Government formation in a two dimensional policy space

Given any allocation of parliament seats among parties, we characterize all the stable government configurations (supported by at least a majority of the parliament) in terms of winning coalitions and policy outcomes. We consider a two dimensional policy space and we assume that there are four parties that care mainly about holding office, and only instrumentally about policy. We find that for any distribution of seats in the parliament only two scenarios are possible: either there is a party that is a member of almost all equilibrium coalitions (dominant party scenario) or there is a party that is never a member of an equilibrium coalition (dominated party scenario). We characterize the key party for each possible scenario and we show that it is sufficient that the key party has intense preferences over one the issues to guarantee the formation of a stable government coalition.