Invited Talk: Steven Brams

Steven Brams Department of Politics New York University United States

Better Ways to Cut a Cake

Procedures to divide a cake among n people with n-1 cuts (the minimum number) are analyzed and compared. For 2 persons, cut-and-choose, while envy-free and efficient, limits the cutter to exactly 50% if he or she is ignorant of the chooser's preferences, whereas the chooser can generally obtain more. By comparison, a new 2-person surplus procedure (SP), which induces the players to be truthful in order to maximize their minimum allocations, leads to a proportionally equitable division of the surplus -- the part that remains after each player receives 50% -- by giving each person exactly the same proportion of the surplus as he or she values it. For n ≥ 3 persons, a new equitable procedure (EP) yields a maximally equitable division of a cake. This division gives all players the highest common value that they can achieve and induces truthfulness, but it may not be envy-free. The applicability of SP and EP to the fair division of a heterogeneous, divisible good, like land, is briefly discussed.

This is joint work with Michael A. Jones and Christian Klamler.