This was actually depicted in Arthur C. Clarke's book "Songs of Distant Earth": a distant robo-seeded colony of Earth is visited by the last starship from dying

This was actually depicted in Arthur C. Clarke's book "Songs of Distant Earth": a distant robo-seeded colony of Earth is visited by the last starship from dying Earth, on the way to another world (this world doesn't have enough land area for all the humans on the starship) to rebuild its ice shield. The society on this world is very small, about the size of a small city, since it's basically one small island on a waterworld. The society has a mayor, who is drafted for the job, with only one disqualification: anyone who actually wants the job is barred from having it.