Donald Trump is something new to the American political landscape. But to many in Latin America he is—stylistically, at least—a far more familiar figure: the caudillo, or authoritarian populist.

In recent weeks, growing numbers of newspapers across Latin America have tried to explain the rise of Mr. Trump to bewildered local audiences by pointing to the region’s own strongmen, a long list that includes Venezuela’s late Hugo Chávez and Ecuador’s current president, Rafael Correa.

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