SAMPLE TEST





1. Explain the Condorcet Winner Criterion.

Answer:


2.

One hundred voters are to elect one of the four candidates A, B, C, or D. Their preference schedule is shown below. Which candidate wins using the Hare system?



Number of Voters


40

32

18

10

First choice

A

B

D

C

Second choice

C

C

C

D

Third choice

B

A

B

A

Fourth choice

D

D

A

B


A.A wins.
B.B wins.
C.D wins.
D.No winner is determined.


3.

One hundred voters are to elect one of the four candidates A, B, C, or D. Their preference schedule is shown below. Which candidate wins using sequential pairwise voting with the agenda A, C, B, D?



Number of Voters


40

32

18

10

First choice

A

B

D

C

Second choice

C

C

C

D

Third choice

B

A

B

A

Fourth choice

D

D

A

B


A.A wins.
B.B wins.
C.C wins.
D.D wins.


4.

One hundred voters are to elect one of the four candidates A, B, C, or D. Their preference schedule is given below. Is there a Condorcet winner?



Number of Voters


40

32

18

10

First choice

A

B

D

C

Second choice

C

C

C

D

Third choice

B

A

B

A

Fourth choice

D

D

A

B


A.Yes, A wins.
B.Yes, B wins.
C.Yes, C wins.
D.No winner is determined.


5.

Consider a thirteen-person committee which is considering three applicants, A, B, and C, for an opening. The individual rankings are summarized in the table below. Which applicant would be accepted if the committee used the plurality method?


Number of Members


5

4

2

2

First choice

B

C

A

A

Second choice

C

B

B

C

Third choice

A

A

C

A


A.A
B.B
C.C
D.There is no plurality winner.


6.

In order to choose which type of music to listen to in a student center music lounge, a Condorcet vote is held by the 15 students present. Below are the preference schedules for the students. Is there a Condorcet winner and if so, which music type?


Number of Students


6

5

4

First choice

classical

rock

rock

Second choice

jazz

jazz

classical

Third choice

rock

classical

jazz



Answer:


7.

Seventeen board members vote on four candidates, A, B, C, or D, for a new position on their board. Their preference schedules are shown below. Which candidate will be selected if they use the Hare system?


Number of Members


7

6

4

First choice

A

D

C

Second choice

B

A

B

Third choice

C

B

D

Fourth choice

D

C

A



Answer:


8.

Seventeen board members vote on four candidates, A, B, C, or D, for a new position on their board, using the Hare system according to the preference schedules shown below. What happens if A rejects the offer before the ranking?


Number of Members


7

6

4

First choice

A

D

C

Second choice

B

A

B

Third choice

C

B

D

Fourth choice

D

C

A



Answer:



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