We study government coalition formation in parliamentary systems. As a basis for our contribution, we consider a set of empirical assumptions formulated by Gamson in 1961, namely, Gamson's Laws, which remain at the heart of government formation forecast. Yet, predictions based on Gamson's Laws rarely point to a correct coalition structure and are limited in their ability to predict the power distribution within a government coalition, especially in the case of smaller parties. While the critical resource postulated in Gamson's approach is the percentage of votes obtained by each political party, other versions of Gamson's Laws can be derived based on a different choice of critical resource. We model the coalition formation process as a cooperative game, and provide axiomatic foundations for a version of Gamson's Laws in which the critical resource is identified as strategic influence, as measured by the Shapley value (Shapley, 1953). We compare the empirical accuracy of forecasts based on the resulting Gamson-Shapley theory versus the original Gamson's Laws for a panel of twenty-five different countries in the two most recent election cycles. We find that the Gamson-Shapley theory leads to a significantly more accurate results both in terms of predicting a correct coalition structure and power distribution within a winning coalition.