Big Brother itself isn't a good setting to make a game on: as it so aptly says, the future is a boot, stamping on a human face forever. The people who could care are controlled to tightly; the masses who could act don't care.
The world in Big Brother is no longer capable of change for the better. Not unless everything is razed and begun again from nothing.
Orwellian dystopias are quite common and perfectly workable, however.
For the dystopias, think of how it came about and why. These things can have an obvious main cause (such as the rise of Nazi Germany or Soviet Russia.)
The players, presumably, are fighting against such a regime. They should have to try to motivate the proles into action: distributing propaganda, sabotaging regime propaganda, assassination.
The players shoukd have to careful of everything. Informants, police... Even each other, if they have conflicting goals. It should be difficult for the players, and even if they win, what then?
It might be interesting if you combined Gig's misinterpretation of Big Brother as the world of 1984, and players were trying to start a revolution on the set of a reality tv series, where the people running it are a bit better at nipping that sort of thing in the bud than the Hunger Game people.
And so the producers of the show are trying to provoke interpersonal drama, and giving into that sort of thing makes the higher-ups trust you more/reduces your heat. Or maybe there's a point system in place, and giving into your emotions gives you points. Or maybe Big Brother is looking for naturally unstable people, so you have a Neurosis stat that gets rolled when you're provoked, and failing (or would it be succeeding?) causes you to freak out.
Also, some players might not be into the revolution. Players might get secret goals when they join, and some might be for the resistance, but others would be trying to get famous or trying to hook up, and there might even be a few counter-revolutionaries in there. So you don't know if your fellow players are trying to help you, might need some convincing to help you, or will absolutely bust your ass if they know for sure you're with the resistance.