PICTURE this: next week in Singapore President Donald Trump and Kim Jong Un crown their summit with a pledge to rid the Korean peninsula of nuclear weapons. A few days later America and China step back from a trade war, promising to settle their differences. And in the summer, as sanctions bite, the streets of Tehran rise up to cast off the Iranian regime.

These gains would be striking from any American president. From a man who exults in breaking foreign-policy taboos, they would be truly remarkable. But are they likely? And when Mr Trump seeks to bring them about with a wrecking ball aimed at allies and global institutions, what is the balance of costs and benefits to America and the world?

Don’t you ever say I just walked away

You may wonder how Mr Trump’s narcissism and lack of detailed understanding could ever transform America’s standing for the better. Yet his impulses matter, if only because he offers a new approach to old problems. Like Barack Obama, Mr Trump inherited a country tired of being the world’s policeman, frustrated by jihadists and rogue states like Iran, and worried by the growing challenge from China. Grinding wars in Afghanistan and Iraq, and the financial crisis of 2008, only deepened a sense that the system of institutions, treaties, alliances and classically liberal values put together after 1945 was no longer benefiting ordinary Americans.

Mr Obama’s solution was to call on like-minded democracies to help repair and extend this world order. Hence the Iranian nuclear deal, choreographed with Europe, Russia and China, which bound Iran into the Nuclear Non-Proliferation Treaty. And hence the Trans-Pacific Partnership, which sought to unite America’s Asian allies around new trading rules that would one day channel Chinese ambitions.

Mr Trump has other ideas. He launched air strikes on Syria after it used nerve gas in the name of upholding international norms—and thus looked better than Mr Obama, who didn’t. Otherwise he treats every relationship as a set of competitive transactions. When America submits to diplomatic pieties, conventions or the sensitivities of its allies, he believes, it is negotiating with one hand tied behind its back.

If any country can bully the world, America can. Its total military, diplomatic, scientific, cultural and economic power is still unmatched. Obviously, that power is there to be exploited, which is why every president, including Mr Obama, has used it to get his way abroad even if that involves threats, intimidation and, occasionally, deception. But it is hard to think of a president who bullies as gleefully as Mr Trump. No other modern president has routinely treated America’s partners so shoddily or eschewed the idea of leading through alliances. None has so conspicuously failed to clothe the application of coercive power in the claim to be acting for the global good.

In the short term some of Mr Trump’s aims may yet succeed. Iran’s politics are unpredictable and the economy is weak. Mr Kim probably wants a deal of some sort, though not full disarmament (see article). On trade, China would surely prefer accommodation to confrontation.

Yet in the long run his approach will not work. He starts from false premises. He is wrong to think that every winner creates a loser or that a trade deficit signifies a “bad deal”. He is wrong, too, to think that America loses by taking on the costs of global leadership and submitting itself to rules. On the contrary, rules help deter aggressors, shape countries’ behaviour, safeguard American interests and create a mechanism to help solve problems from trade to climate change. RAND, a non-partisan think-tank, has spent two years assessing the costs and benefits of the postwar order for America. It powerfully endorses the vision that Mr Trump sneers at—indeed, it concludes, this order is vital for America’s security.

Mr Trump’s antics would matter less if they left the world order unscathed (see Briefing). But four years will spread anarchy and hostility. The trading system will be unable to enforce old rules or forge new ones. Short of a war with, say, Russia, America’s allies will be less inclined to follow its lead. In Europe more voices may complain that sanctions against Russia are harmful. In Asia countries may hedge against America’s unreliability by cosying up to China or by arming themselves, accelerating a destabilising arms race. Countries everywhere will be freer to act with impunity. These changes will be hard to reverse. Sooner or later, America will bear some of the costs.

Worst of all, Mr Trump’s impulses mean that China’s rise is more likely to end in confrontation. He is right to detect a surge in Chinese ambitions after the financial crisis and the arrival of Xi Jinping in 2012. That justifies toughness. But Mr Trump’s dark, zero-sum outlook is destined to lead to antagonism and rivalry, because it refuses to see that China’s rise could benefit America or to follow the logic that China might be content to live within a system of rules that it has helped devise.

I just closed my eyes and swung

If the “master negotiator” so underestimates what he is giving up, how can he strike a good bargain for his people? He values neither the world trading system nor allies, so he may be willing to wreck it for the empty promise of smaller bilateral deficits. That could lead to retaliation (see article). Iran could resume nuclear work, as ruling clerics ape North Korea’s strategy of arming themselves before talking. Mr Trump may give Mr Kim the prize of a summit and an easing of sanctions in exchange for a curb on North Korea’s long-range ballistic missiles. That would protect America (and be better than war), but it would leave Asian allies vulnerable to the North’s nukes. America First today; in the long run America Alone.

America’s unique willingness to lead by fusing power and legitimacy saw off the Soviet Union and carried it to hegemony. The world order it engineered is the vehicle for that philosophy. But Mr Trump prefers to fall back on the old idea that might is right. His impulses may begin to impose a new geopolitics, but they will not serve America or the world for long. Remember the words of Henry Kissinger: order cannot simply be ordained; to be enduring, it must be accepted as just.