A Representation of the Maximal Set in Choice Problems Where Information Is Incomplete

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.