  Committee scoring voting rules are multiwinner analogues of positional
scoring rules which constitute an important subclass of single-winner voting
rules. We identify several natural subclasses of committee scoring rules,
namely, weakly separable, representation-focused, top-$k$-counting, OWA-based,
and decomposable rules. We characterize SNTV, Bloc, and $k$-Approval
Chamberlin--Courant as the only nontrivial rules in pairwise intersections of
these classes. We provide some axiomatic characterizations for these classes,
where monotonicity properties appear to be especially useful. The class of
decomposable rules is new to the literature. We show that it strictly contains
the class of OWA-based rules and describe some of the applications of
decomposable rules.
