On stable rules for selecting committees

A voting rule is said to be stable if it always elects a fixed-size subset of candidates such that there is no outside candidate who is majority preferred to any candidate in this set whenever such a set exists. Such a set is called a Weak Condorcet Committee (WCC). Four stable rules have been proposed in the literature. In this paper, we propose two new stable rules. Since nothing is known about the properties of the stable rules, we evaluate all the identified stable rules on the basis of some appealing properties of voting rules. We show that they all satisfy the Pareto criterion and they are not monotonic. More, we show that every stable rule fails the reinforcement requirement.