Warm Up – 3/7 - Friday

A) Find the Hamilton Apportionment for 200 seats.

B) Find the Hamilton Apportionment for 201 seats.

C) What is the problem withAdding a seat?

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.

Jefferson’s Method

To understand Jefferson’s method

• When I divide two numbers I may get a decimal.

If I increase the number on the bottom, the decimal will go down.

If I decrease the number on the bottom the decimal goes up.

Example #1

Population

Texas 10,030

Illinois 9,030

Alabama 940

Total 20,000

1. Find the lower quotas for each state.

Example #1 • The goal of Jefferson is to pick a SD so that

when we find the lower quotas, all seats are used.

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 196.6.

Population

Texas 10,030

Illinois 9,030

Alabama 940

Total 20,000

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!

Example #2

A B C D E F total

population 1,646 6,936 154 2,091 685 988 12,500

A)Find the Standard Divisor.B) If all the seats are not apportioned, use Jefferson’s method to apportion the remaining seats.

Example #2

We need to give out4 more seats which meansWe need our decimals to go up!

So we pick a Modified DivisorThat is less that our original Divisor of 50.

Example #2