Since the early years of the cold war, foreign policy has generally ceased to be the biggest issue for American voters in presidential elections. Instead, the economy is what matters most.
November's presidential ballot will - probably - continue this pattern. Voters remain most concerned by the sluggish economic recovery which last week prompted the US Federal Reserve to begin a new, third round of quantitative easing.
Nonetheless, Americans are still thinking about foreign policy. In recent days, for instance, many will have reflected upon the tragic murder of four of their countrymen in Libya, and the ongoing protests in numerous Muslim-majority countries at an anti-Islamic film originating in America.
More than a decade after September 11, a critical mass of the electorate believes America should engage more cautiously in international affairs, with the possible exception of Iran. Here, some polls show sizeable public support for efforts to prevent Tehran developing nuclear weapons, even if that necessitates American military action.
Iran is just one of the international issues on which Republican nominee Mitt Romney has articulated a more assertive posture than Democratic candidate Barack Obama. Others examples include Russia, which Romney has declared Washington's "No 1" geopolitical foe. And, China, which the Republican nominee has accused of stealing US technology and intellectual property, and of currency manipulation - with the implicit threat of sanctions should he become president.
Given the large stakes in play, many international audiences are showing a keen interest in the election outcome. According to a Pew Global Attitudes Project report in June, more than a third of populations in countries as diverse as Britain, Germany, Jordan, Lebanon, China, India and Japan are either "closely or somewhat closely" following the campaign.
As in 2008, international publics tend to favour Obama's election in 2012. But there has been a marked decline in international approval of his policies since he took office.
According to Pew, the fall-off in support has been a massive 30 percentage points between 2009 and 2012 in China (from 57 per cent to 27 per cent); in several key European countries, including Britain, France, Germany and Spain, the average reduction is 15 percentage points (from 78 per cent to a still high 63 per cent); and in numerous key Muslim-majority countries (including Egypt, Jordan, Lebanon, Pakistan and Turkey), the average fall-off is 19 percentage points from an already low 34 per cent to 15 per cent.
At least part of the decline in Obama's numbers since 2009 was inevitable inasmuch as international expectations about him where unrealistically high when he entered the White House. Two of the main international criticisms of his foreign policy (as was the case with the Bush administration's) are over-reliance on "hard power", and also unilateralism.
Despite Obama's withdrawal of US troops from Iraq, and his commitment to a similar military pull-out in Afghanistan, there has been much international criticism of his administration's use of unmanned, remotely flown aircraft to kill terrorists. In 17 of the 20 countries surveyed by Pew, more than half of voters disagree with the use of these drone attacks.
These numbers can be expected to fall further if Romney wins and follows through on his assertive foreign policy rhetoric. This could be amplified by the fact that he enjoys less personal popularity overseas than Obama.
A key question is whether Obama and Romney should care about what the rest of the world thinks. The short answer is "yes". Some in America completely dismiss the importance of international opinion. Such short-sightedness neglects the crucial role it can play in facilitating foreign policy co-operation and information-sharing with Washington, both overt and covert.
Many of the diverse foreign policy challenges facing America require extensive international collaboration, especially at a time of budgetary cutbacks. As key members of the Obama team have asserted, such co-operation can be enabled by demonstrating a better combination of soft power (including diplomacy that generates admiration rather than antagonism) and prudent use of hard power.
Combining the two more effectively (into what is now called smart power) was well understood by previous generations of American policymakers. For instance, Washington skilfully used both assets after the second world war to cultivate support for a system of alliances and institutions, such as Nato, the International Monetary Fund, the World Bank and the United Nations that subsequently became a cornerstone of Western success in the second half of the century.
To be sure, today's world is very different from that of the cold war. But the need for smart power endures.
Given the mood of the American electorate, the development of a comprehensive, coherent and well-resourced smart power strategy will not win many votes in November. Nonetheless, this should be a pressing concern for both candidates if they are to fulfil their similar pledges to renew the country's world leadership for a new generation.
Andrew Hammond is associate partner at ReputationInc. He was formerly America editor at Oxford Analytica, and a special adviser in the British government of prime minister Tony Blair