1. Figure 8 shows the preference ballots for an election with 21 voters and 5 candidates. Write out the preference schedule

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10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Question
G
en Alaina and
ne 2011 American Idol.
SC
hove
hat it allows us to find
lly, given any
SUC
a
rwise
EXERCISES
WALKING
1 Ballots and Preference Schedules
1. Figure 8 shows the preference ballots for an election with 21
voters and 5 candidates. Write out the preference schedule
for this election.
Ballot Ballot Ballot Ballot Ballot
1st B
2nd E
3rd
28
1st C
2nd E
3rd D
4th 4
5th B
Ballot
1st B
2nd E
3rd A
4th C
15th D
Ballot
1st B
2nd E
3rd A
14th C
5th D
Ballot
1st C
2nd A
3rd D
4th B
FIGURE 8
Ballot
ilst A
2nd D
3rd B
4th C
1st A
2nd D
3rd B
4th C
5th E
Ballot
1st A
2nd C
3rd D
4th B
Ballot
1st A
2nd B
3rd C
4th D
5th E
FIGURE 9
Ballot
1st C
2nd E
3rd D
4th A
5th B
Ballot
1st B
2nd C
3rd D
4th A
Ballot
1st A
2nd C
3rd D
4th B
4th C
Sth D
Ballot
1st A
2nd D
3rd B
4th C
Ballot
1st D
2nd C
3rd B
4th A
5th E
Ballot
1st A
2nd B
3rd C
4th D
5th E
1st A
2nd B
3rd C
4th D
5th E
Ballot
1st B
2nd C
3rd D
4th A
Ballot
1st D
2nd C
3rd B
4th E
5th A
Ballot
1st C
2nd A
3rd D
4th B
most usefu
er of any pa
didates-cal
how many r
parison. This is
winner of e
etween candida
ometimes also
points is the w
comparison end
like a round-
most points is
gets !
Ballot
1st C
2nd E
3rd D
4th A
5th B
2. Figure 9 shows the preference ballots for an election with 17
voters and 4 candidates. Write out the preference schedule
for this election.
Ballot Ballot
1st A
1st C
2nd D
2nd A
3rd B
3rd D
4th C
4th B
1st C
2nd E
3rd D
4th A
5th B
Ballot
1st A
2nd B
3rd C
4th D
5th E
pom
Ballot
1st A
2nd D
3rd B
4th C
5th E
Asu
Ballot
1st B
2nd C
3rd D
4th A
The Mathematics of Elections
Ballot
1st B
2nd C
3rd D
4th A
Ballot Ballot,
1st D
1st A
2nd C
2nd B
3rd B
3rd C
4th D
4th E
5th A
5th E
Ballot
1st C
2nd E
3rd D
4th A
5th B
Ballot
1st D
2nd C
3rd B
4th A
5th E
Ballot
1st B
2nd C
3rd D
4th A
Ballot
1st C
2nd A
3rd D
4th B
Ballot
1st A
2nd D
3rd B
4th C
5th E
Ballot
1st A
2nd D
3rd B
4th C
Ballot
1st D
2nd C
3rd B
4th E
5th A
Ballot
1st C
2nd A
3rd D
4th B
Exercises 3 through 6 refer to an alternative format for preference
ballots in which the names of the candidates appear on the ballot
and the voter is asked to put a rank (1, 2, 3, etc.) next to each name
ers and is useful when the names are long or when a misspelled
(see Fig. 1(c)]. (This alternative format makes it easier on the vot-
name invalidates the ballot. The main disadvantage is that it tends
to favor the candidates that are listed first.)
Ballot
1st C
2nd A
3rd D
4th B
3. Table 25 shows the preference schedule for an election
based on the alternative format for the preference ballots.
Rewrite Table 25 in the conventional preference schedule
format used in the text. (Use A, B, C, D, and E as shorthand
for the names of the candidates.)
Number of voters
Alvarez
Brownstein
Clarkson
Dax
Easton
TABLE 25
Number of voters
Andersson
Broderick
Clapton
Dutkiewicz
Eklundh
TABLE 26
E
1st
2nd
37
3
3rd
4th
5th
1
4
5
TABLE 27
2
14
2
1
4
5
36
3
-
2
4
3
5
4. Table 26 shows the preference schedule for an election
based on the alternative format for the preference ballots.
Rewrite Table 26 in the conventional preference schedule
format used in the text. (Use A, B, C, D, and E as shorthand
for the names of the candidates.)
Number of voters 14
B
A
10
3
E
1
D
5
с
2
24
2
1
5
4
3
4
8
1
2
5
13
4
E
C
4
3
2
3
5
1
7
5
10 8
B
A
D
A
3
2
B
1
5. Table 27 shows the preference schedule for an election.
Rewrite Table 27 using the alternative preference schedule
format.
