Consistent social ranking solutions

The performance of coalitions is an important measure for evaluating individuals. Sport players, researchers, and firm workers are often judged with their team performances. The social ranking solution (SRS) is a function that maps the ranking on the set of all feasible coalitions (the domain of coalitions) into the ranking of individuals. Importing the axiom of consistency from voting theory, we study consistent SRSs under the variable domains of coalitions. We suppose that there are several domains of coalitions (e.g., a set of research teams made up of only young researchers and a set of research teams including senior researchers), and the individuals are required to be evaluated consistently on each domain of coalition. Such a situation is typical because all the logically possible coalitions are often too huge to deal with. We obtain a new characterization of the lexicographic excellence solution (LES) and its dual (DLES): they are the only SRSs satisfying consistency, neutrality, weak coalitional anonymity, and complete dominance. This characterization is expected to provide a new ground for determining the impacts of individuals based on the lexicographic comparisons of their team performances.