In the context of the classical fair division problem, we show that Efficie
ncy and Resource Monotonicity are incompatible with the following "Conditio
nal Equal Split" condition: If equal split of the collective endowment is e
fficient, it should be among the recommended allocations. (C) 2000 Elsevier
Science S.A. All rights reserved. JEL classification: D51; D63.