Pareto-optimal and strategy-proof distributions of a perfectly divisib
le good among agents with single-dipped preferences are studied. In or
der to satisfy these two properties and, in addition, either a so-call
ed replacement property or a property of consistency, the whole amount
should be assigned to one of the agents. Characterizations of the two
classes of division rules satisfying the above conditions are provide
d. (C) 1997 Elsevier Science S.A.