We characterize a rule in minimum cost spanning tree problems using an additivity property and some basic properties. If the set of possible agents has at least three agents, these basic properties are symmetry and separability. If the set of possible agents has two agents, we must add positivity.

The division problem under constraints consists of allocating a given amount of an homogeneous and perfectly divisible good among a subset of agents with single-peaked preferences on an exogenously given interval of feasible allotments. We characterize axiomatically the family of extended...