Tyler Cowen suggests a simple model, I’ll explain and elaborate a bit below the fold.
Dictatorships are generally most brutal when the fear of being overthrown is strongest. The most benevolent dictatorships, in relative terms, tend to have strong roots in the country’s social and economic power centers. This would help explain, for instance, why the minority Sunni Saddam Hussein was so tyrannical against his potential opponents. Without extreme oppression, he would have lost power and his life.
The optimistic scenario for Iraq was (way back when) that a Shiite autocracy, with broad-based public support, would be considerably less brutal. Once in power, the ruling clique would find it much easier to stay in power without extreme brutality. At least that is how the theory went. [...]
The pessimistic scenario is that there are no broad-based constituencies left, or perhaps there never were any in the first place. Under the former case American policy has been far more harmful, in net terms, than under the latter case. It is possible that our handling of the transition disbanded whatever broad-based groups were in place to eventually rule. Or perhaps Saddam had already destroyed them.
One good reason to think Iraq better-fits the pessimistic scenario is simply that the Shiite Arab majority group in the population is a quite narrow majority. The country is only about 60 percent Shiite Arab. Thus, insofar as there are any significant cleavages within the Shiite bloc, even the broadest possible political group is going to be pretty narrow — i.e., less than a majority. Importantly, from this point of view, members of Muqtada al-Sadr’s movement killed Mohammed Bakir al-Hakim (leader of the Supreme Council for the Islamic Revolution in Iraq) very early on in August 2003. This sort of major intra-Shiite fighting precludes the construstion of any governing coalition with a genuinely broad base of support and it happens so soon after the invasion that it suggests it reflects pre-existing conditions rather than the upshot of US policy choices.
This suggests that any collapse of the Baath regime, whether or not precipitated by direct US military intervention, was likely to lead to a fairly bloody outcome as divergent minoritarian movements (pre-war, at least, some non-trivial segment of the Shiite Arab population was largely secular) among Iraq’s Arab communities contending for power while the two Kurdish groups competed with each other for control of Kurdistan while seeking to maximize that region’s autonomy.