Chapter 1 Quiz
Math 103, Section 11
1/28/11
Name__________________________
Please show your work.
1.
25 points
Problem 1 refers to the election given by the following preference schedule:
Number of
voters
10
7
5
5
4
1
st
choice
A:40
D:28
B:20
C:20
B:16
2
nd
choice
C:30
B:21
C:15
D:15
C:12
3
rd
choice
B:20
A:14
A:10
A:10
D:8
4
th
choice
D:10
C:7
D:5
B:5
A:4
a. How many people voted in this election?
10+7+5+5+4=31
b. Is there a majority candidate in this election?
no
Explain
.
31/2=15.5
16 votes are needed for a majority candidate. No candidate has 16 or more votes.
c.
Which candidate wins using the plurality method?
A
Why?
A has the most
votes: 10.
d. Which candidate wins using the Borda count method?
Show your work!
A has 40+14+10+10+4=78 Borda count points
B has 20+21+20+5+16=82 Borda count points
C has 30+7+15+20+12=84 Borda count points
D has 10+28+5+15+8=66 Borda count points
C wins with 84 Borda count points
e. How many Borda points are given out by each ballot?
1+2+3+4=10
f. Candidate B is a Condorcet candidate. What does that mean?
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 Spring '07
 Berkowitz
 Math, Voting system, Borda count method, Candidate B, f. Candidate B

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