Maths Quiz

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Question 13 pts

An election consists of four candidates A, B, C, and D. The candidates are ranked in order of preference by each of the voters. The preference schedule for this election is given below.

Using the Borda Count Method, how many “points” does candidate B have from the following election? 

Number of voters

14

10

8

3

1st choice

A

C

D

C

2nd choice

B

B

A

B

3rd choice

C

D

B

D

4th choice

D

A

C

A

93

72

97

88

 

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Question 23 pts

An election consists of four candidates A, B, C, and D. The candidates are ranked in order of preference by each of the voters. The preference schedule for this election is given below.

Using the Borda Count Method, rank the contestants. 

Number of voters

14

10

8

3

1st choice

A

C

D

C

2nd choice

B

B

A

B

3rd choice

C

D

B

D

4th choice

D

A

C

A

A, B, C, D

A, C, D, B

C, A, D, B

B, A, C, D

 

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Question 33 pts

According to the preference schedule of the following table, who is ranked  third  using the plurality with Elimination Method? 

Number of voters

14

10

8

3

1st choice

A

C

D

C

2nd choice

B

B

A

B

3rd choice

C

D

B

D

4th choice

D

A

C

A

 

There is a tie.

B

D

A

 

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Question 43 pts

According to the preference schedule shown below,  how many  1st place votes does candidate C have? 

Number of voters

14

10

8

3

1st choice

A

C

D

C

2nd choice

B

B

A

B

3rd choice

C

D

B

D

4th choice

D

A

C

A

14

10

3

13

 

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Question 53 pts

According to the preference schedule shown below, who is the winner of the election using the  Plurality Method ? 

Number of voters

14

10

8

3

1st choice

A

C

D

C

2nd choice

B

B

A

B

3rd choice

C

D

B

D

4th choice

D

A

C

A

A

C

D

B

 

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Question 63 pts

According to the preference schedule shown below, how many  points  does candidate C have using the  Borda Count Method ? 

Number of voters

14

10

8

3

1st choice

A

C

D

C

2nd choice

B

B

A

B

3rd choice

C

D

B

D

4th choice

D

A

C

A

76

88

48

60

 

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Question 73 pts

According to the preference schedule shown below, who is the winner of the election using the  Plurality with Elimination Method ? 

Number of voters

14

10

8

3

1st choice

A

C

D

C

2nd choice

B

B

A

B

3rd choice

C

D

B

D

4th choice

D

A

C

A

B

D

A

C

 

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Question 83 pts

According to the preference schedule shown below: 

Number of voters

14

10

8

3

1st choice

A

C

D

C

2nd choice

B

B

A

B

3rd choice

C

D

B

D

4th choice

D

A

C

A

 When you use the  Method of Pairwise Comparisons , how many “pairwise” comparisons do you have?

5

6

10

8

 

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Question 93 pts

According to the preference schedule shown below:

Number of voters

14

10

8

3

1st choice

A

C

D

C

2nd choice

B

B

A

B

3rd choice

C

D

B

D

4th choice

D

A

C

A

 When you use the  Method of Pairwise Comparisons , who is the winner?

There is a tie.

A

B

C

 

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Question 103 pts

An election is held among five candidates (A, B, C, D, and E). There are 37 votes. Using the Method of Pairwise Comparison it is found that A, B, and C each win one pairwise comparison while D wins four. If E wins the remaining comparisons in this election, then which statement is true?

 

D is the Condorcet candidate.

E is the Condorcet candidate.

Both D and E are Condorcet candidates.

There is no Condorcet candidate.

 

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Question 113 pts

A violation of the Monotonicity Criterion occurs when

the increase in preference, among voters, of the winning candidate causes the outcome of the election to change.

the removal of a losing candidate from the election causes the outcome of the election to change.

the winning candidate is not Condorcet.

the winning candidate receives less than a majority of 1st choice votes.

 

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Question 123 pts

A violation of the Independence of Irrelevant Alternatives Criterion occurs when

 

the winning candidate is not Condorcet.

the winning candidate receives less than a majority of 1st choice votes.

the removal of a losing candidate from the election causes the outcome of the election to change.

the increase in preference, among voters, of the winning candidate causes the outcome of the election to change.

