1.

A group of twelve 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

B

M

S

B

Third choice

S

S

B

M

M


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


2.

A group of twelve 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.


3.

A group of twelve 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.


4.

A group of twelve 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.


5.

A group of twelve 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.


6.

A seventeen-member committee must elect one of four candidates: R, S, T, or W. According to their preference schedule as shown below, R wins using the plurality method. Could those members who most prefer W vote strategically in some way to change the outcome in a way that will benefit them?


Number of Members


6

4

3

4

First choice

R

S

T

W

Second choice

S

R

S

T

Third choice

T

T

R

S

Fourth choice

W

W

W

R



Answer:


7.

A seventeen-member committee must elect one of four candidates: R, S, T, or W. Their preference schedule as shown below. Which candidate wins under pairwise sequential voting with the agenda S, T, W, R?


Number of Members


6

4

3

4

First choice

R

S

T

W

Second choice

S

R

S

T

Third choice

T

T

R

S

Fourth choice

W

W

W

R



Answer:


8.

There are 18 delegates to a political party's convention at which four people A, B, C, and D have been nominated as the party's candidate for governor. The delegates' preference schedule is shown below. What nominee would be elected if the party uses a rank system which assigns 5, 4, 1, and 0 point(s) for a first, second, third, and fourth choice, respectively? Is this result different from that which results from a Borda count?



Number of Delegates


8

9

4

First choice

A

B

C

Second choice

B

A

B

Third choice

C

D

A

Fourth choice

D

C

D



Answer:



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