If you’ve ever rented a home with others, you’ve probably faced the dilemma of deciding who gets what room and how split the rent fairly, given that some rooms might be bigger or better than others. This New York Times calculator, based on a mathematical theory of fair division, comes to the rescue.
Enter the total rent and the number of roommates. Then, each person is proposed different prices for the rooms available and chooses based on what seems fair to him/her. The calculator repeats this several times for each person, switching up the proposed amounts until everyone is satisfied
It’s kind of like eye doctor exams. For example, would you prefer Room 1 for $250 or Room 2 for $400? How about Room 1 for $150 or Room 2 for $350?
The calculator is based on a mathematical theory called Sperner’s Lemma, and the creators describe it this way:
The division method used here is designed to produce an “envy-free” division of the rooms of a shared apartment, i.e. no one will want to swap their room and price for someone else’s.
It is unfortunately beyond the scope of any algorithm to keep you from envying your roommate’s job, sex life or wardrobe — or save you from buyer’s remorse.
With each decision about which room to take at different prices, the algorithm becomes more accurate. It learns more about how much each roommate likes each room and narrows the range of prices it thinks might be fair.
This calculator should work for almost all situations, but there are a few scenarios in which it will fail. It won’t work if for example, there are divisions of the rent where one roommate would find every room unacceptable. It also won’t work if, even when one room is free one roommate would still take the most expensive room.
If you and your potential roommates find you can’t agree even after using the calculator, however, you might want to look for a different apartment (or different roommates).
Divide Your Rent Fairly [The New York Times]