EXAMPLE 1 The Film Selection Committee

The Classic Film Society presents a film each month. A three-member committee—whose members are a faculty adviser, Allen, and two students, Betty and Cao—selects the films. A selection must be approved by Allen and at least one of the students.

The selection committee could make its decisions by using a weighted voting system in which Allen has a voting weight of 2, and each student has a voting weight of 1. Thus, Allen, together with one student, would have a total voting weight of 3, while the two students without Allen, or Allen by himself, would have a voting weight of 2. Therefore if we set the quota to be 3, selections will be approved if and only if the committee’s criteria for approval are satisfied.