  There has been much recent work on multiwinner voting systems. However,
sometimes a committee is highly structured, and if we want to vote for such a
committee, our voting method should be more structured as well. We consider
committees consisting of representatives for disjoint parts of a collective;
for instance, n departments of an organization might each have m possible
representatives to choose from. However, in our model the entire population
still gets to vote on the committee, and we need to respect that symmetry,
which we do by building on earlier work of Barcelo et al. using representation
theory of wreath products. The main thrust of this paper is to advertise and
catalog the surprising variety of possible points-based (linear) voting methods
in this framework. For instance, if a voter ranks all possible structured
committees, it may be reasonable to use weights which depend on the relations
between the ranked committees, and not just their order as in 'traditional'
voting frameworks!
