The constable is the law enforcement official for Serenity on the planet Sectar. Once a person accepts the badge of office, it is that person's job for life (however short that may end up being). Due to the rampaging Borays, the life expectancy of the constable is generally not very long. After Constable Farnes is killed in a Boray raid, Bogan's only hope is for a drifter or other outsider to happen into town, as nobody from Serenity is foolish enough to accept the badge. Half the people in Serenity have held the office, dying while discharging their duty.
The badge is made out of solid gold. It has inscriptions on it in the ancient tongue of the people who first colonized Sectar. Once a person accepts the badge, for whatever reason, they accept all the responsibilities that come with it.
After getting conned into winning the badge in a hand of cards, Starbuck later passes the job onto Nogow, the leader of the Borays, thus relieving himself of the duty and ridding the town of its Boray raiding problem (TOS: "The Magnificent Warriors").