Common ordering extensions
This article provides necessary and sufficient conditions for a collection of binary relations to have a common ordering extension. We also characterize the quasi-ordering that is obtained by taking the intersection over all these ordering extensions. Next, we consider the special case where the collection contains only two relations. In this special case, our necessary and sufficient conditions can be reformulated to include solely binary relations that are defined on a certain subset of the universal domain. The usefullness of our results are illustrated with several examples and we relate our findings to the results in the literature.
|Date of creation:||Jun 2009|
|Date of revision:|
|Contact details of provider:|| Postal: Hoveniersberg 4, B-9000 Gent|
Phone: ++ 32 (0) 9 264 34 61
Fax: ++ 32 (0) 9 264 35 92
Web page: http://www.ugent.be/eb
More information through EDIRC
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.:
- Bossert, Walter & Sprumont, Yves & Suzumura, Kotaro, 2002.
"Upper semicontinuous extensions of binary relations,"
Journal of Mathematical Economics,
Elsevier, vol. 37(3), pages 231-246, May.
- Walter Bossert & Yves Sprumont & Kotaro Suzumura, 2002. "Upper Semicontinuous Extensions of Binary Relations," Discussion Paper Series a423, Institute of Economic Research, Hitotsubashi University.
- BOSSERT, Walter & SPRUMONT, Yves & SUZUMURA, Kotaro, 2002. "Upper Semicontinuous Extensions of Binary Relations," Cahiers de recherche 2002-01, Universite de Montreal, Departement de sciences economiques.
- Bossert, Walter & Sprumont, Yves & Suzumura, Kotaro, 2007. "Ordering infinite utility streams," Journal of Economic Theory, Elsevier, vol. 135(1), pages 579-589, July.
- Herden, Gerhard & Pallack, Andreas, 2002. "On the continuous analogue of the Szpilrajn Theorem I," Mathematical Social Sciences, Elsevier, vol. 43(2), pages 115-134, March.
- Kotaro Suzumura & Yongsheng Xu, 2003. "Recoverability of choice functions and binary relations: some duality results," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 21(1), pages 21-37, 08.
- Demuynck, Thomas & Lauwers, Luc, 2009. "Nash rationalization of collective choice over lotteries," Mathematical Social Sciences, Elsevier, vol. 57(1), pages 1-15, January.
- Svensson, Lars-Gunnar, 1980. "Equity among Generations," Econometrica, Econometric Society, vol. 48(5), pages 1251-56, July.
- Paolo Scapparone, 1999. "Existence of a convex extension of a preference relation," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 22(1), pages 5-11, March.
- Andrikopoulos, Athanasios, 2009. "Szpilrajn-type theorems in economics," MPRA Paper 14345, University Library of Munich, Germany.
- Banerjee, Asis & Pattanaik, Prasanta K., 1996. "A note on a property of maximal sets and choice in the absence of universal comparability," Economics Letters, Elsevier, vol. 51(2), pages 191-195, May.
- Duggan, John, 1999. "A General Extension Theorem for Binary Relations," Journal of Economic Theory, Elsevier, vol. 86(1), pages 1-16, May.
- 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.
- José Alcantud, 2009. "Conditional ordering extensions," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 39(3), pages 495-503, June.
- Demuynck, Thomas, 2009. "A general extension result with applications to convexity, homotheticity and monotonicity," Mathematical Social Sciences, Elsevier, vol. 57(1), pages 96-109, January.
When requesting a correction, please mention this item's handle: RePEc:rug:rugwps:09/593. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Nathalie Verhaeghe)
If references are entirely missing, you can add them using this form.