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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