Before revision:  We introduce the class of counting rules , provide an axiomatic characterization of this class and, in particular, show that counting rules are consistent . Building upon this result, we axiomatically characterize three important consistent multi-winner rules: Proportional Approval Voting, Multi-Winner Approval Voting and the Approval Chamberlin-Courant rule.
After revision:  We introduce the class of counting rules , provide an axiomatic characterization of this class and, in particular, show that counting rules are consistent . Building upon this result, we axiomatically characterize three important consistent multi-winner rules: Proportional Approval Voting, Multi-Winner Approval Voting and the Approval Chamberlin--Courant rule.