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Rationalizability of Choice Functions on General Domains Without Full Transitivity

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Author Info
Bossert, Walter
Sprumont, Yves
Suzumura, Kotaro

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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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File URL: http://hermes-ir.lib.hit-u.ac.jp/rs/bitstream/10086/14474/1/pie_dp28.pdf
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Paper provided by Center for Intergenerational Studies, Institute of Economic Research, Hitotsubashi University in its series Discussion Paper with number 28.

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Length: 29 p.
Date of creation: May 2001
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Handle: RePEc:hit:piedp1:28

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Related research
Keywords: Rational Choice; Quasi-Transitivity; Acyclicity; Base Domains;

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Find related papers by JEL classification:
D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory

References listed on IDEAS
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  1. Bossert, W., 1995. "Choices, Consequences, and Rationality," Working Papers 9501, University of Waterloo, Department of Economics.
  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. [Downloadable!] (restricted)
  3. Suzumura, Kotaro, 1976. "Rational Choice and Revealed Preference," Review of Economic Studies, Blackwell Publishing, vol. 43(1), pages 149-58, February. [Downloadable!] (restricted)
  4. Amartya Sen, 1997. "Maximization and the Act of Choice," Econometrica, Econometric Society, vol. 65(4), pages 745-780, July.
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  5. Herzberger, Hans G, 1973. "Ordinal Preference and Rational Choice," Econometrica, Econometric Society, vol. 41(2), pages 187-237, March. [Downloadable!] (restricted)
  6. Sen, Amartya K, 1971. "Choice Functions and Revealed Preference," Review of Economic Studies, Blackwell Publishing, vol. 38(115), pages 307-17, July. [Downloadable!] (restricted)
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. BOSSERT, Walter, 2006. "Consistent Relations," Cahiers de recherche 2006-03, Universite de Montreal, Departement de sciences economiques. [Downloadable!]
  2. BOSSERT, Walter & SPRUMONT, Yves & SUZUMURA, Kotaro, 2002. "Maximal-Element Rationalizability," Cahiers de recherche 2002-16, Universite de Montreal, Departement de sciences economiques. [Downloadable!]
    Other versions:
  3. BOSSERT, Walter & SUZUMURA, Kotaro, 2006. "Non-Deteriorating Choice without Full Transitivity," Cahiers de recherche 2006-13, Universite de Montreal, Departement de sciences economiques. [Downloadable!]
  4. Lahiri, Somdeb, 2008. "Rationality in a general model of choice," MPRA Paper 10860, University Library of Munich, Germany. [Downloadable!]
  5. 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. [Downloadable!]
  6. BOSSERT, Walter & SUZUMURA, Kotaro, 2005. "Domain Closedness Conditions and Rational Choice," Cahiers de recherche 2005-21, Universite de Montreal, Departement de sciences economiques. [Downloadable!]
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