We study the proportional chore division problem where a protocol wants to
divide an undesirable object, called chore, among n different players. The
goal is to find an allocation such that the cost of the chore assigned to each
player be at most 1/n of the total cost. This problem is the dual variant of
the cake cutting problem in which we want to allocate a desirable object.
Edmonds and Pruhs showed that any protocol for the proportional cake cutting
must use at least Ω(nlogn) queries in the worst case, however,
finding a lower bound for the proportional chore division remained an
interesting open problem. We show that chore division and cake cutting problems
are closely related to each other and provide an Ω(nlogn) lower bound
for chore division