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 -