Extended proportionality in division problems with multiple references

We consider an extension of the classic problem of division with claims to situations in which the characteristics of the agents are multi-dimensional. The proportional rule is the most prominent in the one-dimensional case, however there is no obvious way to define proportionality for the extended model. In this paper we introduce a property which generalizes proportionality, identify the family of rules satisfying it, and characterize a particular rule within this family on the basis of a property of symmetry.