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The impact from the risk British voters took in choosing to exit the European Union extends well beyond the United Kingdom. The world has already felt financial reverberations and may soon suffer political aftershocks. Thoughtful leaders, especially in the West, should limit the damage of Brexit by strengthening — through reformation — essential international institutions that are increasingly under rhetorical and electoral assault.

For the European Union, that means making the 28- (soon to be 27-) nation bloc less bureaucratic and more accountable. But it should not be jettisoned, especially since it exists in no small part to bind a continent historically riven with conflicts. Reforms need to be made quickly in response to rising calls for similar referendums elsewhere in Europe.

Geographic separation does not spare the U.S. from E.U. turmoil. Before the vote, President Obama, mindful of the intrinsic link between the E.U. and NATO, accurately stated the stakes for the West and for the "special relationship" between the U.S. and the U.K. But Brits have chosen. On Friday, Obama rightly committed to use the rest of his term to reinforce this relationship with an essential, albeit altered, partner.

For his part, British Prime Minister David Cameron, an E.U. backer who announced his intention to resign in October, should work to shore up the relationship during his limited tenure, too. But Britain may need to reckon with a divorce that diminishes its global status. "The blunt message, which London will understand over time, is that it has lost relevance to U.S. foreign policy," Charles Lichfield, a Eurasia Group specialist on Europe, told an editorial writer on Friday. "NATO isn't enough. NATO is the hard power, but soft power is very important, and soft power went through E.U. initiatives." Lichfield pointed to the "somewhat successful" sanctions on Russia for cleaving Crimea from Ukraine.

Both Obama's and Cameron's successors will need to carry on relationship repair. This won't be easy. Boris Johnson, an anti-E.U. member of Parliament who may be Britain's next prime minister, made irresponsible remarks about Obama's "part-Kenyan" heritage after Obama pushed for Britain to remain an E.U. member. Meanwhile, Britain's next leader likely will face another key vote, but this time once again on Scottish independence.

Donald Trump, cheering Brexit, blithely commented in pro-E.U. Scotland: "Basically, they took back their country." This revealed his misunderstanding not just of Scotland but of presidential necessity for effective Western institutions. Conversely, Hillary Clinton, deeply steeped in Europe's role in promoting global stability, released a more sober statement stressing respect for voters' choice, the need to ensure that the economic fallout doesn't disproportionately hit working families in America, and a recommitment to transatlantic ties.

Brexit suggests that the anti-establishment, nativist sentiments propelling Trump are a growing global phenomenon. That makes this an especially critical moment for world leaders, who need to hear and heed the rising response to the challenges of globalism by communicating to their constituencies that today's vexing economic, environmental, security, migration and political challenges are best met by reforming — not rejecting — responsible international institutions.