Blocking Coalitions and the Banzhaf Power Index The four members, A, B, C, and D, of an organization adopted the weighted voting system {6: 4, 3, 2, 1}. The table below shows the winning coalitions. Winning coalition Number of votes Critical voters {A, B} 7 A, B {A, C} 6 A, C {A, B, C} 9 A {A, B, D} 8 A, B {A, C, D} 7 A, C {B, C, D} 6 B, C, D {A, B, C, D} 10 None Using the Banzhaf power index, we have BPI(A) = 5 12 . A blocking coalition is a group of voters who can prevent passage of a resolution. In this case, a critical voter is one who leaves a blocking coalition, thereby producing a coalition that is no longer capable of preventing the passage of a resolution. For the voting system from the table above, we have the following. Blocking coalition Number of votes Number of remaining votes Critical voters {A, B} 7 3 A, B {A, C} 6 4 A, C {A, D} 5 5 A, D {B, C} 5 5 B, C {A, B, C} 9 1 None {A, B, D} 8 2 A {A, C, D} 7 3 A {B, C, D} 6 4 B, C If we count the number of times A is a critical voter in a winning or blocking coalition, we find what is called the Banzhaf index. In this case, the Banzhaf index is 10 and we write BI(A) = 10. Using both the winning coalition and the blocking coalition tables, we find that BI(B) = 6, BI(C) = 6, and BI(D) = 2. This information can be used to create an alternative definition of the Banzhaf power index. Applying this definition to the voting system given above, we have BPI(A) = BI(A) BI(A) + BI(B) + BI(C) + BI(D) = 10 10 + 6 + 6 + 2 = 10 24 = 5 12 . Watch the video below then answer the question. Blocking Coalitions and the Banzhaf Power Index View Transcript Using the data in the Check Your Progress, which of the following are blocking coalitions? (Select all that apply.) {B, G} {G, L} {B, G, N} {B, L, N} {B, F, G, L} {B, F, I, N} {B, F, G, I, N} {B, G, I, L, N}

ponts AuExc4 43.EX003 | My Notee Asx Your Te 16 O Blocking Coalitions and the Banzhaf Power Index and I arganization adopted the weighted vating system (6 4, 3, 2, 1. The table below shows the winning coalitions mambers Winning coalition Number of votes Critical voters {A, , A , . ) A. B A . D1 A. C T (. . ? B. C. I {A, , . D) Nene e have BPIA) Using the Banzhaf power index blocking coalition is a group of voters who can prevent passage of a resolution. above, we have the following n this case, a critical votar is one who leaves a blocking coalition, theraby producing a coaltion that is no longer capable of preventing the passage of a resolution. For the voting system from the table Blocking coalition Number of Number of remaining votes Critical voter votes A B) B. C B. A. B. C None A, B. D) A, C. D A B.C. D . Banzhaf index, 1In this care the Banzhaf index i 10 and we write BNA)- winning coalition and the blocking coalition tablees, we find that BIB)-6. Using both AtC) 6and BND) - 2 . This information can be used to create an atemative deinition of the Banzhaf onwerindex Banzhaf Power Index-Alternative Definition Blocking Coaitions and the Banzhaf Powar Index BI(A) Viaw Transcript BPI(A)- sum of all Banzhaf indices for the voting system Using the data in the Check Your Progress, which of the following are blocking coalitions? (Select all that apply.) B. G G. L Applying this definition to the voting system given above, we have BA) BPA) AB 20 (B G, N) B. L N) anguer tl waech the vden helow then euastine B. FG, L) (B FI N (B. FG, I N I, L N ponts AuExc4 43.EX003 | My Notee Asx Your Te 16 O Blocking Coalitions and the Banzhaf Power Index and I arganization adopted the weighted vating system (6 4, 3, 2, 1. The table below shows the winning coalitions mambers Winning coalition Number of votes Critical voters {A, , A , . ) A. B A . D1 A. C T (. . ? B. C. I {A, , . D) Nene e have BPIA) Using the Banzhaf power index blocking coalition is a group of voters who can prevent passage of a resolution. above, we have the following n this case, a critical votar is one who leaves a blocking coalition, theraby producing a coaltion that is no longer capable of preventing the passage of a resolution. For the voting system from the table Blocking coalition Number of Number of remaining votes Critical voter votes A B) B. C B. A. B. C None A, B. D) A, C. D A B.C. D . Banzhaf index, 1In this care the Banzhaf index i 10 and we write BNA)- winning coalition and the blocking coalition tablees, we find that BIB)-6. Using both AtC) 6and BND) - 2 . This information can be used to create an atemative deinition of the Banzhaf onwerindex Banzhaf Power Index-Alternative Definition Blocking Coaitions and the Banzhaf Powar Index BI(A) Viaw Transcript BPI(A)- sum of all Banzhaf indices for the voting system Using the data in the Check Your Progress, which of the following are blocking coalitions? (Select all that apply.) B. G G. L Applying this definition to the voting system given above, we have BA) BPA) AB 20 (B G, N) B. L N) anguer tl waech the vden helow then euastine B. FG, L) (B FI N (B. FG, I N I, L N