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Section 9.3 Applications of the Apportionment Principle

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Section 9.3. Applications 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. - PowerPoint PPT Presentation

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Page 1: Section 9.3

Section 9.3Applications of the Apportionment Principle

Page 2: Section 9.3

Objectives Use the Huntington-Hill principle to

assign additional representatives.

Use a spreadsheet to compute Huntington-Hill numbers.

Page 3: Section 9.3

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.

Page 4: Section 9.3

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.

Page 5: Section 9.3

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

Page 6: Section 9.3

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 9.12Current

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

Page 7: Section 9.3

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.

Page 8: Section 9.3

SeatNumber

Goes To

# of RepsNaxxon

# of Reps Aroco

# of Reps Eurobile

1

2

3

4

5

6

7

8

9

Page 9: Section 9.3

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

Naxxon Aroco Eurobile

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

Page 10: Section 9.3

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

Page 11: Section 9.3

Example 4: 4th Rep Calculate Huntington-Hill number

Naxxon Aroco Eurobile

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

Page 12: Section 9.3

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

Page 13: Section 9.3

Example 5: 5th Rep Calculate Huntington-Hill number

Naxxon Aroco Eurobile

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

Page 14: Section 9.3

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

Page 15: Section 9.3

Example 6: 6th Rep Calculate Huntington-Hill number

Naxxon Aroco Eurobile

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

Page 16: Section 9.3

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

Page 17: Section 9.3

Example 7: 7th Rep Calculate Huntington-Hill number

Naxxon Aroco Eurobile

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

Page 18: Section 9.3

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

Page 19: Section 9.3

Example 8: 8th Rep Calculate Huntington-Hill number

Naxxon Aroco Eurobile

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

Page 20: Section 9.3

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

Page 21: Section 9.3

Example 9: 9th Rep Calculate Huntington-Hill number

Naxxon Aroco Eurobile

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

Page 22: Section 9.3

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

Page 23: Section 9.3

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.

Page 24: Section 9.3

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.

Page 25: Section 9.3

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        

Page 26: Section 9.3

Example 11:Huntington-Hill Principle

SeatNumber

Goes To

# of Seats Alsace

# of Seats Bradford

# of Seats Cambria

123456789

10

Page 27: Section 9.3

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

Page 28: Section 9.3

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

Region 2 44 incidents

Region 3 79 incidents

Total 246 incidents

Page 29: Section 9.3

Example 12:Region 1 123 incidents

Region 2 44 incidents

Region 3 79 incidents

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

Page 30: Section 9.3

Example 12:

Officer Goes To

# Region 1

#Region 2

#Region 3

1234567

Page 31: Section 9.3

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.

Page 32: Section 9.3

Example 13:

Classes to be Taught

Goes To

High-Impact

Low-Impact Jazzercise Step Class

1 HI

2 LI

3 SC

4 Jazz

56

Page 33: Section 9.3

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.