Warm Up – 3/7 - Friday
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Transcript of Warm Up – 3/7 - Friday
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