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When living with roommates, splitting rent is often a dilemma. It's common to divide the rent equally, usually based on the square footage of each person’s room. While this approach seems fair at first glance, it overlooks one crucial factor: personal preferences. The New York Times discusses a mathematical technique, 'Sperner's Lemma,' that can make rent division more equitable.
Albert Sun highlights a flaw in the traditional way of splitting rent:
The issue is that individuals value spaces differently. For instance, natural light may be essential for one person, but not for another. Is having no closet a dealbreaker? Some might prioritize the room's shape or its distance from the bathroom more.
'Sperner’s Lemma,' discovered by mathematician Emanuel Sperner in 1928, is a complex concept. In simple terms, it’s a mathematical formula used to divide things fairly. In 1999, professor Francis Su applied this theory to rent splitting. According to The New York Times article:
'The key is to create a system where everyone acts in their own self-interest and ends up with a fair outcome,' he shared in an interview... The brilliance of this method is that you don't need to come up with the numbers on your own.
How does it work? Roommates take turns answering a series of questions and selecting the room they prefer, based on a proposed price. As the process continues, the hypothetical prices become more accurate, making decisions more complex. The roommates continue this process until an equitable division is reached.
'What this approach ensures is that the outcome is 'envy-free,' as game theorists would say. No one will feel the urge to trade their room and price with anyone else's,' the article explains.
Fortunately, applying Sperner's Lemma is now easier than ever. You can use their rent division calculator to apply it to your own living situation. For a deeper dive, be sure to check out their full article.
Screenshot from NyTimes.com.
