Better Ways to Cut a Cake - Revisited

Abstract

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 a certain proportion of the surplus as he or she values it. 
For n geq 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.