  We model Monroe's and Chamberlin and Courant's multiwinner voting systems as
a certain resource allocation problem. We show that for many restricted
variants of this problem, under standard complexity-theoretic assumptions,
there are no constant-factor approximation algorithms. Yet, we also show cases
where good approximation algorithms exist (briefly put, these variants
correspond to optimizing total voter satisfaction under Borda scores, within
Monroe's and Chamberlin and Courant's voting systems).
