Anarchy has several meanings; and when I talk about it as a political thing (anarcho-capitalism, or just anarchy), I mean a stable system of governance where there is no ruler - an (without) archos (ruler). Here I take ruler to mean, in essence, the State: someone asserting a territorial monopoly on legitimate violence. Unless you have unanimous consent to such a thing, it is illegimate. And given what people are, you never will get unanimous consent to any ruler in a group larger than a few hundred.
The anarchy we are seeing in Iraq is the common meaning of anarchy; I sometimes distinguish it as "mere" anarchy following Yeats. Mere anarchy is certainly a form of anarchy; there is no state. However, neither is there government of any kind.
We aren't hearing about the non-city parts of Iraq; and there are two reasons for that. One is, the reporters are where the people are. The other is, that in the country people are probably much better behaved. They are not anonymous; they know their neighbors. There is probably some score-settling going on, but it will be minor compared to cities.
The cities combine lack of rules, anonymity, and large amounts of loosely defended persons and property; this is a recipe for a tragedy of the commons. Obviously this is bad. Mere anarchy is extremely unstable; within days or weeks at most, government of some kind will evolve. People hate random looting and violence, and where supply fails to meet demand, entrepreneurs will create supply. That's what we are starting to see.
What we are seeing in places (like Saddam city in Baghdad) is the evolution of protection agencies, or mini states. Unfortunately, the only models they have (or we have, really) for how to provide policing are monopoly models. So that's what they are likely to build. It is as if the US had a war where all the teachers were driven off and the schools blown up; in spite of the chance to build something new and different, we'd probably just rebuild the same old daycare prisons in spite of the fact that we know they don't work.
In Iraq, we are seeing the very fascinating process of the evolution of anarchy. It starts with the Hobbesian state of nature. It is every man for himself. Well, every man for himself and his family, and friends, anyway. Human ties exist in the state of nature. Having arms is vital (and we are hearing lots of stories about merchants with kalishnikovs; even hiring a man to help them). We are also seeing some assertion of authority by the US and Britain; but they will be unable control the situation because they are not natives. Government requires, among other things, particular knowledge of the people, and the ground, which occupying armies simply don't have. What is working is the religious leaders organizing protection. This is to be expected; the mosques were the only social organizations of any significance allowed outside of the Ba'athist state. So the imams are the only leaders with any authority. Thus they must serve as the nuclei around which government crystalizes. Leaders who choose not to organize protection groups will see others gaining political power.
We should expect to see the religiously organized militias evolving into police. They will, likely, impose Sharia, perhaps not completely but largely. They will certainly evolve a state, probably an Islamic one.
There is a good reason why mere anarchy never seems to evolve into anarchocapitalism: people are territorial by nature. We properterize stuff, mentally, even things that are not really ours. My girlfriend is mine. My job is mine. My apartment is mine. My little piece of the highway is mine. My country is mine. If you think on it, none of these things is owned by me. Yet I will react emotionally if I am deprived of them, as if there really was some sort of legal title to them. Property is a natural, innate concept to humans.
The case in point is protection agencies: unless they are ideologically motivated not to evolve into states, they will, very naturally. Or to put it another way: policemen in the anarchic state will start to feel territorial about the things they protect. Then they will evolve a state.
This, too, will happen in Iraq. It is likely to lead to fighting, probably not to the level of civil war, but very nasty. I can imagine a civil war breaking out if the Arabs try to rule the Kurds, or if the Sunni try to rule the Shiites or vice versa; but hopefully this won't happen due to fairly clean geographic separation between the various groups.
What would it take for mere anarchy to evolve into anarchocapitalism? I don't know for sure. I think it would help if the territory in question was sparsely settled including having few cities. It would help for the people involved to have a strong anti-state tradition. They should resent being ruled. And it would help if the people had different ideas about legal traditions, perhaps because they are all immigrants. (These things seem to have been true in Iceland, to my knowledge the only functioning anarchic government the world has seen.) The biggest helping factor would be if the people had previous experience with anarchocapitalism, and had thus internalized the idea that statism was an immoral idea, much the way that Americans understand the right to free speech.
I don't think it is likely that the first modern anarchocapitalist society will evolve "upward" from a situation of mere anarchy. Rather I think it will evolve downward in a liberal society, when the statist centers fail to hold. (Yeats had some good lines.)
UPDATE - check this out:
Muslims poured out of mosques and into the streets of Baghdad, calling for an Islamic state to be established, after the first Friday prayers since U.S. forces took control of the Iraqi capital.As predicted.