A coalitional ranking describes a situation where a finite set of agents can form coalitions that are ranked according to a weak order. A social ranking solution on a domain of coalitional rankings assigns a social ranking, that is a weak order over the agent set, to each coalitional ranking of this domain. We introduce two lexicographic solutions for a variable population domain of coalitional rankings. These solutions are computed from the individual performance of the agents, then, when this performance criterion does not allow to decide between two agents, a collective performance criterion is applied to the coalitions of higher size. We provide parallel axiomatic characterizations of these two solutions.
Journal of Mathematical Economics, 102, 102738
Coalitional rankings, Converse consistency, Individual performance, Lexicographic criteria, Path monotonocity