Voting Weights and Formateur Advantages in the Formation of Coalition Governments

Over the last two decades a large and important literature has emerged that uses game theoretic models of bargaining to study legislative coalitions. To test key predictions of these models, we examine the composition of coalition governments from 1946 and 2001. These predictions are almost always expressed in terms of parties' minimal-integer voting weights. We calculate such weights for all parliamentary parties. In addition, we develop a statistical model that nests the predictions of many of these models of the distribution of posts. We find that for parties that join (but did not form) the government, there is a linear relationship between their share of the voting weight in parliament and their share of cabinet posts. The party that forms the government (the formateur) receives a substantial "bonus" relative to its voting weight. The latter finding is more consistent with proposal-based bargaining models of coalition formation and suggests that parties gain disproportionate power not because of their size but because of their proposal power.