Lexicographic solutions for coalitional rankings

Abstract

In many real world situations, the design of social rankings over agents or items from a given raking over groups or coalitions, to which these agents or items belong to, is of big interest. With this aim, we revise the lexicographic excellence solution and introduce two novel solutions which, moreover, take into account the size of the groups. We present some desirable axioms which are interpreted in this context. Next, a comparable axiomatization of these three solutions is established, revealing the main differences among the two new social rankings and the lexicographic excellence solution. Finally, we apply the three social rankings under study to a real scenario. Specifically, the performance of some football players of Paris Saint-Germain during the UEFA Champions League according to these three rules is analyzed.