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Maximal-Element Rationalizability

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  • BOSSERT, Walter
  • SPRUMONT, Yves
  • SUZUMURA, Kotaro

Abstract

We examine the maximal-element rationalizability of choice functions with arbitrary do-mains. While rationality formulated in terms of the choice of greatest elements according to a rationalizing relation has been analyzed relatively thoroughly in the earlier litera-ture, this is not the case for maximal-element rationalizability, except when it coincides with greatest-element rationalizability because of properties imposed on the rationalizing relation. We develop necessary and sufficient conditions for maximal-element rationaliz-ability by itself, and for maximal-element rationalizability in conjunction with additional properties of a rationalizing relation such as re exivity, completeness, P-acyclicity, quasi-transitivity, consistency and transitivity.

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Paper provided by Universite de Montreal, Departement de sciences economiques in its series Cahiers de recherche with number 2002-16.

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Length: 19 ges pages
Date of creation: 2002
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Handle: RePEc:mtl:montde:2002-16

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Keywords: Choice Functions; Maximal-Element Rationalizability.;

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References

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  1. Amartya Sen, 1996. "Maximization and the Act of Choice," Harvard Institute of Economic Research Working Papers 1766, Harvard - Institute of Economic Research.
  2. Bossert, W. & Sprumont, Y. & Suzumura, K., 2002. "Consistent Rationalizability," Cahiers de recherche 12-2002, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  3. Bossert, W. & Sprumont, Y. & Suzumura, K., 2001. "Rationalizability of Choice Functions on General Domains without Full Transitivity," Cahiers de recherche 2001-13, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  4. Suzumura, Kotaro, 1977. "Houthakker's axiom in the theory of rational choice," Journal of Economic Theory, Elsevier, vol. 14(2), pages 284-290, April.
  5. Sen, Amartya K, 1971. "Choice Functions and Revealed Preference," Review of Economic Studies, Wiley Blackwell, vol. 38(115), pages 307-17, July.
  6. Sen, Amartya K, 1977. "Social Choice Theory: A Re-examination," Econometrica, Econometric Society, vol. 45(1), pages 53-89, January.
  7. Suzumura, Kataro, 1976. "Remarks on the Theory of Collective Choice," Economica, London School of Economics and Political Science, vol. 43(172), pages 381-90, November.
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Citations

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Cited by:
  1. BOSSERT, Walter & SUZUMURA, Kotaro, 2005. "Domain Closedness Conditions and Rational Choice," Cahiers de recherche 27-2005, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  2. BOSSERT, Walter & SUZUMURA, Kotaro, 2006. "Non-Deteriorating Choice without Full Transitivity," Cahiers de recherche 10-2006, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  3. BOSSERT, Walter, 2006. "Consistent Relations," Cahiers de recherche 2006-03, Universite de Montreal, Departement de sciences economiques.
  4. Andreas Darmann & Christian Klamler & Ulrich Pferschy, 2011. "Finding socially best spanning trees," Theory and Decision, Springer, vol. 70(4), pages 511-527, April.
  5. 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.

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