The ad starts with a sober, simulated news report. A news anchor, looking directly into the camera, warns viewers about Brazil’s proposed gun ban. “People are misrepresenting the disarmament issue,” she says. “It won’t disarm criminals.” The anchor fades and a news-on-the-march montage begins, highlighting freedom’s red-letter days. Nelson Mandela is released from prison. A single man impedes a row of tanks in Tiananmen Square. The Berlin Wall falls. “Your rights are at risk,” says the anchor, returning after the inspiring film clips. “Don’t lose your grip on liberty.” And then, to bring the message home, archival footage runs of thousands of Brazilians taking to the streets, restoring popular rule after more than two decades of dictatorship.

The ad was the first in a series that aired on Brazilian prime-time television last October, when both sides of the country’s gun control debate engaged in a heated exchange about the future of gun laws in South America’s largest democracy. Proponents of the gun ban proposed outlawing the commercial sale of arms and ammunition to civilians, capping a series of controls enacted in recent years. Unless you were a police officer, a soldier, or a private security guard, you wouldn’t be allowed to acquire a gun or the bullets to fire one. The idea was promoted by nongovernmental organizations in Rio de Janeiro and São Paulo, adopted by two presidential administrations, and then delayed for years due to the lobbying efforts of Brazil’s arms manufacturers. Finally, it was to come to a vote, the first time any country held a popular referendum on gun laws.

But Brazil’s gun poll was never just about Brazil. Brazil was merely the most recent battleground state in a raging global debate over gun rights. A week before the vote,...