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Chapter 5 Review

Seat apportionment, electoral vote counts and voting power, and efficiency-gap tests on a district map, combined in cumulative practice.

Math in Society, Chapter 5 Review

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14 exercises

Exercise 1

In exercises 1-4, determine the apportionment using

  1. Hamilton's Method

  2. Jefferson's Method

  3. Webster's Method

  4. Huntington-Hill Method

A small country consists of four states, whose populations are listed below. If the legislature has 78 seats, apportion the seats.

2.5

Exercise 2

In exercises 1-4, determine the apportionment using

  1. Hamilton's Method

  2. Jefferson's Method

  3. Webster's Method

  4. Huntington-Hill Method

Reapportion the previous problem with 90 seats.

2.5

Exercise 3

In exercises 1-4, determine the apportionment using

  1. Hamilton's Method

  2. Jefferson's Method

  3. Webster's Method

  4. Huntington-Hill Method

A small country consists of five states, whose populations are listed below. If the legislature as 100 seats, apportion the seats.

2.5

Exercise 4

In exercises 1-4, determine the apportionment using

  1. Hamilton's Method

  2. Jefferson's Method

  3. Webster's Method

  4. Huntington-Hill Method

Reapportion the previous problem with 125 seats.

2.5

Exercise 5

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.

A Portland Community College Board member race has four candidates: E, F, G, H. The votes are:

2.5

Exercise 6

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.

A Forest Grove School Board position has four candidates: I, J, K, L. The votes are:

2.5

Exercise 7

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.

A Multnomah County Commissioner's race has five candidates: M, N, O, P, Q. The votes are:

2.5

Exercise 8

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.

The Oregon State Governor's race has five candidates: R, S, T, U, V. The votes are:

2.5

Exercise 9

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.

In this country there is one representative for every 55,000 residents.

2.5

Exercise 10

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.

In this country there is one representative for every 60,000 residents.

2.5

Exercise 11

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…

2.5

Exercise 12

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…

2.5

Exercise 13

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

In this country from problem 9, there is one representative for every 55,000 residents.

2.5

Exercise 14

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

In this country from problem 10, there is one representative for every 60,000 residents.

2.5

Adapted from Math in Society © 2018–2024 Portland Community College Math Instructors. Licensed under CC BY-SA 4.0. Source: Math in Society. Imported at revision 68ee43c.