Reconsideration of some solutions for two dimensional choice problems

Abstract

In this paper, the outstanding problem of axiomatically characterizing what is referred in the paper as additive c hoice function on the classical domain for choice problems is taken into account. Apart from an impossibility result for the additive choice function, there is an axiomatic characterization, which as a by-product provides a counter example to a conjucture for the egalitarian choice function. In an appendic, the proof of an axiomatic characterization of the egalitarian choice function using a supperadditivity axion is provided. Also, in this paper, proofs of axiomatic characterization of the family of non-symmetric Nash choice functions and the family of weighted hierarchies of choice functions is provided. The conclusion is that earlier axiomatizations are essentially preserved on the classical domain for choice porblems. The proofs are significant in being non-trivial and very disimilar to existing proofs on other domains.