1. Warm Up – 3/7 - Friday Find the Hamilton Apportionment for 200 seats.
B) Find the Hamilton
Apportionment for 201 seats.
C) What is the problem with
Adding a seat?

2. Hamilton Method Paradoxes
Alabama Paradox: It is possible for a state to lose a seat just because more seats get added to congress.
Population Paradox: It is possible for a state that is growing in population to lose a seat to a state growing not as fast or not at all.

3. Jefferson’s Method

4. To understand Jefferson’s method
When I divide two numbers I may get a decimal.
7 5 =1.4
If I increase the number on the bottom, the decimal will go down.
7 6 =1.167
If I decrease the number on the bottom the decimal goes up.
7 4 =1.75

5. Example #1 1. Find the lower quotas for each state. Population Texas
10,030
Illinois
9,030
Alabama
940
Total
20,000
1. Find the lower quotas for each state.

6. Example #1
The goal of Jefferson is to pick a SD so that when we find the lower quotas, all seats are used.

7. Example #1
If I need to give out more seats, I want my decimals to go up!
So I decrease my standard divisor.
My SD was 200. I will use a modified divisor of
Population
Texas
10,030
Illinois
9,030
Alabama
940
Total
20,000

8. Example #1
196.6 is a guessed decrease. There is nothing scientific or mathematical about it.
Notice when I use my new lower quota, I have used all of the seats!

10. Example #2 Find the Standard Divisor.B C D E F
total
population
1,646
6,936
154
2,091
685
988
12,500
Find the Standard Divisor.
If all the seats are not apportioned, use Jefferson’s
method to apportion the remaining seats.

11. Example #2 We need to give out 4 more seats which means
We need our decimals to go up!
So we pick a Modified Divisor
That is less that our original
Divisor of 50.

12. Example #2