The United Kingdom has long been a paragon of cautious political centrism. For the past several decades, British prime ministers — Conservative and Labour alike — have governed from the center to great effect, with considerable stability, both political and financial. That stability may now be ending with last week’s vote to leave the European Union.

First and foremost, Brexit is a rejection of the centrist political consensus and a victory for the extreme populism embodied by Nigel Farage, the leader of the far-right UKIP party. For the rest of Europe, Brexit continues a worrying trend, which has seen the empowerment of populist parties, at the expense of the moderate, technocratic status quo. Hungary, Poland, and Slovakia have all elected far-right governments whose nationalistic rhetoric and censorship of dissent echo an earlier, darker period of European history. In France, the Front National, which only a decade ago was led by a rabid anti-Semite, is expected to make major inroads in next year’s presidential elections. In Spain, the far-left party, Podemos, is now the second largest political alignment in the country, and in Italy the self-described populist Five Star Movement scored a major victory when its candidate recently won the Rome mayoral election.

Time and again, history has demonstrated that extremism in politics, whether right or left, is dangerous to the world. Today, voters in Europe seem intent on forgetting that lesson. Slowly but surely, European centrist liberalism is dying, along with centrist conservatism. Indeed, the increasing influence of the hard right has served to increase the influence of the hard left and vice versa. Both weaken the center and move the world away from stability, rationality, tolerance, and nuance — and toward demagoguery, simple mindedness, xenophobia, and intolerance.

At best, this polarized political climate encourages the formation of self-contained opinion echo chambers. At worst, it leads to violence, as we saw with the murder of a pro-EU member of Parliament, Jo Cox, by a suspect who reportedly shouted “Britain first’’ as he pulled out his weapon.

Following the British vote to leave the European Union, former prime minister Tony Blair warned of what could happen to Europe if the center does not hold: “ If we do not succeed in beating back the far left and far right before they take the nations of Europe on this reckless experiment, it will end the way such rash action always does in history: at best, in disillusion; at worst, in rancorous division. The center must hold.’’

It could happen in the United States as well, if the center fails to hold.

The Republicans are about to nominate a candidate who is about as far from the sensible and predictable center as any candidate in recent history. Republican primary and caucus voters rejected centrist candidates such as Jeb Bush, John Kasich, and Marco Rubio. Democratic voters cast millions of ballots for a populist candidate from the extreme left whose supporters included advocates of violence, revolution, and civil disobedience.

Fortunately for the Democrats, America, and the world, a reasonable, centrist, responsible presidential candidate has emerged. The election of Hillary Clinton is now imperative, not only for the stability of our nation but also for the stability of the world.

The election of Clinton will help achieve such stability at a dangerous time. And in order to win, she must present herself as a stabilizing centrist. To do that, she must select a vice presidential candidate who is also a centrist rather than a Sanderista.

A world with wide pendulum swings between the hard right and the hard left is a dangerous place. Clinton should campaign, win, and govern from the center. This will not be easy. Centrism has become synonymous with a boring and dysfunctional political status quo, and there is great temptation — especially at a time of increasing popular unrest — to pander to the extremes embodied by the “movement’’ politics that define the Donald Trump and Bernie Sanders candidacies. But this temptation must be resisted in the name of much-needed stability. The stakes are now higher than the future of the United States. What is at stake in this election is the future stability of the world.

Alan M. Dershowitz is professor emeritus at Harvard Law School and author of “Taking a Stand: My Life in the Law.’’