What kind of relationship do Americans want to build with the world's 6 billion other people in the years ahead? This question is urgent, since the past seven years have seen an unprecedented drop in our country's global favorability rating. In today's hyper-connected world, that has huge consequences for Washington's ability to protect American interests.

To fix this problem, many experts – and even the presidential candidates – are promoting agendas to rebuild America's position of world leadership. They are right to try to repair our image abroad. But their focus on "American leadership" is misplaced. A smarter approach would be for us to build a new relationship with the world that embraces the key principles of human equality and mutual respect among all peoples.

Starting to see themselves as "merely" equal to everyone else may seem slightly scary to some Americans. But history should assure them.

I grew up in a Great Britain that was making a broadly similar shift: from the days of the globe-girdling "British Empire" to a situation in which it was just one, though still quite powerful, nation among many. That change was warmly welcomed by the citizens of the many countries that won their independence from London. But as I explain in my upcoming book, "Re-engage! America and the World After Bush," it ended up being very good for the British, too. As any recent visitor can attest, today's Britain is humming and successful.

Here's another imperfect (but also helpful) comparison. America's current relationship with the rest of humanity has much in common with that between South Africa's apartheid-era whites and their disfranchised non-white compatriots. Back then, most white South Africans argued that they were more civilized and more educated than the others; thus it was "best for everyone concerned" if they dominated national decision-making. A far-fetched analogy? Perhaps. But there are echoes of that mentality in the way some Americans still talk about Washington's role in global affairs.

And the end of the apartheid story really is a hopeful one! After fighting for centuries to maintain control, the whites finally sat down to talk with – and just as important, listen to – the African National Congress leaders. In the process, they found that those others were willing to work with them in building a new order built on equality and nonviolent problem solving.

What would it mean, today, if Americans started to think and act as though all of humanity constituted a single community, with us as just one part of it? Are we ready to seek out and give fair weight to the views of the citizens of other countries on matters that affect everyone?

Climate change is an area in which we urgently need to adopt this approach. The current Bali conference negotiations give us a window to reach a fair international agreement on reducing climate-wrecking emissions. But what does "fairness" entail?

We cannot ask emerging countries such as China or India simply to forgo the economic growth that has brought such benefit to Americans and Europeans for 150 years now. Chinese and Indian leaders have already declared that unacceptable. Instead, we must work together to negotiate emissions caps that may be painful in the short run, but give us all the time and the tools we need to transform our economies into ones the Earth can sustain.

Treating the peoples of other countries as our true equals is the American way. In the Declaration of Independence, the Founders held it self-evident that "all men" (meaning "all men and women") were created equal – not just "all US citizens." Then, in the 1940s, American leaders were visionary in creating the United Nations and the bodies associated with it. These institutions embody the values of human equality and nonviolent problem solving. Yes, they're flawed. But they can be reformed. And they stand today as a supreme achievement of their American creators.

In a world built more truly on principles of equality, might US interests get swamped by the hostile and dictatorial tendencies of China or other emerging nations? Such a fear is exaggerated (and harmful). The US has several important protections for its independence: its geographical sturdiness; the UN's principles of non-aggression and respect for state sovereignty; and, at the military level, its continuing deterrent power.

Consider, too, what happened in the cases of the British Empire and South Africa. After decades of colonial bloodshed, all those once-fearful leaders finally realized that if you offer respect and equality to other people, then they will accord it back to you. There is certainly a lesson there!

Today, America's relationship with the world's 6 billion non-Americans is more vital to our wellbeing than ever before. Let's work on making it the most constructive relationship we can.

• Helena Cobban, a former Monitor correspondent, is a "Friend in Washington" with the Friends Committee on National Legislation. Her latest book is "Re-engage: America and the World After Bush."