Some unpleasant bargaining arithmetic?

It is commonly believed that voting rules that are relatively more inclusive (e.g., unanimity or supermajority), are likely to yield relatively more equitable outcomes than simple-majority rule. We show that this is not necessarily the case in bargaining environments. We study a multilateral bargaining model à la Baron and Ferejohn (1989), where players are heterogeneous with respect to the potential surplus they bring to the bargaining table. We show that unanimity rule may generate equilibrium outcomes that are more unequal (or less equitable) than under majority rule. In fact, as players become relatively more patient, we show that the more inclusive the voting rule, the less equitable the equilibrium allocations.