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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.

Suggested Citation

  • BOSSERT, Walter & SPRUMONT, Yves & SUZUMURA, Kotaro, 2001. "Rationalizability of Choice Functions on General Domains without Full Transitivity," Cahiers de recherche 2001-13, Universite de Montreal, Departement de sciences economiques.
  • Handle: RePEc:mtl:montde:2001-13
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    File URL: http://hdl.handle.net/1866/353
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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. Suzumura, Kotaro, 1977. "Houthakker's axiom in the theory of rational choice," Journal of Economic Theory, Elsevier, vol. 14(2), pages 284-290, April.
    3. Kotaro Suzumura, 1976. "Rational Choice and Revealed Preference," Review of Economic Studies, Oxford University Press, vol. 43(1), pages 149-158.
    4. Amartya K. Sen, 1971. "Choice Functions and Revealed Preference," Review of Economic Studies, Oxford University Press, vol. 38(3), pages 307-317.
    5. Herzberger, Hans G, 1973. "Ordinal Preference and Rational Choice," Econometrica, Econometric Society, vol. 41(2), pages 187-237, March.
    6. Bossert, W., 1995. "Choices, Consequences, and Rationality," Working Papers 9501, University of Waterloo, Department of Economics.
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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. Christopher J. Tyson, 2012. "Behavioral Implications of Shortlisting Procedures," Working Papers 697, Queen Mary University of London, School of Economics and Finance.
    4. 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.
    5. 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.
    6. BOSSERT, Walter & SUZUMURA, Kotaro, 2007. "Social Norms and Rationality of Choice," Cahiers de recherche 08-2007, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    7. Christopher J. Tyson, 2014. "Satisficing Behavior with a Secondary Criterion," Working Papers 725, Queen Mary University of London, School of Economics and Finance.
    8. 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.
    9. BOSSERT, Walter & SUZUMURA, Kotaro, 2005. "Domain Closedness Conditions and Rational Choice," Cahiers de recherche 27-2005, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    10. 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.
    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. BOSSERT, Walter & SUZUMURA, Kotaro, 2006. "Non-Deteriorating Choice without Full Transitivity," Cahiers de recherche 2006-13, Universite de Montreal, Departement de sciences economiques.
    13. BOSSERT, Walter, 2006. "Consistent Relations," Cahiers de recherche 2006-03, Universite de Montreal, Departement de sciences economiques.
    14. Walter Bossert & Yves Sprumont & Kotaro Suzumura, 2005. "Consistent Rationalizability," Economica, London School of Economics and Political Science, vol. 72(286), pages 185-200, May.
    15. 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.
    16. Christopher J. Tyson, 2017. "Rationalizability of Menu Preferences," Working Papers 819, Queen Mary University of London, School of Economics and Finance.
    17. repec:spr:joecth:v:65:y:2018:i:4:d:10.1007_s00199-017-1043-2 is not listed on IDEAS

    More about this item

    Keywords

    rational choice; quasi-transitivity; acyclicity; base domains;

    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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