In 2003, when Kudo-kai reigned unchallenged in the city, 33.9 percent answered “yes” to the same question. The ratio had hovered around 2 percent since 2015.

But that's the real-life mission of a man in this southwestern port city that has long been the home turf for Kudo-kai, arguably Japan’s most violent yakuza organization. “I felt we the ...