Elections, Legislative Outcome, Coalition Formation and Government Stability

In his book ‘ The theory of Political Coalitions’, Riker (1962) introduces the theorem of minimal winning coalition, a game theoretic approach in which rational agents are proved to form coalitions that minimal winning. Mathematical evidence of this theorem have been provided by Austen-Smith and Banks (1988). In this paper we extend Austen-Smith and Banks’ model such that, at the legislative coalition formation stage parties take positive externalities, expressed in terms of government stability, of having a broad coalition into account. We then examine the robustness of the minimal winning coalition theorem for this modification. We show that a slight modification of the Austen-Smith and Banks´ three party model may result in a different composition of the coalition in equilibrium and predicts that it is certainly not always that the largest and smallest parties that form a government coalition in equilibrium. We also show that, if individuals preferences are quadratic on policies, large coalitions are more preferable. Moreover, our extension is simple to incorporate in existing models and allows us to predict government stability for any coalition.