Actually, democracy should work very well in this situation. Not a carving up of the country like Yougoslavia.
Democratic ideals are secular, non-religious. If democracy could have been really implemented, it would be great.
What has happened in Iraq recently is not democracy.
Kaijjakati between religions and sects within the same religion always amount to Ghorar Dim.
Of course, personally, I think the whole religion thing is a big osshodimbo. But that's a different topic.