At the beginning of each football season, the coaching staff at Vista High School must vote to decide which players to select for the team. They use the weighted voting system {8: 7, 6, 1}. In this voting system, the head coach A has a weight of 7, the assistant coach B has a weight of 6, and the junior varsity coach C has a weight of 1.

(a) Compute the Banzhaf power index for each of the coaches. (Round your answers to the nearest hundredth.)

BPI(A) =

BPI(B) =

BPI(C) =

(b) Explain why it seems reasonable that the assistant coach and the junior varsity coach have the same Banzhaf power index in this voting system:

1)As to forming a winning coalition, the two minor coaches are the same.

2)The weightings for the minor coaches are different, so are their critical votes.

3)Winning coalitions often include support of different weight.