George Bush's extravagant inauguration this week - in his own mind nearer to an annunciation - is not what most British and Europeans wanted. This is a second-term President with the lowest approval ratings ever at home; they are even lower abroad. Yet despite everything, from the debacle in Iraq to the tax cuts directed at the rich, it is Bush, not Kerry, presiding over no less than 10 inauguration balls and talking reverentially of his mandate, unsurprisingly, having increased his share of the vote compared to 2000 among almost every category of voter. This is one election he didn't steal.  But given the record, it is an unconvinced majority and it will be this lack of conviction, on top of the increasing lame duckness of a second-term President that promises to constrain some of the wilder instincts of both the man and his supporters.  Already, there are signs of a new emollience: the last British detainees at Guantanamo Bay have been released; the bitter trade row with the EU over the respective subsidies to Airbus and Boeing has been kicked into touch; and the core group of the US, Australia, India and Japan that was to subvert the United Nations by co-ordinating aid to the tsunami victims has been quietly disbanded.  Mr Bush talks about explaining his policies better to his European allies, in sharp contrast to his first-term plans to visit Europe and to do so within a month of the inauguration.  None of this is surprising. The radical neoconservatives who animated the first term have led the President and the country into a foreign policy mess. Donald Rumsfeld, Secretary of State for Defence, is a much reduced figure from the self-confident swaggerer who so grossly underestimated how many troops it would take to pacify Iraq, the impact on world opinion on the flagrant disregard for human rights in Abu Ghraib and Guantanamo, and the consequent collapse in morale in the overstretched US army. He got it wrong and it is a minor miracle he is still in office, protected by a President who prizes loyalty and shares many of his instincts.  Yet it is now blisteringly obvious that the derided State Department view of the world, that it is smart to have allies who can shoulder part of the cost of foreign interventions and that for all the awesome nature of America's military might, 'soft' power matters, too, has a validity that any US President ignores at his peril.  The instinct of Condoleezza Rice, who takes over from Colin Powell may be hawkish, but her newly appointed number two, Bob Zoellick, who spent the first term overseeing US trade interests, could not have been so effective had he been an uncompromising unilateralist. He understands the way globalisation serves US interests and the need to man age it with allies better than almost any other senior Republican; he will be the counsel of reality in an administration anxious not to get deeper into the mire, whatever its predilections for pre-emptive unilateralism.  Zoellick is also a pragmatist on China, a country that has moved from public enemy number one in Bush's former lexicon to a much more nuanced position today. Commentators variously ascribe Bush's victory to his support among evangelical protestants, his clear-cut stance on terrorism and his apparent leadership qualities, but there is another, less well-remarked-on explanation.  Bush's reaffirmation of his commitment to free trade and, in particular, keeping America's borders open to China at a key stage in the campaign, very much Zoellick's position, worked enormously to his advantage. It put Bush on the side of the emerging new American business model, relying on low, valued-added manufacturers from abroad with a dynamic service sector and knowledge economy at home, so positioning the Republicans paradoxically as the party of modernity and the Democrats of yesterday. Zoellick has been justly rewarded.  For when John Kerry and vice-presidential candidate John Edwards were launching their assault on free trade and 'Benedict Arnold' employers (Benedict Arnold famously tried to betray the American Revolution to the British) who exported jobs to foreigners, Bush held the line.  I remember being impressed at the time, but in retrospect it was an obviously smart move. The buoyant profitability of US corporations, the strength of Wall Street, US leadership in the knowledge economy and the rapid growth of jobs in the service sector are all constructed on free trade and, in particular, with the capacity to manufacture in China and Asia. Two-thirds of imports from China are from affiliates of American companies which are certainly exporting manufacturing jobs to Asia. But new jobs are being created distributing and selling the imported low-price goods in the US.  The resulting gigantic US trade deficit is, in part, sustainable for so long as the dollars to finance it are forthcoming. One of the central tasks of the second term will be to maintain this crucial inflow of dollars as the US's foreign debts rise to dizzying and potentially unsustainable levels, the pivot on which job generation and American prosperity in the booming suburbs, the heart of Republican support, depends.  This has enormous implications for federal spending and taxing plans; put bluntly, foreign investors will not put up with another round of tax cuts. They need to see the US government deficit narrow rather than expand, and Bush has been careful to stress in his round of pre-inaugural interviews that he wants to halve it. He talks less of tax cuts and tax reform, now delayed until 2006, more of attacking 'junk law suits' in a scandalously indulgent legal system and of offering US citizens a means of saving for their social security through personalised accounts.  But if the second Bush term promises to be less scary, with Republicans more mindful of reassuring their reluctant   majority that they are more level-headed than they are caricatured, some underlying truths remain.  They have a better line of sight on what makes American capitalism tick, and how to align it with Republican values, than the Democrats, who have lost their way. A Republican majority in the House of Representatives and Senate is going to be hard to dislodge, as is the new coalition in the country.  For the immediate future, a hegemonic US is likely to be run by Republicans and their instincts remain to kick ass and divide the world into those who are for them and those against. The appointments of Alberto Gonzales as Attorney General, who famously wrote that the Geneva accords on the treatment of prisoners were quaint shows that Bush has lost none of his atavistic instincts - he's just cannier.  The second-term Bush may be calmer and more predictable towards the expected. Towards the unexpected - from a run on the dollar to another terrorist attack - we could see a vicious lurch backwards. Europeans are right not to drop their guard.