A Generalization of Arrow’s Lemma on Extending a Binary Relation
2019 ◽
Vol 2019
◽
pp. 1-6
Keyword(s):
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.
2017 ◽
Vol 16
(10)
◽
pp. 1750200
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1961 ◽
Vol 57
(3)
◽
pp. 476-482
◽
Keyword(s):
2013 ◽
Vol 56
(3)
◽
pp. 477-490
◽
Keyword(s):
Keyword(s):
1961 ◽
Vol 57
(2)
◽
pp. 256-264
◽
Keyword(s):
1995 ◽
Vol 03
(01)
◽
pp. 47-55
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