The weighted voting systems for the voters A, B, C, ... are given in the form q: w1,w2,w3,w4,…,wn The weight of voter A is w1, the weight of voter B is w2, the weight of voter C is w3, and so on. Calculate, if possible, the Banzhaf power index for each voter. Round to the nearest hundredth. (If not possible, enter IMPOSSIBLE.) {5: 3, 2, 2} BPI(A)= BPI(B)= BPI(C)=

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The weighted voting systems for the voters A, B, C, ... are given in the form    q: w1,w2,w3,w4,…,wn    The weight of voter A is w1, the weight of voter B is w2, the weight of voter C is w3, and so on.   Calculate, if possible, the Banzhaf power index for each voter. Round to the nearest hundredth. (If not possible, enter IMPOSSIBLE.)   {5: 3, 2, 2}   BPI(A)=   BPI(B)=      BPI(C)=

Margaret Plemons · Accepted Answer

Step 1  Please see the answer below  Step 2  The winning coalitions are listed below, with the critical players bolded.  {A,B}  Total weight: 5. Meets quota.  {A,C}  Total weight: 5. Meets quota.  {B,C}  Total weight: 4. Does not meet quota.  {A,B,C} Total weight: 9. Meets quota.  Altogether, A is critical 3 times, B is critical 1 time, and C is critical 1 time.  Total of all: 5  Divide each player’s count by 5 to convert to fractions  BPI(A)=35=0.60  BPI(B)=25=0.20  BPI(C)=15=0.20

The weighted voting systems for the voters A, B, C, ... are given in t

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