A Generalization of Arrow’s Lemma on Extending a Binary Relation
Author
Source
International Journal of Mathematics and Mathematical Sciences
Issue
Vol. 2019, Issue 2019 (31 Dec. 2019), pp.1-6, 6 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2019-04-01
Country of Publication
Egypt
No. of Pages
6
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
Andrikopoulos, Athanasios. 2019. A Generalization of Arrow’s Lemma on Extending a Binary Relation. International Journal of Mathematics and Mathematical Sciences،Vol. 2019, no. 2019, pp.1-6.
https://search.emarefa.net/detail/BIM-1166365
Modern Language Association (MLA)
Andrikopoulos, Athanasios. A Generalization of Arrow’s Lemma on Extending a Binary Relation. International Journal of Mathematics and Mathematical Sciences No. 2019 (2019), pp.1-6.
https://search.emarefa.net/detail/BIM-1166365
American Medical Association (AMA)
Andrikopoulos, Athanasios. A Generalization of Arrow’s Lemma on Extending a Binary Relation. International Journal of Mathematics and Mathematical Sciences. 2019. Vol. 2019, no. 2019, pp.1-6.
https://search.emarefa.net/detail/BIM-1166365
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1166365