section 9.3 applications of the apportionment principle

Section 9.3Applications of the Apportionment Principle

Objectives

Use the Huntington-Hill principle to assign additional representatives.

Use a spreadsheet to compute Huntington-Hill numbers.

Some Good Advice

Once you have used the largest of the Huntington-Hill numbers to apportion a representative, cross that number off so that you do not use it again.

Huntington-Hill Principle

A labor council is being formed from the members of three unions. The electricians’ union has 25 members, the plumbers have 18 members, and the carpenters have 31 members. The council will have seven representatives, with each union having at least one representative. Use the Huntington-Hill numbers listed in Table 9.12 to answer Examples 1 and 2.

Example 1: Knowing that each union currently has 1

representative, which entries in the Table 9.12 do we use to assign the fourth seat on the council and which union gets that seat?

Current Representation Electricians Plumbers Carpenters

1 312.5 162.0 480.5

2 104.2 54.0 160.2

3 52.1 27.0 80.1

4 31.3 * 48.1

Example 2: Suppose the current council has 5 seats,

apportioned so that the electricians and carpenters have 2 seats each and the plumbers have one. Which entries in the table do we use to assign the sixth seat on the council and which union gets that seat?

Table 9.12

Current Representation Electricians Plumbers Carpenters

1 312.5 162.0 480.5

2 104.2 54.0 160.2

3 52.1 27.0 80.1

4 31.3 * 48.1

Huntington-Hill Principle

Use the Huntington-Hill principle to apportion the oil consortium board. Recall that Naxxon has 4,700 stockholders, Aroco has 3,700, and Eurobile has 1,600. We will assign the 9 representatives one at a time until we have assigned all of them.

A provision on the U. S. Constitution allows us to automatically give each company 1 representative.

SeatNumber

Goes To

# of RepsNaxxon

# of Reps Aroco

# of Reps Eurobile

1

2

3

4

5

6

7

8

9

Example 3: 1 – 3 Rep Calculate Huntington-Hill number

Naxxon Aroco Eurobile

..\..\Xls\Huntington_Hill Number.xlsx

SeatNumber

Goes To

# of RepsNaxxon

# of Reps Aroco

# of Reps Eurobile

1 N 1 0 0

2 A 1 1 0

3 E 1 1 0

4

5

6

7

8

9

Example 4: 4th Rep Calculate Huntington-Hill number



SeatNumber

Goes To

# of RepsNaxxon

# of Reps Aroco

# of Reps Eurobile

1 N 1 0 0

2 A 1 1 0

3 E 1 1 1

4 N 2 1 1

5

6

7

8

9

SeatNumber

Goes To

# of RepsNaxxon

# of Reps Aroco

# of Reps Eurobile

1 N 1 0 0

2 A 1 1 0

3 E 1 1 1

4 N 2 1 1

5 A 2 2 1

6

7

8

9

SeatNumber

Goes To

# of RepsNaxxon

# of Reps Aroco

# of Reps Eurobile

1 N 1 0 0

2 A 1 1 0

3 E 1 1 1

4 N 2 1 1

5 A 2 2 1

6 N 3 2 1

7

8

9

SeatNumber

Goes To

# of RepsNaxxon

# of Reps Aroco

# of Reps Eurobile

1 N 1 0 0

2 A 1 1 0

3 E 1 1 1

4 N 2 1 1

5 A 2 2 1

6 N 3 2 1

7 A 3 3 1

8

9

SeatNumber

Goes To

# of RepsNaxxon

# of Reps Aroco

# of Reps Eurobile

1 N 1 0 0

2 A 1 1 0

3 E 1 1 1

4 N 2 1 1

5 A 2 2 1

6 N 3 2 1

7 A 3 3 1

8 N 4 3 1

9

SeatNumber

Goes To

# of RepsNaxxon

# of Reps Aroco

# of Reps Eurobile

1 N 1 0 0

2 A 1 1 0

3 E 1 1 1

4 N 2 1 1

5 A 2 2 1

6 N 3 2 1

7 A 3 3 1

8 N 4 3 1

9 E 4 3 2

Section 9.2 Assignment

Class work:TB pg. 532/2 – 20 Even (Online)

• Remember you must write the problem and show ALL work to receive credit for this assignment.

Comparing Methods Apportioning a city council. A city is made up

of three boroughs – Alsace, Bradford, and Cambria. Representation on a ten-member city council is allocated in proportion to the population in each of the tree boroughs. Alsace has a population of 23,000, Bradford has 34,000, and Cambria has 14,000. Apportion the ten council seats Using the Hamilton method. Using the Huntington-Hill apportionment

principle.

Example 10:Hamilton Method

Apportioning a city council.

Boroughs Population % Step 1 Step 2 Step 3

Alsace 23,000

Bradford 34,000

Cambria 14,000

Total: 71,000

Example 11:Huntington-Hill Principle

SeatNumber

Goes To

# of Seats Alsace

# of Seats Bradford

# of Seats Cambria

1

2

3

4

5

6

7

8

9

10

Example 11:Huntington-Hill Principle

Seat Number Goes To # of Seats

Alsace# of Seats Bradford

# of Seats Cambria

1 B 0 1 0

2 A 1 1 0

3 C 1 1 1

4 B 1 2 1

5 A 2 2 1

6 B 2 3 1

7 C 2 3 2

8 B 2 4 2

9 A 3 4 2

10 B 3 5 2

Assigning Police Officers Consider the problem of apportioning

police officers given in Example 2, page 531. Suppose we still want to apportion the seven officers among the three regions, but the number of incidents per region has changed. The number of related incidents for regions 1, 2, and 3 are listed in the table. How should the seven officers be assigned to the regions, given this new data?

Region 1 123 incidents



Total 246 incidents

Example 12:




Total 246 incidents

If Given the Next Officer,

the Number a Region Would

Have Is:Region 1 Region 2 Region 3

1 7564.5 968.0 3120.52 2521.5 322.67 1040.23 1260.8 161.3 520.14 756.5 96.8 312.15 504.3 64.5 208.0

Example 12:

Officer Goes To

# Region 1

#Region 2

#Region 3

1

2

3

4

5

6

7

Scheduling Fitness Classes A health club instructor has a course load

that allows her to teach six two-credit-hour classes. A pre-registration survey indicates the following interests.

58 want to take high-impact aerobics 32 want to take low-impact aerobics 11 want to take Jazzercise 39 want to take step exercise

Assume that the instructor will teach at least 1 class for each activity.

a) Use the Huntington-Hill method to apportion the instructor’s remaining two classes among the four activities.

Example 13:

Classes to be Taught

Goes To

High-Impact

Low-Impact Jazzercise Step Class

1 HI

2 LI

3 SC

4 Jazz

56

Section 9.2 Assignment

Class work:TB pg. 532/2 – 20 Even (Online)

• Remember you must write the problem and show ALL work to receive credit for this assignment.

section 9.3 applications of the apportionment principle

Documents