Committee Scoring Rules: Axiomatic Classification and Hierarchy

We consider several natural classes of committee scoring rules, namely, weakly separable, representation-focused, top-k-counting, OWA-based, and decomposable rules. We study some of their axiomatic properties, especially properties of monotonicity, and concentrate on containment relations between them. We characterize SNTV, Bloc, and k-approval Chamberlin-Courant, as the only rules in certain intersections of these classes. We introduce decomposable rules, describe some of their applications, and show that the class of decomposable rules strictly contains the class of OWA-based rules.

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