It is well known that proposers have an advantage in the canonical model of bargaining in legislatures: proposers are sure of being part of the coalition that forms, and, conditional on being in a coalition, a player receives more as a proposer than as a coalition partner. In this paper I show that, if parties differ in voting weight, it is possible for a party to donate part of its proposing probability to another party and be better-off as a result. This can happen even if the recipient never includes the donor in its proposals. Even though actually being the proposer is valuable, having a higher probability of being proposer may be harmful.
legislative bargaining weighted majority games voting paradoxes