The purpose of this paper is to prove by induction the theorem (in Aizerman and Malishevski [1981]) that a choice function which Satisfies Chernoff's axiom an d Outcasting can always be expressed as the union of the solution sets of a finite number of maximization problems. In Moulin[1988], a proof of this result is available. Unlike Moulin [1998], we do not split the proof into two lemmas, the first of which in any case, can always be replaced by the main result in Deb [1983] (an alternative easier proof of which can be found in Lahiri [1998a]. Our framework closely resembles the one of choice theory as developed in Aizerman and Aleskerov [1995]. It is well known that a combination of Chernoff's axiom and Outcasting is equivalent to a property called Path Independence (See Aizerman and Aleskerov [1995]).