The first of four American presidential and vice-presidential debates will be held on October 3.

In an election so far dominated by domestic issues, the debate season will give many voters their first real glimpse of the key foreign policy differences between the Republican team of Mitt Romney and Paul Ryan, and the Democratic ticket of Barack Obama and Joe Biden.

More than a decade after 9/11, a critical mass of the electorate believes America should engage more cautiously in foreign affairs. This sentiment is likely to have been reinforced, in the mind of many voters, by the tragic murder in September of four of their countrymen in Libya, and the ongoing protests in numerous Muslim-majority countries at an anti-Islamic film originating in America.

Perhaps the key exception to this national mood of foreign policy caution is Iran. Here, some polls show sizeable American public support for international efforts to prevent Tehran developing nuclear weapons, even if that necessitates American military action.

Iran is just one of the international issues on which Romney has articulated a more assertive posture than Obama. Others examples include Russia, which Romney has declared Washington’s “number one” 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 apparent differences between the two candidates, and the large stakes, many audiences beyond the American border are showing keen interest in the election. According to a Pew Global Attitudes Project report from June, more than a third of the populations of 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 favor Obama’s reelection. 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 for the president’s policies has been a massive 30 percentage points between 2009 and 2012 in China (from 57% to 27%); in several key European countries including Britain, France, Germany, Spain and Poland, the average reduction in support is 15 percentage points (from 78% to a still high 63%); 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% to 15 percent.

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 American troops from Iraq, and his commitment to a similar military pull-out in Afghanistan, there has been much international criticism for instance 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 international numbers can only be expected to fall further if Romney wins in November 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.

After all, no foreign citizens will vote in November.

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 today require extensive international collaboration, especially at a time of budgetary cutbacks. As key members of the Obama team have asserted, including Secretary of State Hillary Clinton, such cooperation can be enabled by American policy demonstrating a better combination of soft power (including diplomacy that generates admiration rather than antagonism) and prudent use of hard power.

Combining hard and soft power more effectively (into what is now called smart power) was well understood by previous generations of American policymakers.

For instance, Washington skillfully used both assets after the Second World War to cultivate support for a system of alliances and institutions, such as NATO, the IMF, World Bank and the UN, 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 for either Obama or Romney in November.

Nonetheless, this should be a pressing concern for both candidates if they are to fulfill their similar pledges to renew the country’s world leadership for a new generation.

The writer is an 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.

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