Vault 657
The overseer is a different inhabitant every day, picked randomly by a computer. Only a team of 10 people know that the vault runs in this fashion. They cannot be chosen as overseer, and they are sworn to secrecy. Disclosing the system results in immediate extraction and termination of all involved inhabitants, as well as replacement of the involved team member. The transition happens overnight at a scheduled time. The computer picks a name from the list of vault dwellers, and the team takes the chosen person to the room with the computer while they're asleep. Sleeping gas is pumped into sleeping quarters during the night to ensure that no one wakes up. At the same time, the previous overseer is taken out of the computer room and moved into the bed the new overseer was sleeping in. In the morning, the dwellers that knew the person who was moved out will assume that bedding arrangements were changed overnight.
The overseer will wake up in the computer room with no idea what's going on. Three members of the team are stationed in the room to instruct and watch over the overseer. The overseer will be instructed to sit in front of the computer and open up "Vault-Sim.exe". When the program opens, it boots into a running simulation of a Vault-Tec vault. The overseer is told that he has free reign to do whatever he wants in the game, and he just has to have fun.
The game actually directly controls vault 657. Everything you do in the game happens in the vault. Should the overseer get close to destroying the vault, the 3 stationed team members will paralyze the overseer, and the computer will take control of the vault to clean up the overseer's mess. When everyone else in the vault goes to sleep, the overseer will be directed to go to sleep. Then, before the computer selects a new overseer, the team wipes all memory of the day from the overseer's mind.
tl;dr new overseer every day, no one knows the overseer is rotated, no one remembers when they're the overseer, the overseer thinks he's playing a game, the game is real life
