More Fairness

In this chapter, we continue our study of fair division. We start with a closer look at the adjusted winner procedure, introduced in Section 5.6, that guarantees an efficient, equitable, and envy-free allocation of goods for two people. In Section 11.2, we will prove the efficiency of the procedure, and in Section 11.3, we will see that, typically, honesty is the best strategy for the procedure.

Beginning in Section 11.4, we study cake-cutting procedures for three or more people. Just as the addition of a third alternative considerably complicates the search for a perfect social choice procedure, we will see that the addition of a third party also complicates the search for the best fair division method. We present in Section 11.4 a procedure that guarantees each of three parties a proportional share of cake. In Section 11.5, we consider two procedures which each guarantee an envy-free portion of cake. In Section 11.6, we present an envy-free procedure for four parties. None of the methods we consider here are efficient nor equitable, however, and in Section 11.7, we will see that our search for an efficient, envy-free, and equitable procedure for three or more parties will fare no better than our search for a perfect social choice procedure or apportionment method.