Consequence of chernoff and outcasting

Abstract

The purpose of this paper is to prove by induction the theorem (in Aizerman and Malishevsi [1981]) that a choice function which satisfies Chernoff s axiom and Outcasting can always by expressed as the union of the solution sets of a finite number of maximization problems. The proof we offer is considerably simpler than the one in Aizerman and Malishevski [1981]. In Moulin [1985], a discussion of a similar result is available. Our framework closely resembles the one of choice theory as enunciated in Moulin [1985]. It is well known that a combination of Chernoff s axiom and Outcasting is equivalent to a property called Path Independence (See Moulin [1985]).