You are not currently logged in.
Access your personal account or get JSTOR access through your library or other institution:
N-Person Cake-Cutting: There May Be No Perfect Division
Steven J. Brams, Michael A. Jones and Christian Klamler
The American Mathematical Monthly
Vol. 120, No. 1 (January 2013), pp. 35-47
Published by: Mathematical Association of America
Stable URL: http://www.jstor.org/stable/10.4169/amer.math.monthly.120.01.035
Page Count: 13
Preview not available
Abstract A cake is a metaphor for a heterogeneous, divisible good, such as land. A perfect division of cake is efficient (also called Pareto-optimal), envy-free, and equitable. We give an example of a cake that is impossible to divide among three players, so that these three properties are satisfied, however many (finite) cuts are made. It turns out that two of the three properties can be satisfied by a 3-cut and a 4-cut division, which raises the question of whether the 3-cut division, which is not efficient, or the 4-cut division, which is not envy-free, is more desirable (a 2-cut division can at best satisfy either envy-freeness or equitability, but not both). We prove that no perfect division exists for more than 4 cuts and for an extension of this example to more than three players.
Copyright the Mathematical Association of America 2013