  We present a new approximation to ionic conductivity well suited to dynamical
atomic-scale simulations, based on the Nernst-Einstein equation. In our
approximation, ionic aggregates constitute the elementary charge carriers, and
are considered as non-interacting species. This approach conveniently captures
the dominant effect of ion-ion correlations on conductivity, short range
interactions in the form of clustering. In addition to providing better
estimates to the conductivity at a lower computational cost than exact
approaches, this new method allows to understand the physical mechanisms
driving ion conduction in concentrated electrolytes. As an example, we consider
Li$^+$ conduction in poly(ethylene oxide), a standard solid-state polymer
electrolyte. Using our newly developed approach, we are able to reproduce
recent experimental results reporting negative cation transference numbers at
high salt concentrations, and to confirm that this effect can be caused by a
large population of negatively charged clusters involving cations.
