Bargaining between political parties over the allocation of cabinet seats in parliamentary coalitions has received attention from political scientists for over 50 years. For one, coalition bargaining is substantively important, as it determines the power distribution in many governments around the world. Additionally, it is an almost ideal situation to empirically test formal theoretical bargaining models. And yet, one of the most accurate and reliable “laws” in political science is Gamson’s law (GL), a naïve prediction, ignoring any and all strategy. According to GL, established by sociologist William Gamson in the early 1960s, political parties ought to receive a share of cabinet seats proportional to their parties’ legislative seat share in the coalition.
While the empirical regularity with which Gamson’s law is observed is extraordinary, we see several contradictions between theoretical models of cabinet formation and the empirical testing thereof. First, if parties are interested in maximizing cabinet seat shares, coalitions should always be minimum-winning, i.e. hold the smallest legislative seat total that is also a majority. This, however, is not true empirically. Second, based on their seminal bargaining model, Baron and Fehrejohn (1989) come to the conclusion that while 1) ex ante parties should receive cabinet seats according to GL; 2) ex post the formateur of the coalition should receive more cabinet seats than their legislative seat share would predict. In extensions to the original Baron-Fehrejohn model, Ansolabehere et al contend that what ought to determine parties’ bargaining power is not their raw legislative seat share. Instead, to capture actual bargaining power, one ought to focus on the number of winning coalitions a party can help form, calculated as minimum integer weights (MIWs). Furthermore, Ansolabehere et al argue that the coalition formateur should recive additional cabinet seats, which they empirically determine, ex post, as higher cabinet seat share for the prime minister’s party. Summarizing the literature in the words of Anne Bassi (2013): “the most important empirical law in government-formation studies is that coalition partners share cabinet portfolios in proportion to their relative seat shares, which contradicts the predictions of the entire theoretical literature.”
In our article, set to published in the British Journal of Political Science in the January 2016 issue, we argue that part of these contradictions are due to the divide between the formal theoretical literature of bargaining and the empirical models used to test the theoretical predictions. In line with the Empirical Implications of Theoretical Models tradition in political science, we examined how well bargaining models describe actual outcomes in coalition systems. Specifically, we use a statistical approach that includes all parties that, ex ante, could potentially be part of a government coalition. We jointly model whether parties become part of the coalition and if so, what their resulting cabinet seat share is. In addition, we specify a sampling strategy that ensures that our results are not driven by countries with a high likelihood of government breakdown, which results in a high number of coalition bargaining situations.
Given our joint model of a party’s cabinet inclusion, as well as cabinet seat share, we can evaluate the effect of the independent variables with respect to both outcomes. We find that the minimum integer weights (based on the number of coalitions in which a party could be the pivotal partner) are a better predictor than raw parliamentary seats shares when it comes to the party’s inclusion in the coalition. This is in line with the argument by Ansolabehere et al, however, we find no evidence of a formateur effect. On the other hand, conditional on being in the coalition, raw legislative seat shares are a much better predictor of the actual seat share in the cabinet, than are the MIWs. In addition, we show that if bargaining is more complex (more than eight parties in the parliament), the estimated effect of theoretical voting weights (MIWs) on a party becoming a coalition partner is much smaller, and raw legislative seat share becomes more important. Thus, the complexity of the bargaining process matters for what determines bargaining success.
In a nutshell, our results mean that theoretical voting weights give parties more power to establish themselves as coalition partners. Further, conditional on a party being part of the coalition, the parties’ raw seat share in parliament is a much better predictor of their cabinet seat share than are the theoretical voting weights.
What are the lessons from this research? We believe that our findings point to new empirical regularities that raise challenges for current theoretical models of coalition bargaining. Developing a rigorous theoretical model of government formation that can explain these findings is one of the next steps we see going forward. Secondly, we believe the joint modeling of cabinet formation and distribution of seat shares is an important contribution. In many ways, the processes we are interested in as political scientists are not independent from each other and thus ought to be modeled as such. Future empirical work on this topic, for example, should take the bargaining over policy spaces into account. This has been largely ignored to date, but is clearly part of the bargaining process and must be part of future empirical and theoretical models of government formation.