Representing choice functions by a total hyper-order

TL;DR

This paper characterizes choice functions satisfying the Outcast property as those that assign to each set its maximal subset according to some total order on the power set of X, linking choice behavior to order theory.

Contribution

It provides a precise characterization of choice functions with the Outcast property using total hyper-orders on the power set of X.

Findings

Choice functions with the Outcast property correspond to maximal subsets under a total order.

The characterization connects choice functions to total hyper-orders on the power set.

This bridges decision theory with order-theoretic structures.

Abstract

Choice functions over a set $X$ that satisfy the Outcast, a.k.a. Aizerman, property are exactly those that attach to any set its maximal subset relative to some total order of ${2}^{X}$.