Bicameral Winning Coalitions and Equilibrium Federal Legislatures

Abstract

I analyze the legislative interaction between representatives from big and small states in a bicameral legislature that decides on the allocation of a fixed resource among the states. I assume that the two houses are malapportioned and that the big states are underrepresented in the upper house. By studying the effect of this and other institutional features on the relative welfare of big and small states and on equilibrium coalitions, I find that, contrary to common belief, an increase in the representation of small states may reduce those states' expected payoff, ceteris paribus. Also, contrary to interpretations of minimum‐winning‐coalition theorems, I demonstrate that excess majorities may occur in one of the two houses. When proposal making tends to be dominated by big (small) states, excess majorities occur in the upper (lower) house. I also find that higher proposal power increases the payoff of a group of states. Changes in the majority requirements in the two houses and expansion to encompass more small (big) states have non‐monotonic effects on the relative welfare of the two groups. I conclude my analysis with an empirical application using calibrations results for the 103d U.S. Congress and the legislative institutions of the European Union before and after the Treaty of Nice.“The equality of representation in the senate is another point, which, being evidently the result of compromise between the opposite pretensions of the large and the small states, does not call for much discussion.” James Madison (1788)Time: “Did the battle over the relative weight of big and small countries overshadow more important matters at Nice?”Verhofstadt: “It was absolutely necessary. What they tried to do in Nice was make a directorate of the big countries. The European Union can't survive like that.”Interview of Guy Verhofstadt, Prime Minister of Belgium TIME (2000)