There is little doubt as to which candidate most of the world would like to win next Tuesday's US presidential election. Barack Obama may have disappointed the higher hopes of many of his supporters abroad, as he has at home. But he has also proved a safe pair of hands, withdrawing the US from Iraq with speed and efficiency, setting a date for withdrawal in Afghanistan and beating back the demands for precipitate action on Iran.

Mitt Romney is much more of an unknown factor. To give him his due, he is not the first contender for America's highest office to have little grounding in foreign affairs, nor is he likely to be the last. The fact is that almost all eyes in the United States are on domestic matters, just as they are in this country. It was noticeable that even in the third debate between the candidates, which was meant to be on foreign matters, the argument soon slid back to the state of the US economy.

If Mr Obama showed himself in these debates the cooler, more experienced hand, his Republican challenger suggested a more moderate, balanced contender than he had earlier on in the campaign. On the thorny issue of Iran's nuclear plans and Palestinian rights, Mr Romney has pulled well back from his confrontational and wildly pro-Israeli stance. He accepts an early withdrawal from Afghanistan; he concedes that diplomacy still has a course to run with Tehran.

The danger is to deduce from this that, so far as foreign policy is concerned, the world will see little difference whichever candidate wins office next week. In many senses it won't. The ill-fated Afghan adventure will be wound down according to plan. The US will continue to be wary of foreign interventions in Syria or elsewhere. It will remain ambivalent towards China's rise, seeking its partnership as the coming power but resentful of its growing influence in Asia. The Middle East will remain, as it has under successive presidents of whatever party, an issue too delicate to handle.

As for the much-vaunted "special relationship" with the UK, that will continue as it has for the past several generations, more trumpeted in the telling than the practice. The biggest thing for Britain is that we're getting out of the dead end of the Afghan intervention. The biggest hope – and the most likely assumption – is that a new president or a re-elected one will not drag us into the same again.

The world of tomorrow, as of today, is of an America which no longer has the resources or the popular will to act as a global policeman or to throw its military muscle about at will. For that we should all be grateful.

Yet the choice of US president does matter. America remains militarily by far the most powerful country in the world, and its biggest economy. Even at the most basic level of domestic economic policy, it makes a huge difference if the US follows an expansionist path, as preferred by Mr Obama, or one of austerity combined with tax cuts, as promoted by the Republicans. The decision by American voters, and the composition of the two Houses which will result, will affect us all.

Nor can you divorce the choices facing a president abroad from the question of the character and instincts of the incumbent. Foreign policy remains virtually the only area of political action which a president, as head of state and commander-in-chief, has some room to act independently of the legislature. The history of the US over the past four decades has been one of a country sucked into commitments which affect all its allies from small decisions of the moment. The judgement in the White House rightly concerns us.

President Obama's record has been a mixed one. Over Iraq and Afghanistan, he has been purposeful, as his electorate desired. Over the Middle East, he has been weak in the face of political challenge. Over Iran, he has avoided a potentially disastrous military strike but has ratcheted up a policy of sanctions and isolation that has proved largely self-defeating. On the broader issues of relations with China and Russia, he has been ambivalent. On the questions of promoting international institutions, he has proved largely uninterested.

Mr Romney, on all the evidence of his statements so far, would be no improvement, and very probably worse. But the intriguing question of this election is whether Mr Obama, with a popular renewal of his mandate and a more co-operative Capitol Hill, could step out from his safety zone and take some bold initiatives to get Middle East talks going again and to reach a deal with the Iranians. The possibilities are there. One senses his instincts are in favour if his dislike of political confrontation holds him back.

Yes, we hope that Barack Obama is re-elected to the world's most powerful position. He is the cooler head and the safer pair of hands. But, if we wish his success, it is not only because his financial policies are more beneficial for the international economy as a whole, and his judgement on foreign ventures more sound. It is also because we still harbour the hope that he could yet change the world for the better.