Deck 13: Graph Theory

Question 1

(a) Using the pairwise comparison voting method, determine the winner. (b) If candidate S is eliminated and the votes are recounted, does this election violate the irrelevant alternative criterion?

Answer 1

(a) W
(b) No. W still wins.

Question 2

Answer 2

(a) X
(b) No, the winner is still X.

Question 3

(a) How many people voted? (b) Determine the winner using the plurality method.

Answer 3

(a) 30
(b) S

Question 4

Is the monotonicity criterion violated? Explain your answer.

Question 5

Does the election violate the majority criterion? Explain your answer.

Question 6

(a) How many people voted? (b) How many people voted for the candidates in the order of preference BCA? (c) How many people voted for candidate B for their first choice?

Question 7

Question 8

Question 9

(a) Using the pairwise comparison voting method, determine the winner. (b) If candidate X drops out and the votes are recounted, does this election violate the irrelevant alternative criterion?

Question 10

Question 11

(a) Using the Borda count method of voting, determine the winner. (b) Does the election violate the majority criterion?

Question 12

(a) How many people voted? (b) How many people voted for the candidates in the order of preference ZYX? (c) How many people voted for candidate X for their first choice?

Question 13

Question 14

Question 15

Question 16

Question 17

Question 18

If there are 7 candidates in an election, how many pairwise comparisons need to be made in order to determine a winner?

Question 19

Question 20

(a) Using the Borda count method of voting, determine the winner. (b) Does the election violate the majority criterion?

Question 21

A) D
B) A
C) C
D) B

Question 22

A) No, because X is the plurality winner.
B) Yes, because X does not win over Z in a head-to-head comparison.
C) Yes, because X does not win over Y in a head-to-head comparison.
D) No, because X wins over Y and Z in a head-to-head comparison.

Question 23

Question 24

A) Candidate B wins.
B) Candidates A and B tie.
C) Candidate A wins.
D) Candidate C wins.

Question 25

(a) Determine the winner using the Borda method of voting. (b) Is the winner the same as the one determined by the plurality method?

Question 26

Question 27

Question 28

Question 29

A) J
B) Tie between K and L
C) L
D) K

Question 30

Question 31

(a) Determine the winner using the Borda method of voting. (b) Is the winner the same as the one determined by the plurality method?

Question 32

A) Phillips
B) James
C) Hanson
D) Boyd

Question 33

Question 34

A) Y
B) X
C) W
D) Z

Question 35

A) C
B) A
C) B

Question 36

A) Alabama paradox did not occur
B) Alabama paradox occurred

Question 37

A) population paradox occurred
B) population paradox did not occur

Question 38

A) No. In a head-to-head comparison Z won over C and W.
B) Yes. In a head-to-head comparison Z won over W but lost to C.
C) No. Z is the plurality winner.
D) Yes. In a head-to-head comparison Z won over C but lost to W.

Question 39

Question 40

Question 41

A) Q
B) F
C) M
D) L

Question 42

A) Peterson (P)
B) Thomas (T)
C) Jenkins (J)

Question 43

Question 44

Question 45

Question 46

A) 6:00 p.m.
B) 12:00 p.m.
C) 5:00 p.m.
D) 1:00 p.m.

Question 47

A) X
B) Z
C) Y

Question 48

Question 49

A) Robinson
B) Green
C) Morgan
D) Park

Question 50

Question 51

A) Stewart
B) Wong
C) Luby
D) Davis

Question 52

A) Vanilla (V)
B) Strawberry (S)
C) Chocolate (C)

Question 53

Question 54

A) A
B) C
C) B
D) D

Question 55

Question 56

A) Yes
B) No

Question 57

If there are 6 candidates in an election, how many pairwise comparisons need to be made in order to determine a winner?

A) 6
B) 30
C) 21
D) 15

Question 58

A) No
B) Yes