Paths to stability for overlapping group structures

We study the stability of overlapping group structures where 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. We provide a necessary and sufficient condition on preferences that guarantees the existence and the emergence of constitutionally stable group structures. We show that although more blocking power for the individuals might enlarge the set of constitutionally stable group structures, it could happen that the society will never reach a stable group structure.