Tyler Cowen at Marginal Revolution posts a link to a paper by Victor Menaldo, The Middle East and North Africa's Resilient Monarchs.
It's well worth a read; it's not long, though frankly I'll need to spend more time with it than I have this evening.
First and foremost, it's a challenge to the Bueno de Mesquita theory that all that matters is the size of the ruling coalition and the selectorate — a theory that I found valuable but simplistic. Menaldo addresses political culture, observing that the political culture serves to distinguish regime insiders from outsiders. He finds that monarchical governments have less conflict and better economic development.
Particularly interesting to me is the account of elites within the monarchical society. These kingdoms are not the absolute autocracies of my "degenerate formalism", but actually existing monarchies, in which the extended royal family and other important groups hold significant power. Menaldo's argument is that the fact that the political culture defines who shares in power, the struggles between in-groups are limited. Unlike a faction in a revolutionary republic, you can lose a power struggle and still be an insider with some power.
In my view, this is also the strength of our somewhat corrupted democracies: if you're an insider but you're losing, it's still not worth being extremely destructive. Better to admit defeat and preserve the system that keeps you an insider even as a loser.
Because of that, this paper doesn't really make my argument: it shows that monarchy is better than a revolutionary republic, but not that it is better than a western democracy. Still, it's useful that it's showing some of the strengths that monarchy has.
It's not without weaknesses, either. As with other work of this kind, I don't really take the mathematics seriously. Checking that a statistical analysis bears out the impression you get from drawing a couple of graphs and watching CNN is not what I call verifying a testable hypothesis. And a relatively small data set of somewhat subjective categorisations of events seems inadequate for the amount of analysis being done on it.
Also, the paper, as far as I have seen, does not explore the possibility that foreign influence is the explanation for the difference in violence. Bahrain faced nothing like the outside pressure that Libya or Syria did. I don't think foreign action is affected directly by whether the regime is monarchical or republican, but there might be an indirect link with foreign policy stance.