The energy of an eigenstate of a N-electron system can be expressed in terms of a sum of pair-state energies (eigenvalues of the two-particle reduced Hamiltonian) weighted by two-particle density matrix elements. This relation suggests that pair-state basis functions should provide a useful tool for analyzing many-electron systems. In order to provide a preliminary test of this idea, pair-state decompositions of exact solutions to some Hubbard model systems are examined as functions of the coupling strength.