1.

A group of twenty-two young people must decide whether to go to the beach (B), the mountain (M), or the zoo (Z) on a field trip. Their preference rankings are summarized in the table below. Which choice wins using plurality voting?



Number of Voters


10

8

4

First choice

B

M

Z

Second choice

M

B

M

Third choice

Z

Z

B


A.M
B.B
C.Z
D.No winner is determined.


2.

A group of twenty-two young people must decide whether to go to the beach (B), the mountain (M), or the zoo (Z) on a field trip. Their preference rankings are summarized in the table below. Which choice wins using the Borda count?



Number of Voters


10

8

4

First choice

B

M

Z

Second choice

M

B

M

Third choice

Z

Z

B


A.M
B.B
C.Z
D.No winner is determined.


3.

A group of twenty-two young people must decide whether to go to the beach (B), the mountain (M), or the zoo (Z) on a field trip. Their preference rankings are summarized in the table below, and the decision will be made using a Borda count. Can the 4 voters in the last column change the results of the vote by changing their preference rankings?



Number of Voters


10

8

4

First choice

B

M

Z

Second choice

M

B

M

Third choice

Z

Z

B


A.No.
B.Yes.


4.

A group of twenty-two young people must decide whether to go to the beach (B), the mountain (M), or the zoo (Z) on a field trip. Their preference rankings are summarized in the table below. Which choice wins using the Hare system?



Number of Voters


10

8

4

First choice

B

M

Z

Second choice

M

B

M

Third choice

Z

Z

B


A.M
B.B
C.Z
D.No winner is determined.


5.

A group of twenty-two young people must decide whether to go to the beach (B), the mountain (M), or the zoo (Z) on a field trip. Their preference rankings are summarized in the table below. Which choice wins using sequential pairwise voting with the agenda Z, B, M?



Number of Voters


10

8

4

First choice

B

M

Z

Second choice

M

B

M

Third choice

Z

Z

B


A.M
B.B
C.Z
D.No winner is determined.


6.

A group of twenty-two young people must decide whether to go to the beach (B), the mountain (M), or the zoo (Z) on a field trip. Their preference rankings are summarized in the table below. Is there a Condorcet winner?



Number of Voters


10

8

4

First choice

B

M

Z

Second choice

M

B

M

Third choice

Z

Z

B


A.M
B.B
C.Z
D.No winner is determined.


7.

A poll by fifteen sports announcers chooses the best basketball team from among three schools: University of Nevada at Las Vegas (LV), University of North Carolina (NC), and Indiana University (IU). If the individual rankings are as summarized below, which team wins if they use a rank method that assigns 5, 3, and 1 point(s) to each first, second, and third choice respectively?



Number of Announcers


5

6

2

2

First choice

LV

NC

IU

NC

Second choice

IU

LV

NC

IU

Third choice

NC

IU

LV

LV



Answer:



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