Cake division with minimal cuts: envy-free procedures for three persons, four persons, and beyond

Julius B. Barbanel, Steven J. Brams
2004 Mathematical Social Sciences  
The minimal number of parallel cuts required to divide a cake into n pieces is n À 1. A new 3person procedure, requiring two parallel cuts, is given that produces an envy-free division, whereby each person thinks he or she receives at least a tied-for-largest piece. An extension of this procedure leads to a 4-person division, using three parallel cuts, which makes at most one person envious. Finally, a 4-person envy-free procedure is given, but it requires up to five parallel cuts, and some
more » ... es may be disconnected. All these procedures improve on extant procedures by using fewer moving knives, making fewer people envious, or using fewer cuts. D
doi:10.1016/j.mathsocsci.2004.03.006 fatcat:kzdphduf25hzpeizvzhik3prai