In previous posts, I began to describe the changes to my textbook on Formal Models of Domestic Politics, with a second edition planned for next year. Most of those changes involve new material: additional models and exercises, a new chapter on nondemocracy. There are, however, a handful of clarifications—small edits suggested by eagle-eyed students at UW and instructors using the textbook elsewhere, but also one big one in the chapter on regime change. A large portion of that chapter is devoted to the Acemoglu-Robinson model of regime change: an important theoretical framework in its own right, and also an opportunity to teach Markov games and the associated solution concept, Markov perfect equilibrium. Unfortunately, there was an error in the analysis, which nobody seemed to catch until Acemoglu and Robinson posted a correction in 2017.

I discussed this correction shortly after it first circulated. I wrote then:

Daron Acemoglu and Jim Robinson recently posted a correction to the key proposition in "Why Did the West Extend the Franchise? Democracy, Inequality, and Growth in Historical Perspective," the seminal paper in what has proven to be an enormously influential research enterprise. That proposition characterizes equilibrium in terms of the parameter q, which measures the probability of future unrest in an undemocratic regime. When q is large, then promises of future redistribution are fully credible and democratization is unnecessary, whereas when q is small the elite democratize to prevent revolution the first time that the poor pose a credible threat of unrest.

Those results still hold in the corrected proposition, but it turns out that for intermediate values of q, the unique equilibrium is in mixed strategies: the elite democratizes with probability strictly between zero and one, and revolution occurs on the equilibrium path. Technically, this correction is driven by a failure in the original analysis to check for all possible deviations. Substantively, the issue arises because institutional change in the Acemoglu-Robinson model is treated as a discrete choice: democratize/not. This discreteness implies that democratization, when it takes place, leaves the poor with strictly more than their payoff from revolution, thus creating scope for the deviation that Acemoglu and Robinson discuss in their correction.

The basic idea, as I wrote in a subsequent paper with Paul Castañeda Dower, Evgeny Finkel, and Steven Nafziger, is that

[O]ffering maximal redistribution whenever the poor pose a credible threat of unrest, holding constant the elite's equilibrium strategy to extend the franchise the first time that the poor subsequently have de facto political power…is profitable to the elite if the poor respond by not revolting. That this may be possible in principle follows from the fact that democratization only works as a commitment device when the value to the poor from democracy, in which distribution is maximal in every period, is greater than that from revolution. If the poor are sufficiently patient, maximal distribution in the current period, while deferring franchise expansion to the next time that the poor post a credible threat of unrest, is sufficient to prevent revolution.

As I also overlooked this, the main text and a couple of exercises in Formal Models of Domestic Politics required correction. Done. And making lemonade out of lemons, there is some pedagogic value in the revised discussion. In my experience, the one-deviation property is typically not learned on first exposure. What better way to illustrate its application than to walk through a deviation sufficiently subtle that it was missed for nearly twenty years?

What else? Well, the reason I knew about this correction is that Evgeny discovered it just as our article on "Collective Action and Representation in Autocracies" was going to press. In that paper, by way of setting up the empirical work, we generalize the Acemoglu-Robinson model to allow for a continuous institutional choice, which serendipitously—and instructively—sidesteps the issue discussed above. There is a brief discussion of that in the second edition of Formal Models of Domestic Politics. I also riff a bit on equilibrium multiplicity in "global games," building on work by Mehdi Shadmehr and Ethan Bueno de Mesquita, and I provide a couple of new exercises. But mostly the revisions to this chapter—in contrast to all other chapters in the text—are about fixing what was previously incorrect.