MAT 113 – Test on Chapter 1
Prof: Bui
Name ________________________
Date _________________________
1) Given the preference schedule below:
A) How many candidates? __________
B) How many voters? _____________
C) How many first-place votes are needed for a majority? ___________
2) Given the preference schedule below:
Number of voters
1st choice
2nd choice
3rd choice
4th choice
20
A
B
C
D
14
C
B
D
A
8
D
B
A
C
7
C
D
B
A
2
D
A
B
C
A) Using the Plurality method, the winner of the election is ____________
B) Using the Pairwise Comparison, the winner of the election is ____________
Please show work below
C) Do we have a Condorcet winner? If yes, who? ______________
Hint: use the work in part B to figure out the Condorcet winner
Number of voters
1st choice
2nd choice
3rd choice
4th choice
20
A
B
C
D
14
C
B
D
A
8
D
B
A
C
7
C
D
B
A
2
D
A
B
C
D) Using the Borda Count method, the winner of the election is _______________
E) The ranking of the candidates using the extended Borda Count method is:
1st place winner _____________
2nd place winner ____________
3rd place winner _____________
4th place winner _____________
3) Given the preference schedule below:
Number of voters
1st choice
2nd choice
3rd choice
4th choice
15
A
B
C
D
11
C
B
D
A
9
D
C
B
A
6
B
D
C
A
2
C
D
B
A
A) Using the Plurality with Elimination method, the winner of the election is _______________
B) The ranking of the candidates using the extended Plurality with Elimination method is:
1st place winner _____________
2nd place winner ____________
3rd place winner _____________
4th place winner _____________
4) Given the preference schedule below:
Number of voters
41
10
10
st
1 choice
B
F
A
2nd choice
A
A
E
3rd choice
D
E
F
th
4 choice
F
C
D
5th choice
E
D
C
6th choice
C
B
B
15
A
F
E
D
B
C
5
E
F
A
B
D
C
Rank the candidates using the Recursive Plurality method
1st place winner _____________
2nd place winner ____________
3rd place winner _____________
4th place winner _____________
5th place winner _____________
6th place winner _____________
MULTIPLE CHOICE: Number 5-7
5) In an election of 16 candidates, how many comparisons are there?
A) 16
B) 120
C) 136
D) None of the above
6) An election is held among four candidates (A, B, C, and D). Using a voting method X, the winner of
the election is candidate A. Due to an irregularity in the original vote count, a recount is required. Before
the new election takes place, candidate B drops out of the race. In the recount, still using voting method
X, candidate D wins the election. Base on this information, the voting method X violates
A) Independent of irrelevant alternatives criterion
B) Monotonicity criterion
C) Majority criterion
D) Condorcet criterion
7) An election is held among four candidates (A, B, C, and D). Using a voting method X, the winner of
the election is candidate A. Due to an irregularity in the original procedures, a new election is required.
Before the new election takes place, one of the voters changes his mind and moves candidate A from the
third choice to second choice on his ballot. All other voters vote the same way they did in the original
election. In the new, still using the same method, candidate D wins the election. Base on this
information, the voting method X violates
A) Independent of irrelevant alternatives criterion
B) Monotonicity criterion
C) Majority criterion
D) Condorcet criterion