B) consider the weighted voting system (q: 8,4,2,1). find the banzhaf power distribution of this weighted voting systwm when q=15.

Given : (q: 8,4,2,1)

q = 15

List all coalitions ( 2 pair)

Those whose total weight is equal to q or more than q will go further in the list of winning coalitions

Since No pair's total weight is equal to q or more than q . So, we will not consider then further

Coalitions (  3 pair or more)

Those whose total weight is equal to q or more than q will go further in the list of winning coalitions

winning coalitions:

If Player 1 leaves

So, total weight will be 4+2+1 = 7

So, Player 1 is critical

If Player 2 leaves

So, total weight will be 8+2+1 = 11

So, Player 2 is critical

If Player 3 leaves

So, total weight will be 8+4+1 = 13

So, Player 3 is critical

If Player 4 leaves

So, total weight will be 8+4+2 = 14

So, Player 4 is critical

Player          Times critical           Banzhaf power index

 1                        1                  

 2                        1                

  3                        1                

  4                        1                

                     Sum = 4

a. -0.3 > -0.33

300pi

step-by-step explanation: