Yesterday’s New York Times included an article in the Science Times titled “To Divide the Rent, Start With a Triangle” by Albert Sun. He described how Sperner’s lemma could be used for a procedure for fair division of rent in an apartment with three bedrooms of different sizes and other features. Dr. Francis Su had applied the Sperner’s lemma to this challenge, noting that “the trick is to design a procedure to have everyone act in their own self-interest and have an outcome that’s fair.”
Although rent and roommates don’t come up in my practice, the issue of dividing prized possessions in estate planning or estate settlement is a common and thorny problem. The beauty of these fair division procedures, like mediation itself, is the neutrality. No one is treated better than anyone else; each individual’s self-interest determines the value that he or she places on a possession.
