The paper considers a very simple collective decision problem: The partition of a pie of size 1 among n agents. This is a social choice problem of maximal conflict with possibilities to compromise. It is thus a case which is 'unsolvable' by social choice theory, a case where the core of majority voting is empty. We consider a specific sequential decision institution for this problem: An agent proposes a possible alternative, and then the agents vote yes or no to this proposal. If the proposed partition is accepted according to the majority rule, the process stops, if not, another agent proposes another alternative and the agents vote again ... etc. until a partition is accepted. We assume that this process takes time, and that the agents prefer a quick decision and thus discount pie received in the future. The model can be regarded as a majority version of the Herrero (1985) n-person bargaining model. Subgame perfect stationary equilibria of the model are studied. The main result is that the first proposer has a large advantage, in particular if the order of proposing is fixed.
