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Upper Semicontinuous Extensions of Binary Relations

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Author Info
Bossert, W.
Sprumont, Y.
Suzumura, K.

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Abstract

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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Paper provided by Centre interuniversitaire de recherche en économie quantitative, CIREQ in its series Cahiers de recherche with number 2002-01.

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Length: 16 pages
Date of creation: 2002
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Handle: RePEc:mtl:montec:2002-01

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Related research
Keywords: Extensions; upper semicontinuity; consistency;

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Find related papers by JEL classification:
C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - General

References listed on IDEAS
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. Kotaro Suzumura & Yongsheng Xu, 2002. "Recoverability of Choice Functions and Binary Relations: Some Duality Results," Discussion Paper Series a422, Institute of Economic Research, Hitotsubashi University.
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  2. Jaffray, Jean-Yves, 1975. "Semicontinuous extension of a partial order," Journal of Mathematical Economics, Elsevier, vol. 2(3), pages 395-406, December. [Downloadable!] (restricted)
  3. Duggan, John, 1999. "A General Extension Theorem for Binary Relations," Journal of Economic Theory, Elsevier, vol. 86(1), pages 1-16, May. [Downloadable!] (restricted)
  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. [Downloadable!] (restricted)
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  5. Sen, Amartya K, 1969. "Quasi-Transitivity, Rational Choice and Collective Decisions," Review of Economic Studies, Blackwell Publishing, vol. 36(107), pages 381-93, July. [Downloadable!] (restricted)
  6. 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. [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. Andrikopoulos, Athanasios & Zacharias, Eleftherios, 2008. "General solutions for choice sets: The Generalized Optimal-Choice Axiom set," MPRA Paper 11645, University Library of Munich, Germany. [Downloadable!]
  2. T. Demuynck, 2006. "Existence of closed and complete extensions applied to convex, homothetic an monotonic orderings," Working Papers of Faculty of Economics and Business Administration, Ghent University, Belgium 06/407, Ghent University, Faculty of Economics and Business Administration. [Downloadable!]
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