Majority Rules and Coalitional Stability

The aim of this note is to discuss previously unnoticed stability properties of majoritarian decision making. We study collective decisions problems that can be described in terms of symmetric games satisfying various regularity conditions. We show that restricting the objecting power to majoritarian coalitions guarantees the existence of core-stable allocations, independently of the assumptions on the behaviour of players in the minority. We also show that if majorities can extract resources from minorities, stability may require a supermajority rule, whose threshold is increasing in the extraction power