The US election is big news here, but the rest of the world is rather less excited

Iraq has sobered up this administration, curbing its enthusiasm for reshaping the map of the Middle East

It was an odd experience being in Paris while America voted this week. For all the talk of France's obsession with facing up to Bush and America's determination to put France in its place, there was virtually no sign of interest in the US elections at all. Compared to the acres in the British press, detailing every nook and cranny of the electoral college system, French television and newspapers were taking it as just another story.

It's a point repeated in most of Asia and much of Africa. For Britain it matters terribly who's in the White House. For much of the rest of the world, America has come to seem a country a long way away, and Iraq a mess of its own making. Asia's eyes are turned more and more to China. In Latin America the recent Uruguay elections mark the latest in a list of countries, starting with Venezuela and Brazil, that have moved left and inward.

It matters when you consider the more high-flown rhetoric about the effect of another Bush term, the fears of an invasion of Iran, the questions about Iraq, the future relations with Europe. To most of the world it isn't nearly as important as suggested by commentators or the Washington promoters of the US as a country uniquely powerful and especially endowed with a mission to change the world.

Of course the election of John Kerry would have made a difference with his emphasis on multilateralism and on international institutions such as the UN, for a start. Indeed, the more cynical suggest that it was fear that a Kerry administration would ask them to stump up in Iraq that made Paris and Berlin secretly relieved he didn't get in. That is unfair, at least as far as Chancellor Schröder is concerned. Germany, along with Brazil, Japan and India are desperately keen for a seat on the Security Council in a reformed UN. A Kerry victory would have seen them, and the other petitioners, anxious to show their UN colours.

What is difficult to see in a second-term Bush administration is any fresh interest in international institutions, or treaties. All the President's instincts, and the beliefs of those around him, confirm him in his distrust of the UN and even regional organisations such as the EU and the African Union. Bush, Cheney and Rumsfeld remain unilateralists in spirit, a view hardly changed by the experience of taking Iraq to the UN in the first place. The thing to watch is not who is to be the new Secretary of State after Colin Powell's expected departure early next year. It is hard to see anyone more internationalist in spirit than Powell. The important thing would be any indication that foreign policy was being taken back out of the hands of the Defence Department and the offices of the Vice-President and National Security Adviser and returned to the State Department. And of that there is no indication at all.

So what we will see is more case by case initiatives by America, each defined within its own terms of security and interest and each pursued with or without other alliances. Iraq has sobered up this administration. It may well have curbed its initial enthusiasm for successive interventions that would reshape the map of the Middle East and elsewhere. What it has not done is destroy the influence of the neocons. As long as Dick Cheney and Donald Rumsfeld are there, Paul Wolfowitz and most of the rest of them will also be there. The radicalism in Bush's foreign policy will continue, only its ambitions are now tempered by its resources.

Which makes it most unlikely that it will pursue a military solution to the Iranian crisis, for example. It cannot afford to ignore a second time the military assessment of the troops needed and the dangers of being bogged down. It is more likely that Washington will use the nuclear issue to isolate and tighten sanctions on Tehran, while encouraging the opposition within and without the country. If Washington goes in for direct intervention it wil be in Darfur, an issue on which Congress's passions run high, the moral credits are greater and the resources needed are slight.

The really interesting question, however, is how quickly will the US gets out of Iraq? All the talk so far has been of the administration being in it for "the long haul". But behind its enthusiasm to ensure that elections take place on schedule in January, and its preparation to attack Fallujah, may lie a desire to declare a successful election and bring back most of its troops soon after. It was what Bush seemed to be saying in his victory speech on Wednesday and would make sense for an administration that has shown little interest in nation building as such.

The same could be said of the Middle East. Bush is not about to turn from being Israel's closest friend in a generation to acting as its most demanding patron, forcing it into deals with the Palestinians against its will. British politicians who seek this are just day-dreaming. But Arafat's death could remove some of the political obstacles - ones it should be said are entirely of Israel and America's own making. A new, weaker Palestinian leader needing Western support, an Israeli Prime Minister who wants to get rid of a potential Arab majority within Israeli territory and steal a march on his political opponents, a British Prime Minister desperate to show he has done something for Middle East peace and an American President who would dearly love to draw a line under the whole business - add that to the unilateral Israeli withdrawal from Gaza, and you have all the makings of a peace summit in London. It would mean a sell-out of the Palestinians over the West Bank, but none of the parties is above that. As with withdrawal from Iraq, it's presentation that matters. The long-term can take care of itself.

It is a picture of a unilateralist US which is what most of the world probably expects and is prepared for. With Bush's re-election we are not seeing the end of the neocon project. Far from it. This remains an activist government in foreign affairs as in domestic ones. Anyone doubting that need only read Cheney's remarks after Wednesday's victory at the polls. The answer to those who ask if a second-term Bush will be more consensual abroad is the same answer as to the question at home. It's no.

That leaves the rest of the world continuing to do pretty much what they were doing anyway, but with renewed impetus: which is getting on with their own affairs, building up regional alliances such as the EU, becoming more independent of US military and financial assistance. Which puts Tony Blair where? The answer to that is: where no experienced politician likes to be - having lost his freedom of manoeuvre and at the mercy of events.

a.hamilton@independent.co.uk