Path independence and choice acyclicity property

Abstract

In this paper we study lower and upper approximations of choice functions and propose a necessary and sufficient condition for a choice function to have a path independent lower approximation. In an appendix to this paper we provide a simple proof of Theorem 2.10 in Deb (1983) in the case when the universal set is finite. In a final section of this paper, we characterize all batch choice functions using a choice acyclicity property.