Honduras held a presidential election Sunday, and there are many reasons for Americans to be interested in the outcome — 309,000 reasons, to be precise. That is the number of Honduran migrants captured at the U.S.-Mexico border in the 12 months ending Sept. 30. The figure represented a big acceleration in what was already a mass exodus from the Central American country; probably about a tenth of Honduras’s 10 million people live in the United States now. The flow demonstrates how enormously difficult it is for the United States to treat what the Biden administration has called the “root causes” impelling people to take the costly and dangerous trip north: poverty, violence and official corruption.

Can Honduras’s voters and politicians succeed where U.S. policy has failed? Certainly broad-based democratic change and reform, generated within Honduran society itself, would be the best option. Unfortunately, Honduras has had little in the way of good governance for many years, and things have arguably deteriorated since 2009. In that year, a military coup gave way to increasingly corrupt civilian rule. The current president, constitutionally barred from a third term, is Juan Orlando Hernández, who was credibly accused of being reelected through fraud in 2017 and is under investigation by U.S. prosecutors for allegedly accepting bribes from drug traffickers. (The president denies the accusations.)

His ally, the mayor of Tegucigalpa — the capital city — ran as the ruling National Party’s standard-bearer. Spearheading the opposition and claiming victory is Xiomara Castro de Zelaya, a self-described democratic socialist whose husband, Manuel Zelaya, was the president ousted by the military in 2009. The coup took place as he steered Honduras closer to Venezuela’s left-wing regime. Anxiety lingers that Ms. Castro, whose husband ran her campaign, would try to move Honduras back into the Venezuelan-Cuban camp. But at this point, her fellow citizens — those who haven’t already left — seem so understandably fed up with the National Party that they are willing to take the risk. The candidate has made overtures to Honduran business leaders, assuring them that she would pursue reform, not revolution. The president of Honduras’s leading private-sector organization has congratulated Ms. Castro and offered his cooperation.

Mr. Hernández’s party fortunately conceded Tuesday rather than attempt to resist its defeat. So far, though — and contrary to many expectations — there has been no surge in political violence like the one that cost more than 30 lives after the tainted 2017 vote. Partial credit may be due to the Biden administration, which signaled its insistence on a peaceful and transparent process by sending Brian A. Nichols, the State Department’s Latin America specialist, to Honduras a week before the vote. The multiple crises battering Central America have already tipped the politics of one of Honduras’s neighbors, El Salvador, in a populist, authoritarian direction; another, Nicaragua, has tipped into outright dictatorship under Daniel Ortega.

A democratic transition in Honduras, followed by moderate rule, would have stabilizing effects that could extend all the way to the Rio Grande. Those must be the United States’ objectives.