Article ID Journal Published Year Pages File Type
972790 Mathematical Social Sciences 2009 14 Pages PDF
Abstract

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.

Related Topics
Physical Sciences and Engineering Mathematics Applied Mathematics
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