## Section 5.5 Chapter 5 Review

### Exercises Review Exercises

###### Exercise Group.

In exercises 1-4, determine the apportionment using

Hamilton’s Method

Jefferson’s Method

Webster’s Method

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:

How many voters voted in this election?

How many votes are needed for a majority?

Find the winner under the plurality method.

Find the winner under the Instant Runoff Voting method.

Find the winner under the Borda Count Method.

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:

The total number of electors in the state.

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:

The winner of the popular vote in the country and the percentage of votes they won.

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:

The state that has the most electoral power

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:

How many votes are needed for a majority?

How many seats are won by each party?

Calculate the efficiency gap.

Calculate the percentage of the state that each district represents.

Calculate how many district seats the efficiency gap is worth.

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.

###### 16.

This state has 6 districts with 7 people in each.