Committee Scoring Rules: Axiomatic Classification and Hierarchy

We present and advertise the class of committee scoring rules, recently introduced as multiwinner analogues of single-winner scoring rules. We present a hierarchy of committee scoring rules (while includes all previously studied subclasses of committee scoring rules, as well as two new subclasses), discuss their axiomatic properties (while focusing on fixed-majority consistency and monotonicity) as well as their computational properties (while focusing on positive results). 

In the second part of the talk we will focus on one specifc result. We characterize the class of committee scoring rules that satisfy the fixed-majority criterion. In some sense, the committee scoring rules in this class are multiwinner analogues of the single-winner Plurality rule, which is uniquely characterized as the only single-winner scoring rule that satisfies the simple majority criterion. We define top-k-counting committee scoring rules and show that the fixed majority consistent rules are a subclass of the top-k-counting rules. We give necessary and sufficient conditions for a top-k-counting rule to satisfy the fixed-majority criterion.