Common ranking and stability of overlapping coalitions

Mauleon, Roehl and Vannetelbosch (GEB, 2018) develop a general theoretical framework to study the stability of overlapping coalition settings. Each group possesses a constitution that contains the rules governing both the composition of the group and the conditions needed to leave the group and/or to become a new member of the group. They propose the concept of constitutional stability to study the group structures that are going to emerge at equilibrium in overlapping coalition settings. They combine requirements on constitutions and preferences for guaranteeing both the existence and the emergence of constitutionally stable group structures. In this paper, we show that an alternative way to exclude the ocurrence of closed cycles is to look for constitutions that allow for a common ranking.