  We consider the problem of selecting an $n$-member committee made up of one
of $m$ candidates from each of $n$ distinct departments. Using an algebraic
approach, we analyze positional voting procedures, including the Borda count,
as $\mathbb{Q}S_m \wr S_n$-module homomorphisms. In particular, we decompose
the spaces of voter preferences and election results into simple $\mathbb{Q}S_m
\wr S_n$-submodules and apply Schur's Lemma to determine the structure of the
information lost in the voting process. We conclude with a voting paradox
result, showing that for sufficiently different weighting vectors, applying the
associated positional voting procedures to the same set of votes can yield
arbitrarily different election outcomes.
