Back in high school, they always told us that the definition of a "state" was the entity that had the monopoly of power--police/military. I don't disagree with that as a definition. That is why states can act--because they set up laws and can thereby enforce them. And why companies--that may or may not have larger revenues than the governments of the state they are in--cannot.
So why on earth do we tolerate militias in Iraq?
I know the issue is far more complicated, but surely the only real way to stabilize Iraq is to ensure that the national government can project its power and enforce its laws. As it stands now, anyone who gets enough followers and enough guns can effectively defy the state. That doesn't really lead to stability, where any group can ignore laws as it sees fit (particularly when the groups are split along religious or ethnic lines.)
Europe in the 30s would be an instructive example. But then, our current leaders don't seem to care about learning from the past. Or from, say, fact.