On the construction of non-empty choice sets (Journal article)

Andrikopoulos, A.


In this article, we analyze the problem of choice based on potentially ill-behaved binary relations that may fail to possess maximal elements. The approach, which is based on Duggan (Soc Choice Welf 28:491-506, 2007), is to consider every maximal subrelation (resp. minimal superrelation) satisfying a regularity condition (acyclicity, consistency, or negative consistency) and to unify the maximal elements of all such relations. Based on this procedure, we present a characterization of the Smith set, the Duggan set, the Schwartz set, and the generalized stable sets solution of an arbitrary binary relation over non-finite sets. Schwartz's and Van Deemen's results for asymmetric binary relations stated in the finite case, are also extended to this more general framework. Finally, we give a set theoretical description of the Duggan set and show that the Schwartz set offers a refinement of the Duggan set, and the Schwartz and Duggan sets are nested between the union of generalized stable sets and the Smith set.
Institution and School/Department of submitter: Πανεπιστήμιο Ιωαννίνων. Σχολή Οικονομικών και Κοινωνικών Επιστημών. Τμήμα Οικονομικών Επιστημών
Keywords: binary relations
URI: http://olympias.lib.uoi.gr/jspui/handle/123456789/11378
ISSN: 0176-1714
Link: <Go to ISI>://000300585700006
Publisher: Springer-Verlag
Appears in Collections:Άρθρα σε επιστημονικά περιοδικά ( Ανοικτά)

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