There are plenty of scenarios under which the gridlock that characterised Barack Obama’s first term will continue and even get worse, with increasing polarisation of the parties.
Power of the US president is limited by laws of economics
On Tuesday, barring a tight result that is bogged down in legal challenges, we will know who will be the next president of the United States. At this time in the American political calendar a sort of mass hypnosis grips the world, and otherwise sensible people believe the winner can rewrite the laws of nature by sheer force of personality.
Actually we know that the president is not a king-emperor and that his powers are delinerately circumscribed by Congress. We know from Barack Obama's first term that a good candidate does not necessarily make an effective president.
And we sense, too, that with every passing year the tasks expected of a president become greater, too great for any one person to carry out. The jaunty top-hat worn by Uncle Sam is actually too big for a modern politician to wear.
Yet still the world is caught up in the drama of the presidential election. Even more so these days, with Hurricane Sandy crashing in to enliven the last act.
The unfortunate truth is that, whoever wins the election on Tuesday, Mr Obama or the Republican challenger Mitt Romney, the future is pretty much already mapped out. Whatever promises were made on the campaign trail - to restore America's standing in the world or revive the belief that the next generation will have a better life than this one - will bump up against the laws of economics.
The most likely prediction is that the next three to four years will be characterised by low growth and high unemployment. The squeezing of the middle class and increasing income inequality are unlikely to be reversed. Social mobility - an integral part of the American dream - will be reduced, as the children of the rich get better educational qualifications and therefore enhanced job prospects.
The gloom will not continue forever but steady growth when it returns is unlikely ever to match the glorious decades following the end of the Second World War. It looks like this was a period of exceptionally benign circumstances for the US, which cannot return in a globalised world of increasing competition.
After the war ended, the US found itself with an intact industrial base, while all of its competitors - in Europe and Japan - were in ruins. At the same time, the US government offered returning soldiers subsidised higher education, providing a uniquely skilled workforce that helped US companies to dominate the world.
Household incomes were lifted by more women working, while the "baby boom" generation - the Americans born in the decade from 1945 - expanded the workforce. These favourable conditions may have lasted until the 1980s, but with the baby boomers beginning to retire, drawing on state entitlements rather than paying taxes, the process has gone into reverse. Only borrowing has kept the show on the road.
The prospects for any quick solutions to these ills are bleak. There are plenty of scenarios under which the Washington gridlock that characterised Mr Obama's first term will continue and even get worse, with increasing polarisation of the parties ruling out any bipartisan approach.
The US will continue to have the only military that straddles the globe. For the foreseeable future, it will remain unchallenged, on land, at sea, in the air. But it is a strange business when the only superpower depends on borrowing money from China, its main geopolitical rival. This odd couple are shackled together by economic necessity, but how can this last?
China is choosing its own new leadership, which will not be silent in answering this question. Two days after the US presidential poll, more than 2,000 delegates of the Chinese Communist Party will meet at the start of a session to choose the next generation of leaders. As the conference winds up, seven or nine men will file out from behind a screen to show their faces to the world. Almost certainly the leader will be Xi Jinping, widely expected to be the next president.
The challenge facing Mr Xi is even greater than for the next US president. It is not about his character, but about the future of one-party rule: its opaque, top-down style of leadership has dragged the country from its "iron rice bowl" economy to become the workshop of the world, but can it resolve the growing social tensions unleashed by this transformation?
Mr Xi is unlikely to emerge as what used to be called the country's "paramount leader". The conflicts and intrigues that have punctuated the leadership succession will not go away just because the new line-up has emerged. The new men will still have to balance competing interests, between military and civilians, and between reformers who seek more transparency and conservatives who flinch from tampering with a structure that has worked for so long.
In Chinese eyes, American global hegemony is an aberration before the natural order of nations is restored. Up until 1850, China and India were the world's leading economic powers. China, according to some estimates, had been a global power for 18 of the past 20 centuries.
China does not aspire to be a global superpower, although its economic expansion in Africa and Latin America has given it growing security interests. In what it sees as its home waters, the situation is different: it is determined to assert its dominance of the South China Sea, even at the cost of disputes with neighbours, including Vietnam, and a regional arms race.
Ultimately the goal must be to deny the US Navy access to the South China Sea. War is not on the horizon, but we can expect China to test American resolve to defend its allies, first and foremost the Philippines.
With communist ideology fading away, the Chinese leadership is likely to rely on nationalism as a cause to distract people from falling growth rates and rising levels of inequality. We can see this already in the dispute with Japan over the chain of uninhabited islands - Diaoyu in Chinese, Senkaku in Japanese - which has caused protests in both countries.
Mr Romney has promised to boost defence spending if he gets in. The reality is that whoever gets in would love to focus on Asia - the new engine of global prosperity and resurgent nationalism, where the sea lanes need to be kept open - and disengage from lose-lose wars in the Middle East and Afghanistan.
But unresolved problems will persist from Gaza to the Khyber Pass. Inevitably within a couple of years, the next president will have to decide whether to go to war with Iran. Even sooner he must decide what to do about the civil war in Syria. The US is still, in Mr Obama's words, the "indispensable power", and will be for some time.
But amid the crashing of gear changes in Washington and Beijing, the word is out in the world that the US is not going to be indispensable everywhere, forever. Everyone knows the Americans have a nice safe continent to retreat to.
The ebb and flow of US military power was put succinctly by the late Richard Holbrooke, Mr Obama's envoy to Afghanistan and Pakistan, when discussing why US leverage was limited in Pakistan, despite the billions it gave to the military.
"The biggest problem we face," Mr Holbrooke told the journalist David Sanger, "is that the Pakistanis know that sooner or later we're leaving. Because that's what we do. And that drives everything."
That is the frame through which countries view the long-term prospects for US military power, some with hope, others with fear.
On Twitter @aphilps