When is an error not really an error?

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.

Models are abstractions from the real world, and at first blush treating democratization as dichotomous seems like a reasonable stylization. In reality, of course, elites choosing to surrender political power to some previously excluded group have a wide range of options available, such that we can think of "liberalization" as a continuous choice—any level of representation between 0 and 1. And generalizing the Acemoglu-Robinson model in this way resurrects the original insight.

Paul Castañeda Dower, Evgeny Finkel, Steve Nafziger, and I recently developed just such a generalization of the Acemoglu-Robinson model, by way of setting up the empirical work in our forthcoming APSR article on "Collective Action and Representation in Autocracies: Evidence from Russia's Great Reforms." As we show in an accompanying note, the equilibrium level of representation granted by the elite in our generalization leaves the excluded group with precisely their payoff from revolution, thus eliminating the incentive for the elite to deviate in the manner that Acemoglu and Robinson identify.

The key empirical prediction of "Why Did the West Expand the Franchise" thus emerges intact from a generalization of the Acemoglu-Robinson model to allow for a continuous institutional choice. Moreover, the prediction itself generalizes. Not only does the elite not "liberalize" when the excluded group poses a frequent threat of unrest, but conditional on some representation having been granted, the equilibrium level of representation is decreasing in the probability of future unrest. This is the prediction that we empirically examine in "Collective Action and Representation in Autocracies."