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Domain Closedness Conditions and Rational Choice

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  • BOSSERT, Walter
  • SUZUMURA, Kotaro

Abstract

The rationalizability of a choice function on an arbitrary domain under various coherence properties has received a considerable amount of attention both in the long-established and in the recent literature. Because domain closedness conditions play an important role in much of rational choice theory, we examine the consequences of these requirements on the logical relationships among different versions of rationalizability. It turns out that closedness under intersection does not lead to any results differing from those obtained on arbitrary domains. In contrast, closedness under union allows us to prove an additional implication.

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Bibliographic Info

Paper provided by Centre interuniversitaire de recherche en économie quantitative, CIREQ in its series Cahiers de recherche with number 27-2005.

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Length: 22 pages
Date of creation: 2005
Date of revision:
Handle: RePEc:mtl:montec:27-2005

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Keywords: rational choice; domain closedness; coherence properties;

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References

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  1. 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.
  2. BOSSERT, Walter & SPRUMONT, Yves & SUZUMURA, Kotaro, 2002. "Consistent Rationalizability," Cahiers de recherche 2002-12, Universite de Montreal, Departement de sciences economiques.
  3. Walter BOSSERT & Yves SPRUMONT & Kotaro SUZUMURA, 2002. "Maximal-Element Rationalizability," Cahiers de recherche 16-2002, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  4. Donaldson, David & Weymark, John A., 1998. "A Quasiordering Is the Intersection of Orderings," Journal of Economic Theory, Elsevier, vol. 78(2), pages 382-387, February.
  5. 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.
  6. Sen, Amartya K, 1969. "Quasi-Transitivity, Rational Choice and Collective Decisions," Review of Economic Studies, Wiley Blackwell, vol. 36(107), pages 381-93, July.
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Cited by:
  1. 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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