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Common ordering extensions

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Author Info
T. DEMUYNCK ()

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Abstract

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.

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Publisher Info
Paper provided by Ghent University, Faculty of Economics and Business Administration in its series Working Papers of Faculty of Economics and Business Administration, Ghent University, Belgium with number 09/593.

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Length: 13 pages
Date of creation: Jun 2009
Date of revision:
Handle: RePEc:rug:rugwps:09/593

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Related research
Keywords: Common ordering extension; consistency; Szpirajn’s lemma;

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Find related papers by JEL classification:
C60 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - General
D90 - Microeconomics - - Intertemporal Choice and Growth - - - General
D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement

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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. Svensson, Lars-Gunnar, 1980. "Equity among Generations," Econometrica, Econometric Society, vol. 48(5), pages 1251-56, July. [Downloadable!] (restricted)
  2. Duggan, John, 1999. "A General Extension Theorem for Binary Relations," Journal of Economic Theory, Elsevier, vol. 86(1), pages 1-16, May. [Downloadable!] (restricted)
  3. Andrikopoulos, Athanasios, 2009. "Szpilrajn-type theorems in economics," MPRA Paper 14345, University Library of Munich, Germany. [Downloadable!]
  4. Bossert, Walter & Sprumont, Yves & Suzumura, Kotaro, 2007. "Ordering infinite utility streams," Journal of Economic Theory, Elsevier, vol. 135(1), pages 579-589, July. [Downloadable!] (restricted)
  5. 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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  6. 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. [Downloadable!] (restricted)
  7. José Alcantud, 2009. "Conditional ordering extensions," Economic Theory, Springer, vol. 39(3), pages 495-503, June. [Downloadable!] (restricted)
  8. 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)
  9. 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. [Downloadable!] (restricted)
  10. 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. [Downloadable!] (restricted)
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This page was last updated on 2009-11-26.

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