  A total mass is the weighted count of continuous homomorphisms from the
absolute Galois group of a local field to a finite group. In the preceding
paper, the authors observed that in a particular example, two total masses
coming from two different weightings are dual to each other. We discuss the
problem how general such a duality holds and relate it to the existence of
simultaneous resolution of singularities, using the wild McKay correspondence
and the Poincar\'e duality for stringy invariants. We also exhibit several
examples.
