Party formation and coalitional bargaining in a model of proportional representation

We study a game theoretic model of a parliamentary democracy under proportional representation where ideologically motivated citizen groups form parties, voting occurs and governments are formed. We study the coalition governments that emerge as functions of the parties' seat shares, the size of the rents from holding office and their ideologies. We show that governments may be minimal winning, minority or surplus. Moreover, coalitions may be 'disconnected'. We then look at how the coalition formation game affects the incentives for party formation. In particular, we show that when the rents from office are low, the median citizen stands unopposed, and when rents are high, there is more political entry. For intermediate rents, we show that strategic dropouts can happen to influence the final policy. We show that the incentives for strategic dropout can be higher under proportional representation than plurality voting, contrary to Duverger's law. Our model explains the diverse electoral outcomes seen under proportional representation and integrates models of political entry with models of coalitional bargaining.