Better Ways to Cut a Cake

In this paper we show how mathematics can illuminate the study of cakecutting in ways that have practical implications. Specifically, we analyze cakecutting algorithms that use a minimal number of cuts (n − 1 if there are n people), where a cake is ametaphor for a heterogeneous, divisible good, whose parts may be valued differently by different people. These algorithms not only establish the existence of fair divisions—defined by the properties described below—but also specify a procedure for carrying themout. In addition, they give us insight into the difficulties underlying the simultaneous satisfaction of certain properties of fair division, including strategyproofness, or the incentive for a person to be truthful about his or her valuation of a cake.