Suppose an electronics company has three divisions: (D)igital, (C)omputers, and (B)usiness products. Division D has 146 employees, C has 80, and B has 34. Assume that a 10-member quality improvement council has membership on the council proportional to the number of employees in the three divisions. a. Apportion this council using the Hamilton method. b. Now increase the council's size to 11, and then to 12 and apportion this council using the Hamilton method. c. What is the first size above 10 when the Alabama paradox occurs, and what division loses a seat when the size of the council increases? a. With 10 members, the council consists of member(s) from division D, from division C, and member(s) from division B.

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Chapter1: Functions And Models
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**Apportionment of Council Members using the Hamilton Method**

Suppose an electronics company has three divisions: Digital (D), Computers (C), and Business products (B). Division D has 146 employees, C has 80, and B has 34. Assume that a 10-member quality improvement council has membership on the council proportional to the number of employees in the three divisions.

### Tasks:

**a. Apportion the council using the Hamilton method.**

**b. Now increase the council’s size to 11, and then to 12, and apportion this council using the Hamilton method.**

**c. What is the first size above 10 when the Alabama paradox occurs, and what division loses a seat when the size of the council increases?**

**Apportionment Results:**

- **a. With 10 members, the council consists of:**
  - □ member(s) from division D
  - □ from division C
  - □ member(s) from division B

In this educational exercise, students will learn about the Hamilton method of apportionment, which distributes seats based on quotas derived from proportional representation. This method is applied to see how council seats may shift with changes in total council size, highlighting phenomena like the Alabama paradox.
Transcribed Image Text:**Apportionment of Council Members using the Hamilton Method** Suppose an electronics company has three divisions: Digital (D), Computers (C), and Business products (B). Division D has 146 employees, C has 80, and B has 34. Assume that a 10-member quality improvement council has membership on the council proportional to the number of employees in the three divisions. ### Tasks: **a. Apportion the council using the Hamilton method.** **b. Now increase the council’s size to 11, and then to 12, and apportion this council using the Hamilton method.** **c. What is the first size above 10 when the Alabama paradox occurs, and what division loses a seat when the size of the council increases?** **Apportionment Results:** - **a. With 10 members, the council consists of:** - □ member(s) from division D - □ from division C - □ member(s) from division B In this educational exercise, students will learn about the Hamilton method of apportionment, which distributes seats based on quotas derived from proportional representation. This method is applied to see how council seats may shift with changes in total council size, highlighting phenomena like the Alabama paradox.
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