In this paper, we provide an axiomatic characterization of the additive choice function using the additivity property due to Myerson (1981). It is seen that along with Pareto Optimality, symmetry, and a supporting line property the additivity axiom uniquely characterizes the additive choice function. This characterization appears to be a shade more elegant and less reliant on the definition of the additive choice function, than the one available in Lahiri (1997a). It is easy to see that the additive choice function as defined in this paper, does not satisfy Nash's Independence of Irrelevant Alternatives Assumption. The latter is a property required for a choice function to be representable by an utility function i.e. the chosen point is to be the unique maximizer of an utility function. This brings us to the question of when a choice function is representable. This is the question we take up in an appendix to the paper.