TITLE:
A Representation of the Maximal Set in Choice Problems Where Information Is Incomplete
AUTHORS:
Andrikopoulos Athanasios
KEYWORDS:
Binary Relation, Best Element, Maximalel Ement, Optimal Set, Extension of a Binary Relation
JOURNAL NAME:
Theoretical Economics Letters,
Vol.8 No.11,
August
29,
2018
ABSTRACT: Banerjee and Pattanaik [1] proved that the maximal
set generated by a quasi-ordering is equal to the union of the sets of best
elements of its ordering extensions. Suzumura and Xu [2] extended Banerjee and
Pattanaik’s result by relaxing the axiom of transitivity to the axiom that
Suzumura calls consistency. Arló Costa in [3] pointed out that in general, an
optimizing model cannot require the transitivity of the binary relation used in
an optimizing model. In this paper, by using two important ideas of John Duggan [4], I extend the above mentioned results to arbitrary binary relations whose
extensions are complete and not necessarily transitive.