The Iraqis were voting about the proposed new constitution in an unusually peaceful atmosphere. The constitution would make Shiites and Kurds stronger, and therefore the areas dominated by these two groups were expected to vote "Yes".
More generally, the constitution is another step towards the independence of Iraq because it would replace the provisional, U.S.-controlled constitutional laws, and therefore it should not be too surprising if many anti-American people voted "Yes", too.
What do the results look like? The official final results are not available so far. The turnout was high and the national count will show a convincing "Yes" vote. However, there is a rule that if in at least 3 out of 18 provinces more than two thirds of the voters vote "No", the constitution is rejected.
The "No" vote was expected in the provinces where the Sunni Arabs have a majority - especially Ninevah and Diyala. However, unless there has been some kind of fraud in these areas, they voted "Yes"! However, there are two provinces - western Anbar around Fallujah and central Salahuddin - which have already voted a clear "No". The question is whether a third province will join these two.
If the constitution passes, it will be most importantly a victory for the Iraqi people. Second of all, it will be a victory for people like Noah Feldman. Noah - a full professor of law at N.Y.U. - who is now generally accepted to be a rising legal star was a Junior Fellow in the Society of Fellows until 2003 and was chosen by the Bush administration to be the main U.S. brain behind the creation of the new Iraqi constitution. My understanding is that Noah is actually a de facto author of the current provisional laws only, but I guess that he will feel happy if his laws are superseded by a more authentic constitution.
Imagine: Noah who is an American Jew and a Democrat is sent by the G.O.P. administration to Iraq where he had to work with the Iraqis and more or less dictate them how their new crucial document should look like. I must say that I am impressed already by the very fact that they have not killed him (and also grateful, of course). Noah believes that democracy is compatible with Islam, he wrote a book based on this (controversial) basic idea, and it was one of the reasons why he was viewed as an authority. The developments in Iraq have so far been less encouraging than what I have hoped for (and what Noah has hoped for, I think), but all these things may improve substantially in the very near future.