To the OP’s question, it’s apparently pretty difficult to build a stable democracy. Most of the stable democracies we have came about under different circumstances. You can probably group a few of them together, like Canada, NA and Australia followed roughly similar paths, but most of the other ones had unique historical (and often violent) developments on their way to democracy.
But, with regard to Iraq, our State department had a lot of institutional knowledge on how to go about nation building, and actually had plans and recommendations for what to do in Iraq. These plans were ignored because of the ideology and the cronyism of the Bush administration.
But, here’s what I would have done:
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Float the Iraqi government while slowly transitioning it into a democratic one. This means everyone gets their paychecks. That includes the military and it includes state-run industries. If I’m getting a paycheck from the government, I have a pretty big incentive not to mess with the government.
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Allow most Baath party members to participate in the economy – maybe after a Truth and Reconciliation council. Because if the government is excluding me from the economy, I’ve got a pretty big incentive to mess with the government.
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Give each Iraqi over the age of 18 a fixed payment each month. This payment would be reduced by the amount of violence in the country. The more violence, the lower the payment. The payment would be in a hard currency, like dollars. After a period of 10 years, the payment would taper off. And thus, the payment incentives Iraqis not to participate in violence.
What I find funny (in a sad way) is that for all the Bush’s administration’s talk about capitalism, they seem not to have understood one of the basic assumptions of capitalism, which is that people respond to incentives. If you don’t want people fighting your transitional government, then create concrete, tangible, monetary incentives for them not to do so.
All of that would buy you time to transition the government and the economy into – well, I would pick a Scandanavian model, but at the end of the day, the Iraqis would have to decide what the model would be. In the meantime, you need to create various institutions that a democracy requires, such as an independent press or an independent court system (there’s a whole list of these, and I have my own opinion about what should be on the list, but that will blow out the post).
And then, finally, as suggested above, I would have split Iraq into a federation of 3 countries, with options for independence, but with guaranteed protection of minority rights. I would have set up an assistance program for anyone who wanted to move from a country where they were in the minority.
There’s some ancillary stuff also, like expanded visa allocations for Iraqis that I would have done, but this is the gist of it.