Worksheet for Calculating the Banzhaf Power

Problem Number ______Name ______

Worksheet for calculating the “Banzhaf Power” in a weighted voting system with Four players

Q P1 P2 P3 P4

[ : , , , ] (Total number of votes: ______)

List of all coalitions:

{ P1 } { P1, P2 } { P1, P2, P3 } { P1, P2, P3, P4 }

{ P2 } { P1, P3 } { P1, P2, P4 }

{ P3 } { P1, P4 } { P1, P3, P4 }

{ P4 } { P2, P3 } { P2, P3, P4 }

{ P2, P4 }

{ P3, P4 }

1. Cross off all coalitions above that do NOT win.

2. Mark each critical player with an underscore ( _ ) or a circle.

3. For each player, calculate the power. The denominator of each fraction below is the same, it is the total number of marks for all players. The numerator of each fraction is the number of times the particular player is critical. When done, all percentages should add to 100% (or close 10 to 100% if you rounded them off).

P1: ------x 100 = %

P2: ------x 100 = %

P3: ------x 100 = %

P4: ------x 100 = %