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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.

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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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  1. Duggan, John, 1999. "A General Extension Theorem for Binary Relations," Journal of Economic Theory, Elsevier, vol. 86(1), pages 1-16, May.
  2. 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.
  3. 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.
  4. Bossert, Walter & Sprumont, Yves & Suzumura, Kotaro, 2007. "Ordering infinite utility streams," Journal of Economic Theory, Elsevier, vol. 135(1), pages 579-589, July.
  5. Demuynck, Thomas & Lauwers, Luc, 2009. "Nash rationalization of collective choice over lotteries," Mathematical Social Sciences, Elsevier, vol. 57(1), pages 1-15, January.
  6. Paolo Scapparone, 1999. "Existence of a convex extension of a preference relation," Decisions in Economics and Finance, Springer, vol. 22(1), pages 5-11, March.
  7. 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.
  8. José Alcantud, 2009. "Conditional ordering extensions," Economic Theory, Springer, vol. 39(3), pages 495-503, June.
  9. Andrikopoulos, Athanasios, 2009. "Szpilrajn-type theorems in economics," MPRA Paper 14345, University Library of Munich, Germany.
  10. Svensson, Lars-Gunnar, 1980. "Equity among Generations," Econometrica, Econometric Society, vol. 48(5), pages 1251-56, July.
  11. 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.
  12. 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.
  13. 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.
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