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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

- 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.

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.

- TB pg. 532/2 – 20 Even (Online)

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?

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?

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

Example 11: Huntington-Hill Principle

Example 11: Huntington-Hill Principle

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?

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.

- TB pg. 532/2 – 20 Even (Online)

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