Coalitions (Second Edition)

April 25, 2020

Halfway through my posts on the second edition of Formal Models of Domestic Politics, I am reaching the finish line for the manuscript itself. If all goes as planned, Cambridge will have the draft by next weekend. If you are reading this post, you might be reading the manuscript itself in a few weeks. Thank you in advance for your comments!

One of the joys of writing, and now rewriting, this book has been discovering papers that otherwise I might not have known. This is perhaps especially the case for the literature on legislative bargaining and coalition formation, which is not an area in which I have worked. I remember writing the first edition and discovering this amazing paper by Hülya Eraslan that showed that, notwithstanding the multiplicity of equilibria in the Baron-Ferejohn bargaining model, any stationary equilibrium (given particular recognition probabilities and discount factors) generates the same vector of expected payoffs. This is a remarkable result with great potential for applied work, where one might want to "plug in" a legislative bargaining game to proxy for the stakes in some contest for political power.

My reaction upon stumbling across a recent paper by Vincent Anesi and Daniel Seidmann was more bittersweet. The Baron-Ferejohn model that Eraslan examines assumes that bargaining is once-and-for-all: there is just one pie to be divided. In many contexts, however, a budget is negotiated annually or biannually, with the outcome in one period the default in the next. (I discussed a similar environment in my post on veto players last month.) Anesi and Seidmann show that, in this setting, most anything can happen in equilibrium. Contra Riker, winning coalitions may be more than minimal; in some equilibria, everyone gets a piece of the pie. Even more surprisingly, in period after period, some of the pie may be left on the table. (I have a hard time envisioning this with rhubarb pie, but appeals to welfare maximization will not get you far in this environment.) This is an "anything goes" result more typical of equilibria with history dependence, but Anesi and Seidmann work in a world of stationary strategies. It is a brilliant paper that fits naturally in the chapter on coalitions. It is a disappointing result, if you were hoping for predictive power similar to that of the Baron-Ferejohn model.

As with other chapters, I use the exercises to present related work. There is so much that could be included here; I have a long list of ideas for future exams. For the moment, I have stopped at two new exercises--one based on Maggie Penn's model of farsighted voting, in which the status quo is endogenous but broad societal forces rather than legislators drive the agenda, and one on Craig Volden and Alan Wiseman's model of bargaining over public and private goods. If I include any more, I will be past my deadline and over my page limit.