A Generalization of Arrow’s Lemma on Extending a Binary Relation

Athanasios Andrikopoulos

International Journal of Mathematics and Mathematical Sciences, 2019, vol. 2019, 1-6

Abstract:

By examining whether the individualistic assumptions used in social choice could be used in the aggregation of individual preferences, Arrow proved a key lemma that generalizes the famous Szpilrajn’s extension theorem and used it to demonstrate the impossibility theorem. In this paper, I provide a characterization of Arrow’s result for the case in which the binary relations I extend are not necessarily transitive and are defined on abelian groups. I also give a characterization of the existence of a realizer of a binary relation defined on an abelian group. These results also generalize the well-known extension theorems of Szpilrajn, Dushnik-Miller, and Fuchs.

Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:5397036

DOI: 10.1155/2019/5397036

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