Some properties of solutions for two-dimensional choice problems reconsidered

The problem of axiomatically characterizing what is called in the paper the additive choice function on the classical domain for choice problems is taken up. Apart from an impossibility result for the additive choice function, there is an axiomatic characterization, which as a by-product provides a counterexample to a conjecture for the egalitarian choice function. In an appendix, a proof of an axiomatic characterization of the egalitarian choice function using a superadditivity axiom is provided. Likewise proofs of axiomatic characterizations of the family of non-symmetric Nash choice functions and the family of weighted hierarchies of choice functions are given. The conclusion is that earlier axiomatizations are essentially preserved on the classical domain for choice problems. The proofs are significant in being non-trivial and very dissimilar to existing proofs for other domains.