Voting and Apportionment. The spirit club at Lakeview High School is voting for President, Vice...

Chapter 15 Test Review

Voting and Apportionment

The spirit club at Lakeview High School is voting for President, Vice President, and Treasurer. Their Choices are Ken Walters (KW), Jocelyn Suthers (JS), and Amelia Crest (AC). The preference table follows.

How many members of the spirit club voted?

A) 25 B) 20 C) 8 D) 21

# of Votes 8 5 4 3

First KW JS AC AC

Second JS KW KW JS

Third AC AC JS KW


Does any choice have a majority of votes?

A) KW B) JS C) AC D) No

# of Votes 8 5 4 3

First KW JS AC AC

Second JS KW KW JS

Third AC AC JS KW


Determine the winner using the plurality method

A) KW B) JS C) AC

# of Votes 8 5 4 3

First KW JS AC AC

Second JS KW KW JS

Third AC AC JS KW


Determine the winner using the Borda count method

A) KW B) JS C) AC

# of Votes 8 5 4 3

First KW JS AC AC

Second JS KW KW JS

Third AC AC JS KW


Determine the winner using the plurality with elimination method

A) KW B) JS C) AC

# of Votes 8 5 4 3

First KW JS AC AC

Second JS KW KW JS

Third AC AC JS KW


Determine the winner using the pairwise comparison method

A) KW B) JS C) AC

# of Votes 8 5 4 3

First KW JS AC AC

Second JS KW KW JS

Third AC AC JS KW

The spirit club is also given the responsibility of picking the new school color. The choices are Navy Blue (N), Maroon (M), and Gold (G). The results of the election are given in the following preference table.

Which color wins this election if the plurality method is used?

A) M B) G C) N

# of Votes 5 6 3 6

First N N M G

Second M G N M

Third G M G N


Which color wins this election if the Borda count method is used?

A) M B) G C) N

# of Votes 5 6 3 6

First N N M G

Second M G N M

Third G M G N


Which color wins this election if the plurality with elimination method is used?

A) M B) G C) N

# of Votes 5 6 3 6

First N N M G

Second M G N M

Third G M G N


Which color wins this election if the pairwise comparison method is used?

A) M B) G C) N

# of Votes 5 6 3 6

First N N M G

Second M G N M

Third G M G N

Which voting method(s) – plurality, Borda count, plurality with elimination, or pairwise comparison – violate the head-to-head criterion using the following election data?

A) Plurality and Borda count

B) Plurality, Borda Count, and Plurality w/Elimination

C) All methods

D) None

# of Votes 20 32 24 50 41

First A B C A D

Second D C A C B

Third B A D B A

Fourth C D B D C

The board of a local country club is voting for the date of their golf tournament. The choices for the date are June 14 (14), June 21 (21), or June 28 (28). The 21 board members rank their choices according to the following preference table. Using the data provided, does the Borda count method violate the majority criterion?

A) Yes

B) No

# of Votes 3 7 5 6

First 14 21 28 21

Second 28 28 14 28

Third 21 14 21 14

A country has four states and 50 seats in the legislature. The population of each state is shown below.

A) 5, 13, 13, 19

B) 6, 11, 13, 20

C) 5, 12, 13, 20

D) 6, 12, 13, 20

State A B C D Total

Population 1013 2542 2731 4004 10,290

Determine each state’s apportionment using Hamilton’s method.

A country has four states and 50 seats in the legislature. The population of each state is shown below.

A) 5, 13, 13, 19

B) 6, 11, 13, 20

C) 5, 12, 13, 20

D) 6, 12, 13, 20

State A B C D Total

Population 1013 2542 2731 4004 10,290

Determine each state’s apportionment using Jefferson’s method.

Voting and Apportionment. The spirit club at Lakeview High School is voting for President, Vice...

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