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Assignment 1: The Apportionment Problem

You are a census officer in a newly democratic nation and you have been charged with using the census data from the table below to determine how 100 congressional seats should be divided among the 10 states of the union.

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Being a fan of United States history, you are familiar with the many methods of apportionment applied to this problem to achieve fair representation in the US House of Representative. You decide that apportionment is the best approach to solving this problem, but need to compare several methods and then determine which is actually fair.

1. Using the Hamilton method of apportionment, determine the number of seats each state should receive.
2. Using the numbers you just calculated from applying the Hamilton method, determine the average constituency for each state. Explain your decision making process for allocating the remaining seats.
3. Calculate the absolute and relative unfairness of this apportionment.
4. Explain how changes in state boundaries or populations could affect the balance of representation in this congress. Provide an example using the results above.
5. How and why could an Alabama Paradox occur?
6. Explain how applying the Huntington-Hill apportionment method helps to avoid an Alabama Paradox.
7. Based upon your experience in solving this problem, do you feel apportionment is the best way to achieve fair representation? Be sure to support your answer.
8. Suggest another strategy that could be applied to achieve fair representation either using apportionment methods or a method of your choosing.

You must show some calculations in your document to demonstrate that you know how to perform these tasks.

Solution Preview

You are a census officer in a newly democratic nation and you have been charged with using the census data from the table below to determine how 100 congressional seats should be divided among the 10 states of the union.
Using the Hamilton method of apportionment, determine the number of seats each state should receive.
To figure out how many seats the each state should get you first need to come up with a standard divisor. This is simply the number that each state will be divided by.
Standard Divsior (SD)=(total Population of all states(P) )/(Number of seats available(h)) in this case total population is the sum of all the populations. 15475+35644+98756+88346+369+85663+43427+84311+54730+25467=532188
Plug into the equation to come up with SD: SD=P/h=532188/100=5321.88. This is the number that every state population will divided by to determine the number of seats they get. This is called the Standard Quota (q)
In Hamiltion's method, always start out assigning the lower quota (means round down to nearest whole number aka the whole number without the decimals). Then you will be able to add seats if needed. The additional seats are given out based on the decimals from largest to smallest until all extra seats are gone. Each state must be represented!

State Population Quota Lower Quota Additional Seats Final #of seats
1 15475 15475/5321.88=2.91 2 +1 seat 3
2 35644 35644/5321.88=6.70 6 +1 seat 7
3 98756 98756/5321.88=18.56 18 18
4 88346 88346/5321.88=16.60 16 16
5 369 369/5321.88=0.06 0 +1 seat 1
6 85663 85663/5321.88=16.10 16 16
7 43427 43427/5321.88=8.16 8 8
8 84311 84311/5321.88=15.84 15 +1 seat 16
9 54730 54730/5321.88=10.28 10 10
10 25467 25467/5321.88=4.79 4 +1 ...

Solution Summary

The expert uses the Hamilton method of apportionment to determine the number of seats each state should receive.

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