TY - JOUR

T1 - Two-person pie-cutting

T2 - The fairest cuts

AU - Barbanel, Julius B.

AU - Brams, Steven J.

PY - 2011/1

Y1 - 2011/1

N2 - Barbanel, Brams, and Stromquist (in 2009) asked whether there exists a twoperson moving-knife procedure that yields an envy-free, undominated, and equitable allocation of a pie. We present two procedures: One yields an envy-free, almost undominated, and almost equitable allocation, whereas the second yields an allocation with the two "almosts" removed. The latter, however, requires broadening the definition of a "procedure," which raises philosophical, as opposed to mathematical, issues. An analogous approach for cakes fails because of problems in eliciting truthful preferences.

AB - Barbanel, Brams, and Stromquist (in 2009) asked whether there exists a twoperson moving-knife procedure that yields an envy-free, undominated, and equitable allocation of a pie. We present two procedures: One yields an envy-free, almost undominated, and almost equitable allocation, whereas the second yields an allocation with the two "almosts" removed. The latter, however, requires broadening the definition of a "procedure," which raises philosophical, as opposed to mathematical, issues. An analogous approach for cakes fails because of problems in eliciting truthful preferences.

UR - http://www.scopus.com/inward/record.url?scp=80052705733&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=80052705733&partnerID=8YFLogxK

U2 - 10.4169/college.math.j.42.1.025

DO - 10.4169/college.math.j.42.1.025

M3 - Article

AN - SCOPUS:80052705733

SN - 0746-8342

VL - 42

SP - 25

EP - 32

JO - College Mathematics Journal

JF - College Mathematics Journal

IS - 1

ER -