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

Thomas Demuynck

Mathematical Social Sciences, 2009, vol. 57, issue 1, 96-109

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.

Keywords: Binary; extensions; Convexity; Homotheticity; Monotonicity (search for similar items in EconPapers)
Date: 2009
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (16)

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Working Paper: A general extension result with applications to convexity, homotheticity and monotonicity (2009)
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matsoc:v:57:y:2009:i:1:p:96-109

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