Whoever runs Washington heads a global empire. American politics affects people's lives in every part of the world, often as a matter of life or death. So it's scarcely surprising that more than 40% of those polled around the world say they want the right to vote in US presidential elections.

After all, the American revolution was fought on the slogan of "no taxation without representation". So long as the US government arrogates to itself the right to impose its "leadership" by force across the world, a contemporary version of the colonists' demand might be: "no global power without accountability".

And with George Bush's blood-drenched presidency still fresh in the memory, it's only to be expected that 81% want to see the less belligerent Barack Obama re-elected. Only in Pakistan, target of relentless civilian-slaughtering US drone attacks, do a larger number prefer his Republican opponent, Mitt Romney.

Of course, enfranchising foreigners is fantasy. Only US citizens will have a say in these elections, and barely half of them are likely to bother to vote. Their choice will be made overwhelmingly on domestic issues, not how the administration should deploy its fearsome arsenal on the other side of the world.

The race is tight mainly because the economy is still hobbled and poverty has risen 19% since 2000. But for all Obama's disappointments and an electoral system in the grip of the wealthy, the domestic choice is real enough: from spending and taxes to healthcare and abortion – facing a challenger who thinks 47% of Americans are scroungers.

But for most of Monday night's candidates' TV debate on foreign policy, it was hard to put a credit card between them. They competed to demonstrate unconditional commitment to Israel, determination to prevent Iran developing nuclear weapons at all costs and their firm intention to compel China to "play by the rules".

Romney had sharply toned down his more menacing rhetoric. Apart from grumbling about Obama's lack of "strong leadership", his inner hawk only really broke cover to insist on direct arming of the Syrian rebels and the necessity of yet further deficit-defying increases in the already gargantuan US military budget.

At one point the Republican rightwinger even criticised Obama for behaving as if the US could "kill our way out of this mess" in the Muslim world. That shouldn't be taken too literally. If nothing else, the experience of Bush – who presented himself as a compassionate conservative with a "humble foreign policy" in 2000 and went on to launch the most devastating war of aggression in modern American history – is an object lesson.

But Romney's determination to shake off his image as a warmonger reflects the need at least to nod to US public opinion. Unlike the Washington establishment, large majorities of Americans believe neither the Iraq nor Afghanistan wars were worth fighting, polling shows; more than three-quarters think the US plays "world policeman" more than it should; and most want military spending cut, reject a US strike on Iran, and oppose arming Syria's opposition. But that also underlines how little influence most people in the US (as in Britain) have on their government's foreign policy and military adventures.

For all Obama's tone of reason and his stand against the Iraq war, his record is anything but pacific. He accelerated withdrawal from Iraq, but escalated the war in Afghanistan and failed to subdue armed resistance, at a cost of thousands of extra deaths. He sharply intensified the drone war in Pakistan, spreading it to Somalia and Yemen, personally vetting the "kill lists" while expanding "legitimate targets" to include all military-age males.

He backed Nato's war in Libya, ratcheting up the death toll at least tenfold and unleashing mass ethnic cleansing; supported the suppression of Gulf protest; and managed a violent coup in Honduras to a "successful conclusion". With a little help from Congress, he reneged on his pledge to close the Guantánamo internment camp, acquiesced in Israel's refusal to end illegal colonisation of Palestinian territory, and has now dispatched US troops to sub-Saharan Africa and Jordan.

Whatever the personal views of the politician at the top, the US empire is a system, not a policy, underpinned by corporate and military interests. Romney would very likely be a more dangerous leader, but almost every US president has sanctioned military action, and the risk of war with Iran or growing intervention in Syria would remain under a second Obama term.

But it's also a system in evident decline, hastened by overreach in the war on terror and paid for in blood and treasure both by Americans and across the world. US military spending is larger than the combined spending of the next 20 powers combined, its troops stationed in a majority of countries.

Of course the rest of the world doesn't really want a vote in American elections but the US off its back. Far better for most Americans, too, if that bloated military budget were to be slashed, troops withdrawn and bases closed – and the money spent instead on jobs, schools and health in the US itself.

Twitter: @SeumasMilne