Question 1

Use the weighted voting system [10: 7, 4, 3, 3, 1] to answer the following Questions
-Which of the following is a blocking coalition?

Accepted Answer

A)  {C, D} 
B)  {A, E} 
C)  both (
A)  and (
B)  
D)  neither (
A)  nor (
B)  
A)  {C, D} 
B)  {A, E} 
C)  both (
A)  and (
B)  
D)  neither (
A)  nor (
B)

Question 2

Explain why the weighted voting system [13: 10, 6, 5, 3, 2] is not a legitimate weighted voting system.

Accepted Answer

The system given is not a legitimate wei

Question 3

Given the weighted voting system [4: 1, 2, 3], list all winning coalitions.

Accepted Answer

{A, C}, {B

Question 4

Calculate the Shapely-Shubik power index for each voter in the weighted voting system [6: 3, 1, 1, 1, 1, 1, 1].

Accepted Answer

A)  (3/7, 2/21, 2/21, 2/21, 2/21, 2/21, 2/21) 
B)  (1/2, 1/12, 1/12, 1/12, 1/12, 1/12, 1/12) 
C)  (1/3, 1/9, 1/9, 1/9, 1/9, 1/9, 1/9) 
D)  (2/3, 1/18, 1/18, 1/18, 1/18, 1/18, 1/18) 
A)  (3/7, 2/21, 2/21, 2/21, 2/21, 2/21, 2/21) 
B)  (1/2, 1/12, 1/12, 1/12, 1/12, 1/12, 1/12) 
C)  (1/3, 1/9, 1/9, 1/9, 1/9, 1/9, 1/9) 
D)  (2/3, 1/18, 1/18, 1/18, 1/18, 1/18, 1/18)

Question 5

In a weighted voting system, all blocking coalitions would become winning coalitions if each voter switched his or her vote from NO to YES.

Accepted Answer

A) True 
 B)False

Question 6

A committee has three members with the system [10: 5, 4, 3, 2, 1]. Which voters are critical in the coalition {A, B, C, E}?

Accepted Answer

A)  A only 
B)  A and B 
C)  A and E 
D)  E only 
A)  A only 
B)  A and B 
C)  A and E 
D)  E only

Question 7

Given the weighted voting system [8: 5, 4, 3], which of the coalitions given are minimal winning coalitions?

Accepted Answer

A)  {A, B, C} 
B)  {A, B} 
C)  {B, C} 
D)  There are no minimal winning coalitions. 
A)  {A, B, C} 
B)  {A, B} 
C)  {B, C} 
D)  There are no minimal winning coalitions.

Question 8

Use the weighted voting system [12: 4, 4, 3, 3, 2, 1] to answer the following questions
-Give a winning coalition that is not a minimal winning coalition.

Accepted Answer

Answers ma

Question 9

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

Accepted Answer

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

Question 10

Use the weighted voting system [10: 7, 4, 3, 3, 1] to answer the following Questions
-Which of the following is a winning coalition?

Accepted Answer

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

Question 11

Given the weighted voting system [30: 20, 17, 10, 5], find the pivotal voter in the permutation {B, D, C, A}.

Accepted Answer

The answer of Given the weighted voting system [30: 20,...

Use the weighted voting system [10: 7, 4, 3, 3, 1] to answer the following Questions -Which of the following is a blocking coalition?

Explain why the weighted voting system [13: 10, 6, 5, 3, 2] is not a legitimate weighted voting system.

Given the weighted voting system [4: 1, 2, 3], list all winning coalitions.

Calculate the Shapely-Shubik power index for each voter in the weighted voting system [6: 3, 1, 1, 1, 1, 1, 1].

In a weighted voting system, all blocking coalitions would become winning coalitions if each voter switched his or her vote from NO to YES.

A committee has three members with the system [10: 5, 4, 3, 2, 1]. Which voters are critical in the coalition {A, B, C, E}?

Given the weighted voting system [8: 5, 4, 3], which of the coalitions given are minimal winning coalitions?

Use the weighted voting system [12: 4, 4, 3, 3, 2, 1] to answer the following questions -Give a winning coalition that is not a minimal winning coalition.

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

Use the weighted voting system [10: 7, 4, 3, 3, 1] to answer the following Questions -Which of the following is a winning coalition?

Given the weighted voting system [30: 20, 17, 10, 5], find the pivotal voter in the permutation {B, D, C, A}.

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Exploring Data: Relationships

Data for Decisions

Probability: the Mathematics of Chance

Social Choice: the Impossible Dream

The Manipulability of Voting Systems

Electing the President

Fair Division

Apportionment

Game Theory: the Mathematics of Competition

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Symmetry and Patterns

Tilings

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Borrowing Models

The Economics of Resources

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Exam 11: Weighted Voting Systems

Use the weighted voting system [10: 7, 4, 3, 3, 1] to answer the following Questions -Which of the following is a blocking coalition?

Explain why the weighted voting system [13: 10, 6, 5, 3, 2] is not a legitimate weighted voting system.

Given the weighted voting system [4: 1, 2, 3], list all winning coalitions.

Calculate the Shapely-Shubik power index for each voter in the weighted voting system [6: 3, 1, 1, 1, 1, 1, 1].

In a weighted voting system, all blocking coalitions would become winning coalitions if each voter switched his or her vote from NO to YES.

A committee has three members with the system [10: 5, 4, 3, 2, 1]. Which voters are critical in the coalition {A, B, C, E}?

Given the weighted voting system [8: 5, 4, 3], which of the coalitions given are minimal winning coalitions?

Use the weighted voting system [12: 4, 4, 3, 3, 2, 1] to answer the following questions -Give a winning coalition that is not a minimal winning coalition.

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

Use the weighted voting system [10: 7, 4, 3, 3, 1] to answer the following Questions -Which of the following is a winning coalition?

Given the weighted voting system [30: 20, 17, 10, 5], find the pivotal voter in the permutation {B, D, C, A}.

Urban Services

Business Efficiency

Planning and Scheduling

Linear Programming

Exploring Data: Distributions

Exploring Data: Relationships

Data for Decisions

Probability: the Mathematics of Chance

Social Choice: the Impossible Dream

The Manipulability of Voting Systems

Electing the President

Fair Division

Apportionment

Game Theory: the Mathematics of Competition

Identification Numbers

Information Science

Growth and Form

Symmetry and Patterns

Tilings

Savings Models

Borrowing Models

The Economics of Resources

Filters