Multi-winner elections address the need for more nuanced surveys of opinion, and may be feasible with the internet and increasing computational capacity. Procedures are typically adapted from single-winner elections. But few procedures for single-winner elections apply in a natural way to Variable Number of Winners (VNW) elections, in which the voters must determine not only which candidates win, but also how many winners there are--for example, for honorary status or a place on a hiring shortlist.
Approval ballots are natural for multi-winner elections, and can be counted in many ways. But many methods eo not apply in a VNW context, and properties are not well understood. IHere, axioms--some adapted from single-winner elections but others meaningful only in the VNW context--are proposed, and their consequences identified. The new axioms are used to characterize at least one new VNW electoral system.
