Some properties of solutions for two-dimensional choice problems reconsidered

Ill this paper, we take up the problem, of axiomatically characterizing wha t we have referred to ill the paper as the additive choice function on the classical domain for choice::problems,.Apart from an impossibility result f or the additive choice function:!, there is an axiomatic characterization:, which as a by ,product: provides a counterexample to a conjecture , for th e egalitarian c:choice:cl function. In an appendix, we provide a proof of a n axiomatic: c:acterization of the egalitarian choice function using a supe radditivity axiom. In this paper, we also provide proofs of axiomatic characterizations;lc:;ti ons of the family of non-symmetric Nash choice functions: illld the family of weighted hierarchics of choice functions:. Our conclusion is that earlie r axiomatizations are essentially preserved oil tilt: c:classical domain fo r choice problems. The proofs are significant, ill being, non-trivial and v ery dissimilar to existing proofs for other I domains.