Ordinal comparisons in choice problems: a diagrammatic exposition

Abstract

The basic problem in choice theory is to choose a point from a set of available points. A large literature has grown where the central issue is the choice of a vector from a compact, convex and comprehensive (terms to be defined later) subset of a finite dimensional Euclidean space. A significant solution for such choice problems is the egalitarian solution which selects the highest possible vector with equal co-ordinates that is available under the given circumstances. There are several axiomatic characterizations of the egalitarian solution available in the literature. Of particular interest is an axiomatic characterization due to Nielsen (1983). There the egalitarian solution is axiomatically characterized using an assumption called independence of Common Monotone Transformations (ICMT). Our objective in this paper is to provide a simple diagrammatic (yet completely rigorous) proof of the same result, when the feasible sets of attribute vectors are assumed (in addition to those essentially available in Nielsen (1983) to be strictly convex.