Some remarks on properties for choice functions

In this paper, we present five categories of results by studying the interr elationships be tween properties for choice functions. The first category i s about the localization assumption. The second category is about the relat ive egalitarian solution. The third category provides an axiomatic characte rization of the equal loss solution. The fourth and fifth categories consis t of lexicographic extensions of the equal loss and relative egalitarian so lutions respectively.