Question 1

Given the weighted voting system [12: 1, 3, 5, 7], what is the probability that the voter C is a critical voter?

Accepted Answer

A)  1/4 
B)  3/8 
C)  1/2 
D)  5/8 
A)  1/4 
B)  3/8 
C)  1/2 
D)  5/8

Question 2

Calculate the Shapley-Shubik power index for the weighted voting system [30: 20, 17, 10, 5].

Accepted Answer

(5/12, 1/4

Question 3

Give an example of a weighted voting that is equivalent to the [8: 5, 4, 3].

Accepted Answer

Answers ma

Question 4

Given the weighted voting system [51: 45, 43, 7, 5], list all blocking coalitions.

Accepted Answer

(A, B) (A, C) (A, B,

Question 5

For the system [q: 30, 10, 6], which of the following cannot be the quota q?

Accepted Answer

A)  24 
B)  32 
C)  40 
D)  47 
A)  24 
B)  32 
C)  40 
D)  47

Question 6

A committee has six voters with the system [8: 5, 2, 2, 2, 2, 2]. How many extra votes does the coalition {B, C, E, F} have?

Accepted Answer

A)  0 
B)  1 
C)  2 
D)  8 
A)  0 
B)  1 
C)  2 
D)  8

Question 7

Use the weighted voting system [12: 4, 4, 3, 3, 2, 1] to answer the following questions
-Calculate the Banzhaf power index for each voter.

Accepted Answer

(20, 20, 1

Question 8

Given the weighted voting system [51: 45, 43, 7, 5], which of the following is a blocking coalition? 
$I \{ A \}$
II $\{ B , C \}$
III $\{ \mathrm { C } \}$

Accepted Answer

A)  II only 
B)  I and II 
C)  I, II, and III 
D)  none 
A)  II only 
B)  I and II 
C)  I, II, and III 
D)  none

Question 9

Use the weighted voting system [12: 8, 4, 4, 3, 3] to answer the following questions
-Which of the following is a winning coalition?

Accepted Answer

A)  {A, E} 
B)  {B, D, E} 
C)  {A, D} 
D)  {C, D, E} 
A)  {A, E} 
B)  {B, D, E} 
C)  {A, D} 
D)  {C, D, E}

Question 10

Given the weighted voting system [8: 4, 3, 2, 1], who is the pivotal voter for the permutation {A, B, C, D}?

Accepted Answer

A)  A 
B)  B 
C)  C 
D)  D 
A)  A 
B)  B 
C)  C 
D)  D

Question 11

Which voters in the system [30: 20, 17, 10, 5] have veto power?

Accepted Answer

A)  A only 
B)  A and B 
C)  A, B, and C 
D)  none 
A)  A only 
B)  A and B 
C)  A, B, and C 
D)  none

Question 12

Given the weighted voting system [6: 4, 3, 2, 1], which of the coalitions listed are minimal winning coalitions? 
$$\text { I } \{ A , B \} \quad \text { II } \{ A , C \} \quad \text { III } \{ B , C , D \}$$

Accepted Answer

A)  I only 
B)  I and II 
C)  II and III 
D)  I, II, and III 
A)  I only 
B)  I and II 
C)  II and III 
D)  I, II, and III

Question 13

Given the weighted voting system [14: 10, 6, 5, 3], find the Banzhaf power index for each voter.

Accepted Answer

The answer of Given the weighted voting system [14: 10,...

Question 14

Given the weighted voting system [51: 45, 43, 7, 5], list all minimal winning coalitions.

Accepted Answer

(A, B) (A,

Question 15

Calculate ${ } _ { 10 } C _ { 0 }$

Accepted Answer

A)  0 
B)  1 
C)  10 
D)  15 
A)  0 
B)  1 
C)  10 
D)  15

Question 16

Given the weighted voting system [34: 30, 18, 6], calculate the Banzhaf power index.

