The vote took 11 minutes. At the end of it, the seven members of the municipal council of Fedje, an island of granite and heather at the mouth of the Fensfjord, had decided, 5 to 2, that after 79 years as a self-governing municipality the island would ask to be absorbed by Austrheim, its neighbor on the mainland, 35 minutes away by ferry.

“Nobody wanted this,” said Solveig Husa, the mayor, who voted in favor. “But the choice was not between being Fedje and being part of Austrheim. It was between being part of Austrheim and being a place that cannot hire a nurse.”

Fedje has 520 residents, down from more than 900 in the 1970s, when the island’s fishing fleet was larger and a fish-processing plant employed 60 people. It has a school with 31 pupils, a nursing home with 12 beds, a grocery store, and a municipal administration of 14 full-time staff. Its budget this year is 68 million kroner, about 5.8 million euros, of which roughly 80 percent comes from transfers from the national government.

The island famously resisted a 2017 national reform that cut the number of Norwegian municipalities from 428 to 356. In a referendum that year, 71 percent of residents voted to stay independent. Since then, the nursing home has gone through four directors, the school has struggled to recruit teachers, and the council has been unable to fill the post of municipal doctor for 19 months, relying instead on a physician who flies in from Bergen two days a week.

A nonbinding advisory vote held last month showed 61 percent of residents in favor of merging, a near reversal of 2017. “People got tired,” said Arne Fedøy, 68, a retired fisherman who voted no both times. “I understand them. I also think in 10 years the ferry will run less often and nobody in Austrheim will notice.”

The Local Government Ministry, which must approve the merger, has encouraged small municipalities to combine but has avoided forcing the issue since the 2017 reform proved unpopular in rural districts. A ministry spokeswoman, Ingrid Solberg, said the application would be processed “with respect for a decision that was made locally and, by all accounts, reluctantly.” If approved, the merger would take effect in January 2028, and Fedje would become a ward of Austrheim with a guaranteed seat on the joint council for 12 years.

After the vote, the council members walked to the community hall for coffee and waffles, which Ms. Husa said had been planned regardless of the outcome. “We are still Fedje,” she said. “The post code does not change. The weather does not change. It will just be someone else’s job to find the doctor.”