IF REPORTS from Iraq yesterday are right, then the polls marked a triumph for the attempt to bring democracy to a large Arab country.

The enthusiasm for voting shown by so many Iraqis is only part of the story. Much more will depend on whether the resulting administration is capable of sharing power between Iraq’s disparate groups.

We can judge that only over the next few months, as the newly elected National Assembly makes its first decisions. It would be foolish to predict that a kind of peace could emerge until those decisions are clear.

But equally, it would be wrong to make too little of yesterday’s extraordinary scenes, which confounded the gloomiest predictions — as did Ukraine and the Palestinian territories recently with their emphatic messages of their people’s desire to choose their own leaders. It is not a prescription for instant peace, but it is a reason for optimism.

First, the qualifications. There is a lot we do not yet know about the conduct of the elections. In particular, we do not know how many in the Sunni-majority areas defied the threat of violence and voted.

But yesterday’s reports, down to the anecdotal level, were hugely encouraging. In Shia-majority areas in the south, it was striking not just how many voted, but how many women turned out too.

In the Sunni areas, there was less violence than on some days in the run-up to the polls. The security operation worked, itself a hugely encouraging sign. And it appears that even in some of the most troubled areas many braved the journey to the polls.

In the past black months one of the few arguments for hope about Iraq’s future has been the eagerness for elections expressed by its people. True, elections do not on their own make a democracy, or a governable State, or hold civil war at bay if parts of the country reject the result.

Nor did the US and the Iraqi Government have much alternative to pushing ahead with the elections. If they had not, the Shia south, which had chosen to keep comparatively peaceful in the expectation of leading the new government, would have had cause to start its own insurgency.

But those constraints do not discount the value of yesterday’s spectacle. It was unequivocally a demonstration of Iraqis’ desire to choose their own future, and the belief by a large number of them that this can be done by voting, not fighting.

It is hard to think that this was not influenced by the recent elections in Ukraine and the Palestinian territories. Their circumstances are different; in the case of Ukraine, the culture is very different.

But the symbolic importance crosses boundaries — and with television coverage, does so very easily these days.

If there was such an effect, it is of course impossible to measure. But such influence, even at a distance, should not be underestimated.

Last May, after the shock of the Indian elections, when the Hindu nationalist BJP party was thrown out against expections, a Saudi official remarked on the effect that this had had in his own country. A decade earlier it would have had no impact at all, but thanks to television, he said, the message from the world’s most populous democracy was impossible to miss.

There have been false “turning points” in Iraq in the past two years. The capture of Saddam Hussein yielded the coalition a boost of confidence, which fell away; the same happened after the transfer of power to the coalition authority in June. But even if there are setbacks in the coming weeks, there is no value in denying that yesterday’s polls marked a huge step forward.

Times Recommends

• 'Great Schlep' may seal deal for Obama
• Hindu 'storm troopers' flex their muscles
• Ahtisaari: deserved reward for (failed) plan