The purpose of this paper is to prove by induction the theorem (in Aizerman and Malishevski [1981]) that a choice function which satisfies Chernoffs axiom and Outcasting can always by expressed as the union of the solution sets of a finite number of maximization problems. In this paper we also show that the Slater solution for abstract games (see Slater [1961]) satisfies the Chernoff, Outcasting and Expansion axioms. On the other hand the solution due to Copeland [1951], which has subsequently been axiomatically characterized Henriet [1985], does not satisfy any of these three properties.