TY - JOUR

T1 - Better Ways to Cut a Cake - Revisited

AU - Brams, Steven J.

AU - Jones, Michael A.

AU - Klamler, Christian

N1 - Publisher Copyright:
© 2007 Dagstuhl Seminar Proceedings. All rights reserved.

PY - 2007

Y1 - 2007

N2 - Procedures to divide a cake among n people with n-1 cuts (the minimum number) are analyzed and compared. For 2 persons, cut-and-choose, while envy-free and efficient, limits the cutter to exactly 50% if he or she is ignorant of the chooser’s preferences, whereas the chooser can generally obtain more. By comparison, a new 2-person surplus procedure (SP’), which induces the players to be truthful in order to maximize their minimum allocations, leads to a proportionally equitable division of the surplus—the part that remains after each player receives 50%—by giving each person a certain proportion of the surplus as he or she values it. For n ≥ 3 persons, a new equitable procedure (EP) yields a maximally equitable division of a cake. This division gives all players the highest common value that they can achieve and induces truthfulness, but it may not be envy-free. The applicability of SP’ and EP to the fair division of a heterogeneous, divisible good, like land, is briefly discussed.

AB - Procedures to divide a cake among n people with n-1 cuts (the minimum number) are analyzed and compared. For 2 persons, cut-and-choose, while envy-free and efficient, limits the cutter to exactly 50% if he or she is ignorant of the chooser’s preferences, whereas the chooser can generally obtain more. By comparison, a new 2-person surplus procedure (SP’), which induces the players to be truthful in order to maximize their minimum allocations, leads to a proportionally equitable division of the surplus—the part that remains after each player receives 50%—by giving each person a certain proportion of the surplus as he or she values it. For n ≥ 3 persons, a new equitable procedure (EP) yields a maximally equitable division of a cake. This division gives all players the highest common value that they can achieve and induces truthfulness, but it may not be envy-free. The applicability of SP’ and EP to the fair division of a heterogeneous, divisible good, like land, is briefly discussed.

UR - http://www.scopus.com/inward/record.url?scp=85174419324&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85174419324&partnerID=8YFLogxK

M3 - Conference article

AN - SCOPUS:85174419324

SN - 1862-4405

VL - 7261

JO - Dagstuhl Seminar Proceedings

JF - Dagstuhl Seminar Proceedings

T2 - Fair Division 2007

Y2 - 24 June 2007 through 29 June 2007

ER -