A general extension result with applications to convexity, homotheticity and monotonicity
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.
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.:
- Walter Bossert & Yves Sprumont, 2009.
London School of Economics and Political Science, vol. 76(302), pages 337-363, 04.
- BOSSERT, Walter & SPRUMONT, Yves, 2001. "Non-Deteriorating Choice," Cahiers de recherche 2001-01, Universite de Montreal, Departement de sciences economiques.
- Bossert, W. & Sprumont, Y., 2001. "Non-Deteriorating Choice," Cahiers de recherche 2001-01, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
- Duggan, John, 1999. "A General Extension Theorem for Binary Relations," Journal of Economic Theory, Elsevier, vol. 86(1), pages 1-16, May.
- 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.
- 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.
- 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.
When requesting a correction, please mention this item's handle: RePEc:eee:matsoc:v:57:y:2009:i:1:p:96-109. 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: (Zhang, Lei)
If references are entirely missing, you can add them using this form.