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00925njm 22002777a 4500 dc Bergantiños, Gustavo author Massó, Jordi author Moreno de Barreda, Inés author Neme, Alejandro author Universitat Autònoma de Barcelona. Unitat de Fonaments de l'Anàlisi Econòmica author 2013 We study how to partition a set of agents in a stable way when each coalition in the partition has to share a unit of a perfectly divisible good, and each agent has symmetric single-peaked preferences on the unit interval of his potential shares. A rule on the set of preference profiles consists of a partition function and a solution. Given a preference profile, a partition is selected and as many units of the good as the number of coalitions in the partition are allocated, where each unit is shared among all agents belonging to the same coalition according to the solution. A rule is stable at a preference profile if no agent strictly prefers to leave his coalition to join another coalition and all members of the receiving coalition want to admit him. We show that the proportional solution and all sequential dictator solutions admit stable partition functions. We also show that stability is a strong requirement that becomes easily incompatible with other desirable properties like e¢ ciency, strategy-proofness, anonymity, and non-envyness. Division problem Symmetric single-peaked preferences Stable partition Stable partitions in many division problems : the proportional and the sequential dictator solutions