A Model of Government Formation with a Two Dimensional Policy Space

Given any allocation of parliament seats among parties, we characterize all the stable government configurations in terms of winning coalitions and policy outcomes. We consider a two dimensional policy space and we assume that there are four parties, none of which has a majority of the seats, that care mainly about holding office, and only instrumentally about policy. We also assume that to form a government it is necessary to have the support of a majority of the parliament. 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.