The prettiest Iraqi woman I know told me recently that election day here was "orgasmic." It certainly started with a bang for me, as a mortar shell landed at about 7:30 am not far from where I was living in Sadr City. As I walked the streets, the voting was especially brisk between eight and nine in the morning, and then it appeared to tail off in the late morning.

There was the usual violence in my neighbourhood: a car bomb that killed three people, four mortar shells, sporadic gunfire popping away. By noon, the morning's eager tone seemed to me to have been replaced by nerves. The prospect of failure and prolonged uncertainty felt on the verge of tipping the balance of confidence and keeping the lazy or doubtful at home.

In Sadr City, according to numerous conversations I have had among Muqtada al-Sadr's inner echelon, a call had gone out from the young cleric's headquarters in Najaf that prominent clerics and Mahdi army soldiers were to make themselves seen to be voting. In that huge Shia slum, and elsewhere in Baghdad according to friends I have spoken to, the floodgates burst halfway through the day when people saw that friends and neighbours had had the courage to vote.

By the time the polls closed, at 5pm, the city was stretching smugly out for its post-coital smoke. I walked for miles. There was no traffic for once, so football games were going on everywhere. The cops who in the morning had terrified me with their nerves were now relaxed, and that relaxed everyone else.

The violence, in fact, seemed to spur voters on. There is a fine defiance here. In one incident I did not see but that has been widely reported, a Baghdad policeman spotted a suicide bomber outside a polling station and dragged him away from the crowd before the bomber detonated his belt, killing them both. The queues rose tenfold as the story of the policeman's martyrdom spread.

Iraq is not about America any more. This has been increasingly true every day since last June, and the failure - or refusal - to recognise this has underpinned much of the misleading coverage of Iraq. In the evenings leading up to the election, I sat on carpets on the floors of a variety of shabby houses in the Baghdad slums. But the daily BBC message I watched with my various Iraqi hosts never budged. The refrain was Iraq's "atmosphere of intimidation and violence," and the message was that the elections could never work. What about the "atmosphere of resolve and anticipation" that I felt around me? Or the "atmosphere of patience and restraint" among those whom the terrorists were trying to provoke?

I try to avoid the hotels and the green zone and the Fort Apache press compounds when I am here. Sometimes it seems as though I am on a different planet from my colleagues in big media, and at those moments I worry briefly that I am getting the story wrong. The people at NBC news are not even allowed to go to the restaurant in their hotel. They report from the roof. When I went to the BBC's Baghdad bunker for some interviews after the election, the reporters I had been watching on television asked me, "So what's it like out there in the real world?" They meant the Iraqi street.

Before I became a writer, I dealt in the stock and bond markets. The markets tell you every day whether you are right or wrong. You don't have to have philosophical arguments with your boss or your clients: if you make money you are good, and if you lose money you are bad. Elections are one of the few news occasions that provide editors and reporters with the clarity of numbers to help us to judge whether or not we are doing a decent job. January 30th turned out to be a better day for Iraqis than it was for reporters.

The failure of "hotel journalism" might be forgivable if it were truly about prudence or even laziness. But there has been something wilful about the bad reporting of this story. It is weirdly personal: Iraq must fail. It is in fact the press that failed, on a scale for which I cannot think of a precedent. Will the big media outlets demand the same accountability of themselves that they demand of everyone else? They should, for the success of these elections was not so surprising to those who dug below the surface of Iraq.

One reason it was important that this year's electoral process should start well was that if this first stage were approached with resolve, as it was, Iraq's political outsiders would not want the train to leave the station without them. Iraq's biggest, loudest anti-occupation political movements have indeed reacted encouragingly to the success of 30th January.

With a monopoly over the most potent force in Iraqi politics, the Shia street, the al-Sadr movement holds the country's future in its hands to a greater extent than any other radical group. Al-Sadr is sending at least 20 followers to the new national assembly. These people are not window dressing for the Shia establishment. They have each signed declarations saying that they will follow Muqtada's bidding.

The two political groups closest to the Sunni insurgency, the Association of Muslim Scholars and the Islamic party of Iraq, are also participating in Iraq's political process. The former is one of 13 Sunni groups - many of which boycotted the election - to have agreed to take part in drafting Iraq's new constitution, the main job of this new assembly. The Islamic party has announced, "We should respect the choice of the Iraqi people. The drafting of the constitution is a very important issue for all Iraqis. We will have a role." The Shias are already making sure that the Sunnis are well represented in top jobs and on the constitutional drafting committees.

The huge turnout has cemented the new Iraqi state as an accomplished fact, and Muqtada and the radical Sunni political groups have shifted their rhetoric to make demands within the new paradigm. It is a momentous shift. No longer is everything illegitimate. Now the conversation is about governing, rather than about the illegality of the state. Here is al-Sadr, for example, soon after the poll: "I call on all religious and political powers that pushed towards the elections and took part in them to issue an official statement calling for a timetable for the withdrawal of the occupation forces."

This from the passionate cleric who used to say his men would not stop fighting in Najaf "until the last drop of our blood" had been spilled, and that while the occupier remained in Iraq no government was acceptable. A process has been unleashed that now has very little to do with America and with our opinions about US power. The process is in the hands of a people who on 30th January showed that they have what freedom requires: deep reserves of patience, tolerance and courage.