Coalition Provisional Authority advisor Larry Diamond tries to explain, in Foreign Affairs:
"It now seems unlikely that the weak and besieged new Iraqi government will have the will or capacity to enforce the demobilization plan. In fact, the new Iraqi state is caught in a Catch-22: to be viable, it must build up its armed forces as rapidly as possible. But the readiest sources of soldiers and police are the most powerful militias, which will probably allow their fighters to join the new military only if their command structures remain intact. Thus, if the fledgling Iraqi state hopes to truly defeat the militias, it may have to go to war with itself. That seems hard to imagine. Yet if Iraq tries to hold elections while the militias remain intact (in one guise or another), the campaign is likely to become a very bloody and undemocratic affair. Candidates will face assassination, weaker political opponents will be run out of town, and the electoral machinery will be hijacked by those with the most guns.
"Even if the security situation improves enough to allow elections to go forward on time, Iraq could still get into further trouble if it follows the UN's recommendation and uses a national-list system, apportioning seats in parliament on the basis of nationwide voting, since this would give the big regional and religious parties an added incentive to inflate their numbers through force and fraud. Should that occur, the biggest winners will be the best-armed and most-organized forces-the Kurds in the far north and the Iranian-backed Islamist parties in the Shiite south. The American occupation could wind up paving the way for the 'election' of an Iranian-linked Islamist government in Baghdad."
