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Consistent Rationalizability

Author

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

Abstract

Consistency of a binary relation requires any preference cycle to involve indifference only. As shown by Suzumura (1976b), consistency is necessary and sufficient for the existence of an ordering extension of a relation. Because of this important role of consistency, it is of interest to examine the rationalizability of choice functions by means of consistent relations. We describe the logical relationships between the different notions of rationalizability obtained if reflexivity or completeness are added to consistency, both for greatest-element rationalizability and for maximal-element rationalizability. All but one notion of consistent rationalizability are characterized for general domains, and all of them are characterized for domains that contain all two-element subsets of the universal set.

Suggested Citation

  • Bossert, Walter & Sprumont, Yves & Suzumura, Kotaro, 2002. "Consistent Rationalizability," Discussion Paper 82, Center for Intergenerational Studies, Institute of Economic Research, Hitotsubashi University.
  • Handle: RePEc:hit:piedp1:82
    Note: June 2002, Financial support through grants from the Social Sciences and Humanities Research Council of Canada, the Fonds pour la Formation de Chercheurs et l'Aide à la Recherche of Québec, and a Grant-in-Aid for Scientific Research for Priority Areas (B) Number 603 from the Ministry of Education, Science and Culture of Japan is gratefully acknowledged.
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    References listed on IDEAS

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    1. 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.
    2. Kotaro Suzumura, 1976. "Rational Choice and Revealed Preference," Review of Economic Studies, Oxford University Press, vol. 43(1), pages 149-158.
    3. Suzumura, Kataro, 1976. "Remarks on the Theory of Collective Choice," Economica, London School of Economics and Political Science, vol. 43(172), pages 381-390, November.
    4. Amartya K. Sen, 1971. "Choice Functions and Revealed Preference," Review of Economic Studies, Oxford University Press, vol. 38(3), pages 307-317.
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    Citations

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    Cited by:

    1. Walter Bossert & Kotaro Suzumura, 2015. "Expected utility without full transitivity," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 45(4), pages 707-722, December.
    2. Bossert, Walter & Suzumura, Kotaro, 2008. "A characterization of consistent collective choice rules," Journal of Economic Theory, Elsevier, vol. 138(1), pages 311-320, January.
    3. Walter Bossert & Yves Sprumont & Kotaro Suzumura, 2005. "Maximal-Element Rationalizability," Theory and Decision, Springer, vol. 58(4), pages 325-350, June.
    4. 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.
    5. Walter Bossert & Kotaro Suzumura, 2012. "Revealed preference and choice under uncertainty," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 3(1), pages 247-258, March.
    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. João Ferreira & Nicolas Gravel, 2017. "Choice with Time," Working Papers halshs-01577260, HAL.
    8. Geir Asheim & Walter Bossert & Yves Sprumont & Kotaro Suzumura, 2010. "Infinite-horizon choice functions," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 43(1), pages 1-21, April.
    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. Susumu Cato, 2013. "Quasi-decisiveness, quasi-ultrafilter, and social quasi-orderings," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 41(1), pages 169-202, June.
    11. Walter Bossert & Marc Fleurbaey, 2015. "An Interview with Kotaro Suzumura," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 44(1), pages 179-208, January.
    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. Douglas Bernheim & Antonio Rangel, 2007. "Beyond Revealed Preference Choice Theoretic Foundations for Behavioral Welfare Economics," Discussion Papers 07-031, Stanford Institute for Economic Policy Research.
    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. Shaofang Qi, 2016. "A characterization of the n-agent Pareto dominance relation," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 46(3), pages 695-706, March.
    17. Cato, Susumu, 2013. "Remarks on Suzumura consistent collective choice rules," Mathematical Social Sciences, Elsevier, vol. 65(1), pages 40-47.

    More about this item

    Keywords

    Rational Choice; Consistency; Binary Domains;

    JEL classification:

    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory

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