Government Officials
In our utopia, we have 12 elected officials running the facility, each person having a specific job.
Every 7 years, new officials are elected, whether they are new or returning. Every adult votes for an official in each profession (i.e, Secretary of Education, etc. ) . The officials are in charge and can even be blamed for problems under certain circumstances. Every choice is made by them, unless someone creates a petition and stops them.
Punishment
Usually, everyone gets along to some degree. But when someone gets in trouble, it's not a good thing. The first time, you get a warning and a probation from free time for a while. The time of probation grows as the amount of punishments increase, until the tenth one. On the tenth one, you have to leave the island (sad, right ?) .
Court System
In our utopia, the court judges are elected just like the officials. They are fair (very, very fair) . The rules and procedures are just like any court.