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

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 1: 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 1

4

5

6

7

8

9

Example 2: 4th 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 1

4 N 2 1 1

5

6

7

8

9

Example 3: 5th 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 1

4 N 2 1 1

5 A 2 2 1

6

7

8

9

Example 4: 6th 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 1

4 N 2 1 1

5 A 2 2 1

6 N 3 2 1

7

8

9

Example 5: 7th 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 1

4 N 2 1 1

5 A 2 2 1

6 N 3 2 1

7 A 3 3 1

8

9

Example 6: 8th 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 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

Example 7: 9th 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 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.

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 8 and 9.

Example 8: 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 9: 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

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

Region 2 44 incidents

Region 3 79 incidents

Total 246 incidents

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

Example 12:

Officer Goes To

# Region 1

#Region 2

#Region 3

1

2

3

4

5

6

7

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.