Maximal domain of preferences in the division problem

The division problem consists of allocating an amount of a perfectly divisi ble good among a group of n agents. Sprumont (1991) showed that if agents h ave single-peaked preferences over their shares, then the uniform allocatio n rule is the unique strategy-proof, efficient, and anonymous rule. We iden tify the maximal set of preferences, containing the set of single-peaked pr eferences, under which there exists at least one rule satisfying the proper ties of strategy-proofness, efficiency, and strong symmetry. In addition, w e show that our characterization implies a slightly weaker version of Ching and Serizawa's (1998) result. (C) 2001 Academic Press.