Accepted Answer

A)  (6, 4, 2) 
B)  (6, 2, 2) 
C)  (6, 6, 6) 
D)  (6, 4, 0) 
A)  (6, 4, 2) 
B)  (6, 2, 2) 
C)  (6, 6, 6) 
D)  (6, 4, 0)

Question 17

Are the weighted voting systems [18: 10, 9, 8] and [15: 8, 7, 6] equivalent?

Accepted Answer

A) True 
 B)False

Question 18

In the weighted voting system [9: 10, 5, 3], voter A is a dictator.

Accepted Answer

A) True 
 B)False

Question 19

What would be the quota for a voting system that has a total of 41 votes and uses a simple majority quota?

Accepted Answer

A)  20 
B)  21 
C)  31 
D)  41 
A)  20 
B)  21 
C)  31 
D)  41

Question 20

In the weighted voting system [8: 5, 2, 2, 2, 2, 2], find the Banzhaf power index for voter A.

Accepted Answer

A)  8 
B)  10 
C)  15 
D)  40 
A)  8 
B)  10 
C)  15 
D)  40

Exam 11: Weighted Voting Systems

Given the weighted voting system [12: 1, 3, 5, 7], what is the probability that the voter C is a critical voter?

Calculate the Shapley-Shubik power index for the weighted voting system [30: 20, 17, 10, 5].

Give an example of a weighted voting that is equivalent to the [8: 5, 4, 3].

Given the weighted voting system [51: 45, 43, 7, 5], list all blocking coalitions.

For the system [q: 30, 10, 6], which of the following cannot be the quota q?

A committee has six voters with the system [8: 5, 2, 2, 2, 2, 2]. How many extra votes does the coalition {B, C, E, F} have?

Use the weighted voting system [12: 4, 4, 3, 3, 2, 1] to answer the following questions -Calculate the Banzhaf power index for each voter.

Given the weighted voting system [51: 45, 43, 7, 5], which of the following is a blocking coalition? I{A}I \{ A \}I{A} II {B,C}\{ B , C \}{B,C} III {C}\{ \mathrm { C } \}{C}

Use the weighted voting system [12: 8, 4, 4, 3, 3] to answer the following questions -Which of the following is a winning coalition?

Given the weighted voting system [8: 4, 3, 2, 1], who is the pivotal voter for the permutation {A, B, C, D}?

Which voters in the system [30: 20, 17, 10, 5] have veto power?

Given the weighted voting system [6: 4, 3, 2, 1], which of the coalitions listed are minimal winning coalitions? I {A,B} II {A,C} III {B,C,D}\text { I } \{ A , B \} \quad \text { II } \{ A , C \} \quad \text { III } \{ B , C , D \} I {A,B} II {A,C} III {B,C,D}

Given the weighted voting system [14: 10, 6, 5, 3], find the Banzhaf power index for each voter.

Given the weighted voting system [51: 45, 43, 7, 5], list all minimal winning coalitions.

Calculate 10C0{ } _ { 10 } C _ { 0 }10​C0​

Given the weighted voting system [34: 30, 18, 6], calculate the Banzhaf power index.

Are the weighted voting systems [18: 10, 9, 8] and [15: 8, 7, 6] equivalent?

In the weighted voting system [9: 10, 5, 3], voter A is a dictator.

What would be the quota for a voting system that has a total of 41 votes and uses a simple majority quota?

In the weighted voting system [8: 5, 2, 2, 2, 2, 2], find the Banzhaf power index for voter A.

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Given the weighted voting system [51: 45, 43, 7, 5], which of the following is a blocking coalition? $I \{ A \}$ II $\{ B , C \}$ III $\{ \mathrm { C } \}$

Given the weighted voting system [6: 4, 3, 2, 1], which of the coalitions listed are minimal winning coalitions? $\text { I } \{ A , B \} \quad \text { II } \{ A , C \} \quad \text { III } \{ B , C , D \}$

Calculate ${ } _ { 10 } C _ { 0 }$