HIME ISLAND, Japan — If Marxism had ever produced a functional, prosperous society, it might have looked something like this tiny southern Japanese island.

At first glance, there is little to set Hime (pronounced HEE-may) apart from the hundreds of other small inhabited islands that dot the coasts of Japan’s main isles. The 2,519 mostly graying islanders subsist on fishing and shrimp farming, and every summer hold a Shinto religious festival featuring dancers dressed as foxes.

But once off the ferry, the island’s sole public transportation link to the outside, visitors are greeted by an unusual sight: a tall, bronze statue of Hime’s previous mayor, rare in a country that typically shuns such political aggrandizement. Rarer still is that the statue was erected by his son, who is the island’s current mayor.

In fact, the father, who died in 1984, and the son, who succeeded him, have won every mayoral election in Himeshima, the island’s village, for 49 years — without once being challenged by a rival candidate.