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Math in Society, 2nd Edition: Tools for decision making

Portland Community College Math Department

Exercises 5.5 Chapter 5 Review

Exercise Group.

In exercises 1-4, determine the apportionment using
  1. Hamilton’s Method
  2. Jefferson’s Method
  3. Webster’s Method
  4. Huntington-Hill Method

1.

A small country consists of four states, whose populations are listed below. If the legislature has 78 seats, apportion the seats.
A B C D
96,400 162,700 119,900 384,900

2.

Reapportion the previous problem with 90 seats.

3.

A small country consists of five states, whose populations are listed below. If the legislature as 100 seats, apportion the seats.
A B C D E
584,000 226,600 88,500 257,300 104,300

4.

Reapportion the previous problem with 125 seats.

Exercise Group.

In exercises 5-8, complete the following:
  1. How many voters voted in this election?
  2. How many votes are needed for a majority?
  3. Find the winner under the plurality method.
  4. Find the winner under the Instant Runoff Voting method.
  5. Find the winner under the Borda Count Method.
  6. Find the winner under Copeland’s method.

5.

A Portland Community College Board member race has four candidates: E, F, G, H. The votes are:
Number of voters 12 16 17 15 34 13 19 8
1st choice G H E E F G H G
2nd choice E F F H G H G F
3rd choice F G G F H E F E
4th choice H E H G E F E H

6.

A Forest Grove School Board position has four candidates: I, J, K, L. The votes are:
Number of voters 15 13 25 16 18 10 7 11 2
1st choice K I J L K L I I L
2nd choice J L L I I J K J K
3rd choice L J I K J I J K J
4th choice I K K J L K L L I

7.

A Multnomah County Commissioner’s race has five candidates: M, N, O, P, Q. The votes are:
Number of voters 31 18 35 37 33 12
1st choice M Q O N P Q
2nd choice P O Q P M N
3rd choice O M P O N M
4th choice N P N M Q O
5th choice Q N M Q O P

8.

The Oregon State Governor’s race has five candidates: R, S, T, U, V. The votes are:
Number of voters 22 45 20 47 43 18 26
1st choice R S R U T V V
2nd choice T V S T U S T
3rd choice S T V S V U S
4th choice U R U V R R U
5th choice V U T R S T R

Exercise Group.

In each fictional country in problems 9-10, use the rules of the U.S. government to complete the table and determine the following:
  1. The total number of electors in the state.
  2. The number of electoral votes needed for a majority and win a presidential election.

9.

In this country there is one representative for every 55,000 residents.
State Population Number of
Representatives		 Number of
Senators		 Number of
Electors
Fonville 825,000
Gurley 550,000
Nevarez 275,000
Total

10.

In this country there is one representative for every 60,000 residents.
State Population Number of
Representatives		 Number of
Senators		 Number of
Electors
Arbery 720,000
Monterrosa 360,000
Bland 240,000
Davis 480,000
Total

Exercise Group.

In each fictional country in problems 11-12, use the rules of the U.S. government (assume that all of a state’s electoral votes go to the candidate who received the majority of the votes in that state) to complete the table and determine the following:
  1. The winner of the popular vote in the country and the percentage of votes they won.
  2. The winner of the electoral college who becomes the president and the percentage of electoral votes they won.

11.

In this country from problem 9, there is one representative for every 55,000 residents.
State Votes for
Candidate A		 Votes for
Candidate B		 Number of
Electoral
Votes for A		 Number of
Electoral
Votes for B
Fonville 684,750 140,250
Gurley 257,400 292,600
Nevarez 132,275 142,725
Total Votes

12.

In this country from problem 10, there is one representative for every 60,000 residents.
State Votes for
Candidate A		 Votes for
Candidate B		 Number of
Electoral
Votes for A		 Number of
Electoral
Votes for B
Arbery 372,240 347,760
Monterrosa 38,880 321,120
Bland 134,640 105,360
Davis 104,160 375,840
Total

Exercise Group.

In each fictional country in problems 13-14, use the rules of the U.S. government to complete the table and determine the following:
  1. The state that has the most electoral power
  2. The state that has the least electoral power

13.

In this country from problem 9, there is one representative for every 55,000 residents.
State Population Number
of
Representatives		 Number
of
Senators		 Number
of
Electors		 Electoral
Votes per
55,000 people
Fonville 825,000
Gurley 550,000
Nevarez 275,000

14.

In this country from problem 10, there is one representative for every 60,000 residents.
State Population Number
of
Representatives		 Number
of
Senators		 Number
of
Electors		 Electoral
Votes per
60,000 people
Arbery 720,000
Monterrosa 360,000
Bland 240,000
Davis 480,000

Exercise Group.

For each map in problems 15-16, complete the following:
  1. How many votes are needed for a majority?
  2. How many seats are won by each party?
  3. Calculate the efficiency gap.
  4. Calculate the percentage of the state that each district represents.
  5. Calculate how many district seats the efficiency gap is worth.
  6. Explain whether you think the map is fair and why or why not.

15.

This state has 5 districts with 9 people in each district.
A map with 5 districts drawn; Districts 1, 2, 4 and 5 have 4 D’s and 5 R’s each; District 3 has 9 D’s and 0 R’s.

16.

This state has 6 districts with 7 people in each.
A map with 6 districts drawn; Districts 1 through 5 have 4 D’s and 3 R’s; District 6 has 1 D and 6 R’s.
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