5
3
E
D
4
5
C
1
4
2
4
3
2
4
5
C
1
7 4
D
B
E
A
E
B
A
C
D
Transcribed Image Text:G en Alaina and ne 2011 American Idol. SC hove hat it allows us to find lly, given any SUC a rwise EXERCISES WALKING 1 Ballots and Preference Schedules 1. Figure 8 shows the preference ballots for an election with 21 voters and 5 candidates. Write out the preference schedule for this election. Ballot Ballot Ballot Ballot Ballot 1st B 2nd E 3rd 28 1st C 2nd E 3rd D 4th 4 5th B Ballot 1st B 2nd E 3rd A 4th C 15th D Ballot 1st B 2nd E 3rd A 14th C 5th D Ballot 1st C 2nd A 3rd D 4th B FIGURE 8 Ballot ilst A 2nd D 3rd B 4th C 1st A 2nd D 3rd B 4th C 5th E Ballot 1st A 2nd C 3rd D 4th B Ballot 1st A 2nd B 3rd C 4th D 5th E FIGURE 9 Ballot 1st C 2nd E 3rd D 4th A 5th B Ballot 1st B 2nd C 3rd D 4th A Ballot 1st A 2nd C 3rd D 4th B 4th C Sth D Ballot 1st A 2nd D 3rd B 4th C Ballot 1st D 2nd C 3rd B 4th A 5th E Ballot 1st A 2nd B 3rd C 4th D 5th E 1st A 2nd B 3rd C 4th D 5th E Ballot 1st B 2nd C 3rd D 4th A Ballot 1st D 2nd C 3rd B 4th E 5th A Ballot 1st C 2nd A 3rd D 4th B most usefu er of any pa didates-cal how many r parison. This is winner of e etween candida ometimes also points is the w comparison end like a round- most points is gets ! Ballot 1st C 2nd E 3rd D 4th A 5th B 2. Figure 9 shows the preference ballots for an election with 17 voters and 4 candidates. Write out the preference schedule for this election. Ballot Ballot 1st A 1st C 2nd D 2nd A 3rd B 3rd D 4th C 4th B 1st C 2nd E 3rd D 4th A 5th B Ballot 1st A 2nd B 3rd C 4th D 5th E pom Ballot 1st A 2nd D 3rd B 4th C 5th E Asu Ballot 1st B 2nd C 3rd D 4th A The Mathematics of Elections Ballot 1st B 2nd C 3rd D 4th A Ballot Ballot, 1st D 1st A 2nd C 2nd B 3rd B 3rd C 4th D 4th E 5th A 5th E Ballot 1st C 2nd E 3rd D 4th A 5th B Ballot 1st D 2nd C 3rd B 4th A 5th E Ballot 1st B 2nd C 3rd D 4th A Ballot 1st C 2nd A 3rd D 4th B Ballot 1st A 2nd D 3rd B 4th C 5th E Ballot 1st A 2nd D 3rd B 4th C Ballot 1st D 2nd C 3rd B 4th E 5th A Ballot 1st C 2nd A 3rd D 4th B Exercises 3 through 6 refer to an alternative format for preference ballots in which the names of the candidates appear on the ballot and the voter is asked to put a rank (1, 2, 3, etc.) next to each name ers and is useful when the names are long or when a misspelled (see Fig. 1(c)]. (This alternative format makes it easier on the vot- name invalidates the ballot. The main disadvantage is that it tends to favor the candidates that are listed first.) Ballot 1st C 2nd A 3rd D 4th B 3. Table 25 shows the preference schedule for an election based on the alternative format for the preference ballots. Rewrite Table 25 in the conventional preference schedule format used in the text. (Use A, B, C, D, and E as shorthand for the names of the candidates.) Number of voters Alvarez Brownstein Clarkson Dax Easton TABLE 25 Number of voters Andersson Broderick Clapton Dutkiewicz Eklundh TABLE 26 E 1st 2nd 37 3 3rd 4th 5th 1 4 5 TABLE 27 2 14 2 1 4 5 36 3 - 2 4 3 5 4. Table 26 shows the preference schedule for an election based on the alternative format for the preference ballots. Rewrite Table 26 in the conventional preference schedule format used in the text. (Use A, B, C, D, and E as shorthand for the names of the candidates.) Number of voters 14 B A 10 3 E 1 D 5 с 2 24 2 1 5 4 3 4 8 1 2 5 13 4 E C 4 3 2 3 5 1 7 5 10 8 B A D A 3 2 B 1 5. Table 27 shows the preference schedule for an election. Rewrite Table 27 using the alternative preference schedule format. 5 3 E D 4 5 C 1 4 2 4 3 2 4 5 C 1 7 4 D B E A E B A C D
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