Electrolytes featuring negatively-charged polymers such as nonaqueous polyelectrolyte solutions and polymerized ionic liquids are currently under investigation as potential high cation transference number (t+) electrolytes for lithium ion batteries. Herein, we use coarse-grained molecular dynamics simulations to characterize the Onsager transport coefficients of polyelectrolyte solutions as a function of chain length and concentration. For all systems studied, we find that the rigorously computed transference number is substantially lower than that approximated by the ideal solution (Nernst-Einstein) equations typically used to characterize these systems due to the presence of strong anion-anion and cation-anion correlations. None of the polyelectrolyte solutions achieve t+ greater than that of the conventional binary salt electrolyte, with some solutions having negative t+. This work demonstrates that the Nernst-Einstein assumption does not provide a physically meaningful estimate of the transference number in these solutions and calls into question the expectation of polyelectrolytes to exhibit high cation transference number.