Majority rule is a good way to choose between two alternatives



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1.

Majority rule is a good way to choose between two alternatives.




A) True B) False




2.

Majority rule is a good way to choose between three alternatives.




A) True B) False




3.

Every set of voters' preference lists produces a Condorcet winner.




A) True B) False




4.

For a given set of voters' preference lists, different voting procedures may produce different winners.




A) True B) False




5.

For a given set of voters' preference lists, different agendas for sequential pairwise voting may produce different winners.




A) True B) False




6.

The Borda count method of voting satisfies the independence of irrelevant alternatives criterion.




A) True B) False




7.

Sequential pairwise voting satisfies the Condorcet criterion.




A) True B) False




8.

How many votes are needed for a majority winner if there are 20 voters?




A) 10 B) 11 C) 15 D) 20




9.

How many votes are needed for a majority winner if there are 25 voters?




A) 12 B) 12.5 C) 13 D) 25




10.

In how many ways can a voter rank five candidates, without allowing ties?




A) 5 B) 32 C) 60 D) 120




11.

In how many ways can a voter rank three candidates, without allowing ties?




A) 3 B) 6 C) 8 D) 12




12.

A group of 12 students have to decide among three types of pizza: Sausage (S), Mushroom (M), and Beef (B). Their preference rankings are shown below. Which choice will the group make if they use majority rule?






Number of Students




3

3

2

2

2

First choice

B

M

S

B

S

Second choice

M

B

M

S

B

Third choice

S

S

B

M

M







A) S B) M C) B D) No winner can be chosen.




13.

A group of 12 students have to decide among three types of pizza: Sausage (S), Mushroom (M), and Beef (B). Their preference rankings are shown below. Which choice will the group make if they use plurality voting?






Number of Students




3

3

2

2

2

First choice

B

M

S

B

S

Second choice

M

S

M

S

B

Third choice

S

B

B

M

M







A) S B) M C) B D) No winner can be chosen.




14.

A group of 12 students have to decide among three types of pizza: Sausage (S), Mushroom (M), and Beef (B). Their preference rankings are shown below. Which choice will the group make if they use the plurality runoff voting method?






Number of Students




3

3

2

2

2

First choice

B

M

S

B

S

Second choice

M

S

M

S

B

Third choice

S

B

B

M

M







A) S B) M C) B D) No winner can be chosen.




15.

A group of 12 students have to decide among three types of pizza: Sausage (S), Mushroom (M), and Beef (B). Their preference rankings are shown below. Which choice will the group make if they use the Borda count?






Number of Students




3

3

2

2

2

First choice

B

M

S

B

S

Second choice

M

B

M

S

B

Third choice

S

S

B

M

M







A) S B) M C) B D) No winner can be chosen.




16.

A group of 12 students have to decide among three types of pizza: Sausage (S), Mushroom (M), and Beef (B). Their preference rankings are shown below. Which choice will the group make if they use the Hare system?






Number of Students




3

3

2

2

2

First choice

B

M

S

B

S

Second choice

M

B

M

S

B

Third choice

S

S

B

M

M







A) S B) M C) B D) No winner can be chosen.




17.

A group of 12 students have to decide among three types of pizza: Sausage (S), Mushroom (M), and Beef (B). Their preference rankings are shown below. Which choice will the group make if they use sequential pairwise voting with agenda B, M, S?






Number of Students




3

3

2

2

2

First choice

B

M

S

B

S

Second choice

M

B

M

S

B

Third choice

S

S

B

M

M







A) S B) M C) B D) No winner can be chosen.




18.

A group of 12 students have to decide among three types of pizza: Sausage (S), Mushroom (M), and Beef (B). Their preference rankings are shown below. Is there a Condorcet winner among the pizza types?






Number of Students




3

3

2

2

2

First choice

B

M

S

B

S

Second choice

M

B

M

S

B

Third choice

S

S

B

M

M







A) S B) M C) B D) No winner can be chosen.




19.

Thirty board members must vote on five candidates: X, Y, Z, U, and V. Their preference rankings are summarized in the table below. Find the winner using the Borda count.






Number of Members




12

10

8

First choice

X

Y

Z

Second choice

U

Z

U

Third choice

Y

X

X

Fourth choice

Z

U

V

Fifth choice

V

V

Y







A) X B) Y C) Z D) No winner is chosen.




20.

Thirty board members must vote on five candidates: X, Y, Z, U, and V. Their preference rankings are summarized in the table below. Find the winner using the Hare system.






Number of Members




12

10

8

First choice

X

Y

Z

Second choice

U

Z

U

Third choice

Y

X

X

Fourth choice

Z

U

V

Fifth choice

V

V

Y







A) X B) Y C) Z D) No winner is chosen.




21.

Thirty board members must vote on five candidates: X, Y, Z, U, and V. Their preference rankings are summarized in the table below. Find the winner using sequential pairwise voting with the agenda X, Y, Z, U, V.






Number of Members




12

10

8

First choice

X

Y

Z

Second choice

U

Z

U

Third choice

Y

X

X

Fourth choice

Z

U

V

Fifth choice

V

V

Y







A) X B) Z C) U D) V



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