Gamson-Shapley Laws: a formal approach to parliamentary coalition formation

We consider a set of empirical assumptions formulated by Gamson (1961), namely, Gamson's Laws, which remain at the heart of government formation forecast in parliamentary systems. While the critical resource postulated in Gamson's approach is the proportion of votes received by each party, other versions of Gamson's Laws can be defined by a different choice of critical resource. We model coalition formation as a cooperative game, and provide axiomatic foundations for a version of Gamson's Laws in which the critical resource is identified with strategic influence, as measured by the Shapley value. We compare the empirical accuracy of the resulting Gamson-Shapley theory against the original Gamson's Laws in a panel of 33 parliamentary elections, and find that it leads to significantly more accurate predictions of both coalition structure and power distribution. Finally, we propose an extension of the Gamson-Shapley approach which also incorporates information about policy distance among coalition partners. In particular, we discuss the advantages of the extended approach in the context of the German elections in 1987 and 2017.