This paper addresses conditions for the existence of additive separable utilities. It considers
mainly two-dimensional Cartesian products in which restricted solvability holds wrt one
component, but some results are extended to n-dimensional spaces. The main result shows
that, in general, cancellation axioms of any order are required to ensure additive
representability. More precisely, a generic family of counterexamples is provided, proving
that the (m+ 1) st order cancellation axiom cannot be derived from the mth order cancellation …