We provide a general theory of collective decision making one that relates
social choices to the strategic incentives of individuals, by generalizing
the Baron-Ferejohn (1989) model of bargaining to the multidimensional spati
al model. We prove existence of stationary equilibria upper hemicontinuity
of equilibrium outcomes in structural and preference parameters, and equiva
lence of equilibrium outcomes and the cove in certain environments, includi
ng the one-dimensional case. The model generates equilibrium predictions ev
en when the cope is empty, and it yields a "continuous" generalization of t
he core in some familiar environments in which the core is nonempty. As the
description of institutional detail in the model is sparse, it applies to
collective choice in relatively unstructured settings and provides a benchm
ark for the general analysis of legislative and parliamentary politics.