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?

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. 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

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.

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 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.

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.

Example #2