 

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Question 133 pts

An election is held among five candidates (A, B, C, D, and E). There are 37 votes. Using the Method of Pairwise Comparison it is found that A, B, and C each win one pairwise comparison; D wins four and E wins the remaining comparisons in this election. How many “pairwise” comparisons did A  lose ?

 

3

4

5

2

 

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Question 143 pts

Tim and his three friends Beth, Jane, and Sam pool their money to buy a pizza. Tim gives $4; Beth gives $3; while both Jane and Sam each give $2. If there are two choices for pizza and each person gets to vote proportionally to the amount of money he or she gave, then which weighted voting system models scenario if the  quota  is a simple majority of votes?

 

[6: 3, 2, 1, 1]

[8: 4, 3, 2, 2]

[6: 4, 3, 2, 2]

[5: 4, 3, 2, 2]

 

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Question 153 pts

Consider the weighted voting system [40: 20, 18, 12, 8, 7, 5]. 

What's the  weight  of P2?

 

40

12

18

20

 

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Question 163 pts

Consider the weighted voting system [40: 20, 18, 12, 8, 7, 5].

In a coalition of {P2, P3, P4, P6, P5, P1}  find  all the  pivotal  players.

P2, P3, P4, P6

All of the players.

P5

P6

 

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Question 173 pts

Consider the weighted voting system [40: 20, 18, 12, 8, 7, 5].

In a coalition of {P2, P3, P4, P5},  find  all the  critical  players.

P2, P3, P4

P4, P5

P2, P3

P2, P3, P4, P5

 

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Question 183 pts

An election with four candidates (A, B, C, and D) and 200 voters will use the Plurality Method to choose a winner.  How many  first-place votes are needed for a  majority ?

99

200

100

101

 

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Question 193 pts

Consider the weighted voting system [11: 7, 5, 2, 1]. Which player(s), if any, have  veto  power?

P2

P1 & P2

All of the players.

P1

 

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Question 203 pts

A committee consists of  four  members. How many different  coalitions  are possible?

31

16

4

15

 

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Question 213 pts

In a weighted voting system, when the quota is too small, it’s possible for both YES’s and NO’s to have enough votes to a certain issue. For example, [10: 8, 7, 3, 2], one can see a mathematical version of ________________________. Fill the blank.

dictator

anarchy

gridlock

veto

 

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Question 223 pts

On the other hand, if the quota is too big, you can never have enough votes to pass a motion. For example, [22: 8, 7, 3, 2], one can see a ________________________. Fill the blank.

anarchy

dictator

veto

gridlock

 

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Question 233 pts

In the weighted voting system [13: 10, 6, 5], consider a  sequential  coalition <P2, P3, P1>. Who is the  pivotal  player?

All three players.

P1 & P2

P3

P1

 

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Question 243 pts

Consider the weighted voting system [13: 10, 6, 5]. What is the Shapely-Shubik Power of P1?

2/6

1/5

4/6

3/6

 

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Question 253 pts

Consider the weighted voting system [20: 13, 11, 8].

In a coalition of {P1, P2, P3} who is the  critical  player(s)?

P1

P3

P1 & P2

P2

 

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Question 263 pts

Consider the weighted voting system [20: 13, 11, 8]. What is the Banzhaf Power of P3?

1/4

2/5

1/5

1/6

 

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Question 273 pts

If there are 16 teams to play in a tournament, where each team will play every other team once. Then  how many matches  will take place?

16

15

120

240

 

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Question 283 pts

Consider the weighted voting system [q: 6, 4, 2, 2]. 

Find the  smallest  value that the quota q can take.

12

9

7

8

 

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Question 293 pts

Consider the weighted voting system [q: 6, 4, 2, 2].

What is the  largest  value that the quota q can take?

8

15

14

7

 

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Question 303 pts

Consider the weighted voting system [q: 8, 6, 4]. Find the smallest value of q for which all three players have  veto  power.

16

14

13

15

 

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Question 313 pts

Consider the weighted voting system [q: 8, 6, 4]. Find the smallest value of q for which P2 has  veto  power but P3 does not.

13

14

12

15

 

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Question 323 pts

Consider the weighted voting system [18: 12, 10, 6].

Consider a  sequential  coalition {P1, P3, P2}. Who is the  pivotal  player?

P3

P1

P2

P1 & P3

 

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Question 334 pts

Consider the weighted voting system [18: 12, 10, 6].

What is the Shapley-Shubik Power of P3?

1/6

1/5

2/7

2/6