The election of Donald Trump has been welcomed by autocrats and demagogues across the world, from Moscow to the Philippines. The reaction of democratic leaders, especially in Europe, has on the contrary been a mixture of awe, anxiety and an effort to put a brave face on an event that might threaten a rules-based world order. This is the first daunting question raised by America’s choice of a man whose only experience in international relations has been as a real estate investor, and whose presidential campaign was marked by utterances which reflected either ignorance or disdain for what the US has traditionally stood for in the world.

Trump has called Nato “obsolete”, he wants to upend free trade, he has fawned over autocrats, he has suggested Japan and South Korea should develop nuclear weapons, he has criticised the Iran nuclear deal, he wants a wall on the border with Mexico, he believes the fight against terrorism can include torture and he cares not one bit about climate change. And that is only what is known about Trump’s foreign policy programme – that is, if he actually has one.

Yet the very fact that the survival of the international order in which the US has historically played such a key role now seems in question, speaks volumes about the dimensions of his election. The world is stunned. Because Trump has said so little that was coherent on foreign affairs, so much that was alarming, and because he has kept silent on so many of the complexities of what a US president may be confronted with, many are now reduced to mere speculation about the future policies of the man.

The victory of Donald Trump shatters the notion that the US can be counted on by its allies not just for defence guarantees and economic cooperation, but even as a defender of liberal democracy, rather than a threat to it. It calls into question the traditional US role as a protector of a UN-based global architecture of multilateralism. No one knows who will be appointed to his team, although the names of Jeff Sessions and General Michael Flynn have circulated in no reassuring way. All these risks are reflected in global reactions. Those countries and leaders who want America to continue to play an essential role in underwriting the international principles and alliances that stand at the heart of global governance are now aghast and scrambling for any reassurances that may be on offer. Those who want to challenge a US-led global order or see it eroded, as well as those who expect that a new dawn of US isolationism will best serve their interests, are rejoicing. So the news of the election outcome was greeted with a round of applause in the Russian parliament. The Kremlin will no doubt be hoping that Trump’s frequent overtures to Putin, including his expressions of admiration for the strongman, will offer areas of negotiation to Russia’s benefit. This could apply to Syria, a move likely to further empower Assad, to Ukraine, which could lead to the lifting of sanctions, or to the wider question of Europe’s security architecture and Nato.

In Europe, the reactions pointed as much to the difficult state of the continent’s politics as they do to attitudes towards the US. While Theresa May, contemplating a post-Brexit world, emphasised the “special relationship”, Angela Merkel suggested her cooperation with Trump would be conditional on respect for democratic values. In Brussels, EU and Nato officials scrambled to underscore the importance of transatlantic links. But among Europe’s populists, there was an outflow of glee and celebration. In France, Marine Le Pen cheered the “American people, free”, the Dutch far-right leader Geert Wilders gloated that “politics will never be the same”, and Hungary’s Viktor Orbán declared: “Great news. Democracy is still alive.” Across the world there are leaders eagerly anticipating the chance of capitalising on an entirely new version of US leadership – or absence of. In Israel, the far right believes the Palestinian state is over. China has been circumspect, hedging for the unknown, perhaps concerned about the risk of a trade war.

For Donald Trump, politics – like business – is about dealmaking. He thinks man-to-man talk with dictators can instantly dissolve problems, and approaches foreign affairs as zero sum game in which making America great can mean demeaning its traditional friends. His election makes the world a more dangerous place and also a more uncertain place, for it is too early to say precisely how those dangers will materialise – nor how the next US president will face up to them.