Dividing up the rent in a manner both fair and equitable is basically the worst part of having roommates. Anna has a window, so that’s worth something, but also her room is the smallest and she shares a wall with Carla, who has loud sex all the time, so she should get a discount for that. Meanwhile, Tom has the biggest room, and so should probably pay the most, except that, wait, the room has no closet — it’s enough to send you running to the nearest studio apartment. You’ll be broke, but at least you won’t be arguing over the monetary value of natural light.
Alternately, you could follow the advice of Albert Sun at the New York Times, and use Sperner’s lemma, a mathematical proposition for dividing things. Important things like deep-sea mining rights, or Germany after WWII. Also, roommate rent.
The NYT lays out the whole method, which uses triangles to track all the possible combination of preferences and prices. It’s not not complicated, but, as a reward, you get a rent structure that’s “envy free,” in game theorist speak. Theoretically, at least, everyone will be happy with their room and price, and no one will want to swap with anyone else. It’s going to be great. They’ve even put together a handy rent division calculator to do all the work for you, no hand-drawn triangles required.