Arrow's original proof of his impossibility theorem proceeded in two steps: showing the existence of a decisive voter, and then showing that a decisive voter is a dictator. Barbera replaced the decisive voter with the weaker notion of a pivotal voter, thereby shortening the first step, but...

Approval voting has attracted considerable interest among voting theorists, but they have rarely investigated it in the Arrovian frame-work of social welfare functions (SWF) and never connected it with Arrow's impossibility theorem. This note explores these two directions. Assuming that voters...