The only nation aboard the Precipice is called the National Government. While technically subordinate to Commander Pastor and the Precipice (well, you wouldn't try to piss off someone who's letting you stay at their house), neither of them interferes in the National Government's business unless it affects them or the crew.
The National Government is governed by a council of three, also known as the Triumvirate. Members of the Triumvirate are known as 'Consuls'. They are elected to 8 year terms by the Senate. The Senate itself is a directly elected (by the people of the National Government)
unicameral legislature, elected by the people of the National Government.
Crew members of the Precipice are given special privileges. Any crimes a crew member commits on board will be dealt by the Commander himself. Though that might not be a privilege, considering how Commander Pastor changes his personality utterly when dealing with errant crew members.
The technology of the Precipice is very much still under investigation by the Research team. It seems like the Precipice conducts all his own repairs, and never needs physical maintenance of public areas. Even vandalism disappears in the night. Whatever belongs in the interiors of this ship, no one has found out.
The technology level of the society itself, though, quite differs. Though technically in a world filled with plasma and lasers, special armors that rely on electricity to shield you without weighing you down, machines that materialise food and a virtual reality internet, the National Government is split up into 5 wings, each corresponding to each of Precipice's metal wings. (There's 5 of them. The Precipice would look like a weird starship if he stretched himself out.)
The Lionheart Wing: People that used to belong in a medieval society usually live in the Old Wing. Though specially designed to look like a huge medieval city (even the sky looks blue), the technologies that characterise the Precipice are very well hidden (A TV screen can be hidden in a wooden cabinet. A phone is disguised as a statue. Only the washrooms look obviously modern.). It's pretty much the only place that has farmland though, and food made from real animals is considered a luxury delicacy aboard the Precipice.
The Einstein Wing: Imagine our current technological level.
The Shepard Wing: The most 'modern' of all wings.
The Victorian Wing: This wing has a Victorian look. It is strangely one of the more popular wings for people who stay in the Einstein Wing to visit.
The Caesar Wing: This wing looks like the ancient era.
No matter how 'backwards' a wing might look, every wing has access to modern technology. Each wing is populated with roughly 200 million people.