IA procedure, the main BTP procedure creates IAs for all ordered pairs of partners. For example, when there are 4 partners, there are 12 ordered pairs of partners. For each such pair (X,Y), we run a sub-procedure which guarantees that partner X has an IA over partner Y. After every partner has an IA over every other partner, we can just give the remainder to an arbitrary partner and the result is an envy-free division of the entire cake. See also Brams–Taylor–Zwicker procedure – a moving-knife procedure for 4 partners, which uses a finite number of cuts. Envy-free cake-cutting – older and newer procedures for the same problem. Adjusted winner procedure – procedure designed by Brams and Taylor addressing the similar, but distinct, problem of dividing goods between two agents. References Fair division protocols Cake-cutting