Better Ways to Cut a Cake

In Inthis this paper paper we weshow showhow howmathematics mathematics can can illuminate illuminatethe thestudy studyofof cake-cutting cake-cuttingin inways ways that that have have practical practical implications. implications. Specifically, Specifically, we we analyze analyze cake-cutting cake-cutting algorithms algorithms that that use use a a minimal minimal number number of of cuts cuts (n (n − −1 1if if there there are are n n people), people), where where a cake a cake is is a metaphor a metaphor for for a heteroge-a heterogeneous,neous, divisible divisible good, good, whose whose parts parts may may be be valued valued differently differently by by different different people. people. These Thesealgorithms algorithmsnot not only onlyestablish establishthe theexis existencetence of of fair fair divisions—defined divisions—definedby bythe the properties properties described described below—but below—but also also specify specify a procedure a procedure for fo