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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"Upper semicontinuous extensions of binary relations,"
Journal of Mathematical Economics,
Elsevier, vol. 37(3), pages 231-246, May.
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- 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.
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