Fourth, the ill-defined concepts of strength and credibility are the ultimate currency in world affairs. Last weekend, Romney’s foreign-policy spokesperson stated, “Romney’s foreign-policy doctrine is he will do whatever it takes to make America stronger.” The following day, Ryan vowed: “Peace through strength is not just a slogan. It’s not just something we say; it’s what we do. It’s our doctrine.” Set aside the image of Uncle Sam building muscle through one of Ryan’s P90X workouts; what is left unsaid is what grand strategy such strength would be marshaled to achieve or how Romney’s foreign-policy objectives ultimately differ from Obama’s.

Likewise, the president boasted during the final debate about “how we’ve restored American credibility and strength around the world” and how his administration’s “credibility is precisely why we’ve been able to show leadership on a wide range of issues facing the world right now.” The Obama administration has played a leadership role in coordinating more effective multilateral approaches to things like the Nuclear Security Summit and the sanctions regime on Iran. The willing participation of other countries, however, is not due to the size of the U.S. military or the Obama administration’s credibility — which has only diminished throughout the world in the past three years — but because it was in their own self-interest to do so.

We know from recent history that America’s “strength” — crudely defined by politicians and the media as defense spending — and threats do not compel others to do what Washington wants. Most countries balance against threats, form coalitions to mitigate threatening behavior, or remain neutral nonparticipants whenever Washington demands they do something, rather than jump on the U.S. bandwagon. Moreover, as international relations scholar Daryl Press demonstrated, credibility is not determined by reputations that are earned through past behavior, but by the power and national interests associated with a current challenge.

Romney often repeats his conviction that it is a duty, honor, privilege, and responsibility of the United States to shape and lead the world because of a “longing for American leadership.” This week, Romney adviser Eliot A. Cohen claimed: “If you don’t even try to shape events, then for sure you are going to get a bad outcome.”

Democrats conceive of America’s shaping role for slightly different outcomes, but the eagerness to take on this global chore is the same. Before the Democratic National Convention, Sen. John Kerry declared, “Global leadership is a strategic imperative for America, not a favor we do for other countries.” Or, as Obama told a private audience in May:

The truth is, as we travel everywhere, we continue to be the agenda setters. Folks continue to look to us. . . . We continue to be the one indispensable nation. And because we project it with our values and our ideals, and restored a sense of rule of law, people are paying attention, people are listening, and people are hungry for our leadership.

This is not the world I see. When I travel and speak to admittedly lower-level officials, I do not hear a global craving for U.S. involvement and influence. What I hear constantly is a desire for clarity over U.S. policies toward a specific country or issue, such as climate change, the Middle East peace process, or the Arab Spring. Furthermore, when not seeking clarity, foreign officials expound on the vast hypocrisy in how the United States treats some countries versus others. When foreign governments and their citizens publicly express a desire for U.S. leadership, and when it is in the U.S. national interest to act on that desire, the United States should play a central role. Yet, more often than not, American policymakers would be better off doing nothing.

Micah Zenko is the Douglas Dillon fellow with the Center for Preventive Action at the Council on Foreign Relations.