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A general extension result with applications to convexity, homotheticity and monotonicity

  • Demuynck, Thomas

A well-known result in the theory of binary relations states that a binary relation has a complete and transitive extension if and only if it is consistent ([Suzumura K., 1976. Remarks on the theory of collective choice, Economica 43, 381-390], Theorem 3). A relation is consistent if the elements in the transitive closure are not in the inverse of the asymmetric part. We generalize this result by replacing the transitive closure with a more general function. Using this result, we set up a procedure which leads to existence results for complete extensions satisfying various additional properties. We demonstrate the usefulness of this procedure by applying it to the properties of convexity, homotheticity and monotonicity.

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Article provided by Elsevier in its journal Mathematical Social Sciences.

Volume (Year): 57 (2009)
Issue (Month): 1 (January)
Pages: 96-109

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Handle: RePEc:eee:matsoc:v:57:y:2009:i:1:p:96-109
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  1. Bossert, W. & Sprumont, Y., 2001. "Non-Deteriorating Choice," Cahiers de recherche 2001-01, Centre interuniversitaire de recherche en ├ęconomie quantitative, CIREQ.
  2. 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.
  3. 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.
  4. Duggan, John, 1999. "A General Extension Theorem for Binary Relations," Journal of Economic Theory, Elsevier, vol. 86(1), pages 1-16, May.
  5. 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.
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