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Upper Semicontinuous Extensions of Binary Relations

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

Suzumura shows that a binary relation has a weak order extension if and only if it is consistent. However, consistency is demonstrably not sufficient to extend an upper semi-continuous binary relation to an upper semicontinuous weak order. Jaffray proves that any asymmetric (or reflexive), transitive and upper semicontinuous binary relation has an upper semicontinuous strict (or weak) order extension. We provide sufficient conditions for existence of upper semicontinuous extensions of consistence rather than transitive relations. For asymmetric relations, consistency and upper semicontinuity suffice. For more general relations, we prove one theorem using a further consistency property and another with an additional continuity requirement.

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File URL: http://hdl.handle.net/1866/369
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Paper provided by Universite de Montreal, Departement de sciences economiques in its series Cahiers de recherche with number 2002-01.

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Length: 16 pages
Date of creation: 2002
Date of revision:
Handle: RePEc:mtl:montde:2002-01
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Web page: http://www.sceco.umontreal.ca

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  1. Kotaro Suzumura & Yongsheng Xu, 2003. "Recoverability of choice functions and binary relations: some duality results," Social Choice and Welfare, Springer, vol. 21(1), pages 21-37, 08.
  2. 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.
  3. Duggan, John, 1999. "A General Extension Theorem for Binary Relations," Journal of Economic Theory, Elsevier, vol. 86(1), pages 1-16, May.
  4. Sen, Amartya K, 1969. "Quasi-Transitivity, Rational Choice and Collective Decisions," Review of Economic Studies, Wiley Blackwell, vol. 36(107), pages 381-93, July.
  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. Jaffray, Jean-Yves, 1975. "Semicontinuous extension of a partial order," Journal of Mathematical Economics, Elsevier, vol. 2(3), pages 395-406, December.
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