This paper discusses whether the equilibrium of a popular formal bargaining model due to Baron and Ferejohn (1989) satisfies the postulates that Felsenthal and Machover (1998) consider essential in any power measure. It is well known that the equilibrium does not satisfy two adequacy postulates, namely ignoring dummies and vanishing only for dummies. This paper shows that it does not respect dominance either. It is also argued that the equilibrium displays one of the less intuitive instances of the paradox of new members.
Montero, M. (in press). Postulates and paradoxes of voting power in a noncooperative setting. In Voting Power and Procedures: Essays in Honour of Dan Felsenthal and Moshé MachoverSpringer. doi:10.1007/978-3-319-05158-1