Characterization of linear symmetric solutions for allocation problems

•This paper provides an analysis of solutions from an axiomatic point of view.•We propose a decomposition for the space of allocation problems.•We obtain characterizations of certain classes of linear symmetric solutions.

This paper provides an analysis of solutions for allocation problems from an axiomatic point of view, proposing a decomposition for the space of such problems into direct sum of irreducible subspaces that are relevant to the study of linear symmetric solutions. In particular, we obtain characterizations of certain classes of linear symmetric solutions involving the properties of efficiency and compatibility.