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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://hdl.handle.net/1866/353
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Publisher Info
Paper provided by Universite de Montreal, Departement de sciences economiques in its series Cahiers de recherche with number 2001-13.

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Length: 29 pages
Date of creation: 2001
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Handle: RePEc:mtl:montde:2001-13

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Related research
Keywords: rational choice quasi-transitivity acyclicity base domains

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Find related papers by 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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  1. 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)
  2. Suzumura, Kotaro, 1976. "Rational Choice and Revealed Preference," Review of Economic Studies, Blackwell Publishing, vol. 43(1), pages 149-58, February. [Downloadable!] (restricted)
  3. Amartya Sen, 1997. "Maximization and the Act of Choice," Econometrica, Econometric Society, vol. 65(4), pages 745-780, July.
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  4. Herzberger, Hans G, 1973. "Ordinal Preference and Rational Choice," Econometrica, Econometric Society, vol. 41(2), pages 187-237, March. [Downloadable!] (restricted)
  5. 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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(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, W. & Sprumont, Y. & Suzumura, K., 2002. "Maximal-Element Rationalizability," Cahiers de recherche 16-2002, Centre interuniversitaire de recherche en économie quantitative, CIREQ. [Downloadable!]
    Other versions:
  2. BOSSERT, Walter, 2006. "Consistent Relations," Cahiers de recherche 2006-03, Universite de Montreal, Departement de sciences economiques. [Downloadable!]
  3. BOSSERT, Walter & SUZUMURA, Kotaro, 2005. "Domain Closedness Conditions and Rational Choice," Cahiers de recherche 2005-21, Universite de Montreal, Departement de sciences economiques. [Downloadable!]
  4. BOSSERT, Walter & SUZUMURA, Kotaro, 2006. "Non-Deteriorating Choice without Full Transitivity," Cahiers de recherche 2006-13, Universite de Montreal, Departement de sciences economiques. [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!]
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