LASA 2 The Apportionment Problem

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Assignment 1: LASA 2: The Apportionment Problem

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Assignment 1: LASA 2: 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.

State Population
1 15475
2 35644
3 98756
4 88346
5 369
6 85663
7 43427
8 84311
9 54730
10 25467

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 Representatives. You decide that apportionment (chapter 11, sections 1-4 in your textbook) is the best approach to solving this problem, but need to compare several methods and then determine which is actually fair.

Solution:

The essay states and explains on how the division of 100 congressional seats should be made among the 10 states of the union. In any fair distribution, the number of seats in a state should be proportional to its ratio in the population. Therefore, according to some rule that is acceptable, rounding should be applied.

Using the Hamilton method of apportionment, determine the number of seats each state should receive.

The table below shows the Hamilton method of apportionment used to determine the number of seats each state would receive.

State Population Quotient 1st Allocation Remaining Decimal 2nd Allocation Total Seats Constituents/ Representative Deviation
1 15475 2.908 2 0.908 1 3 5158 164
2 35644 6.698 6 0.698 1 7 5092 230
3 98756 18.557 18 0.557   18 5486 165
4 88346 16.601 16 0.601 1 17 5197 125
5 369 0.069 0 0.069   0 0 5322
6 85663 16.096 16 0.096   16 5354 32
7 43427 8.160 8 0.160   8 5428 106
8 84311 15.842 15 0.842 1 16 5269 52
9 54730 10.284 10 0.284   10 5473 151
10 25467 4.785 4 0.785 1 5 5093 228
Total 532188   95     100    

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.

By using the numbers that I calculated from applying the Hamilton method, I determined the average constituency for each state. My decision was to divide the states with the largest critical divisor and the state was allocated the remaining seats.

That is:

Total population = 532188

Total number of seats = 100

Average population per seat = 5321.88

Calculate the absolute and relative unfairness of this apportionment.

The absolute unfairness of an apportionment is defined as the absolute value of the difference between the smallest and the largest average constituency state A and the smallest and the largest average constituency of state B. it can also be applied when making a decision where investments are most productive or detrimental. That is:

Population/representative=consistency

(Average consistence of state A – Average consistence of state B) = unfairness of apportionment

State A 369/1 = 369

State B 25467/4 = 6367

6367-369 = 5998

The unfairness of apportionment will therefore be 5998.

Explain how changes in state boundaries or populations could affect the balance of representation in this congress. Provide an example using the results above.

It is unfair that state number 5 gets no representation at all. This means that state number 5 is to be merged with state number 4, so it can fix the deviation at state number 2, which is the largest at 230. Changes in the state boundaries or populations could affect the balance of representation in the congress. The reason being, that when the population increases it affects the total representative’s results as in when state number 5 merges with number four. Therefore, these are the changes, explained in the table below.

State Population Quotient 1st Allocation Remaining Decimal 2nd Allocation Total Seats Constituents Per Representative Deviation
1 15475 2.908 2 0.908 1 3 5158 164
2 35644 6.698 6 0.698 1 7 5092 230
3 98756 18.557 18 0.557   18 5486 165
4 88715 16.670 16 0.670 1 17 5219 103
6 85663 16.096 16 0.096   16 5354 32
7 43427 8.160 8 0.160   8 5428 106
8 84311 15.842 15 0.842 1 16 5269 52
9 54730 10.284 10 0.284   10 5473 151
10 25467 4.785 4 0.785 1 5 5093 228
Total 532188   95     100    

Now, it is a bit fair for the population and allocation, since the number at constituency 5 was very little.

How and why could an Alabama Paradox occur?

The Alabama Paradox is an increase in the total number of seats that is to be apportioned and this results to a state to lose a seat. The reason why an Alabama Paradox could occur, is if we added a seat and someone lost the representation. If in this case we added an extra seat, nobody lost a seat. An example is seat number 3 gained the extra seat.

State Population Quotient 1st Allocation Remaining Decimal 2nd Allocation Total Seats Constituents Per Representative Deviation
1 15475 2.937 2 0.937 1 3 5158 164
2 35644 6.765 6 0.765 1 7 5092 230
3 98756 18.742 18 0.742 1 19 5198 124
4 88715 16.837 16 0.837 1 17 5219 103
6 85663 16.257 16 0.257   16 5354 32
7 43427 8.242 8 0.242   8 5428 106
8 84311 16.001 16 0.001   16 5269 52
9 54730 10.387 10 0.387   10 5473 151
10 25467 4.833 4 0.833 1 5 5093 228
Total 532188   96     101    

Explain how applying the Huntington-Hill apportionment method helps to avoid an Alabama Paradox.

The Huntington-Hill Method can be explained as the modified version of the Webster method, but it uses somehow, a less different rounding method. While the Webster’s method rounds at 0.5, the Huntington-Hill method rounds at the geometric mean. If a state’s quotient is higher than its geometric mean, this means that it will be allocated an additional seat. This method will almost always result in the desired number of seats and this therefore helps to avoid an Alabama Paradox.

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.

Apportionment can achieve either a fair and unfair representation as to what I have discovered while researching the assignment. This also depends on the apportionment method where it is used that plays a factor in your results as well.

Suggest another strategy that could be applied to achieve fair representation either using apportionment methods or a method of your choosing.

In order to achieve optimal fairness, the Huntington-Hill method displays the most fairness as compared to others like Adams method, Dean’s method, Webster’s method, or Jefferson’s method. If one has concerns on the relative differences, then achieving optimal fairness through the criteria formulas works only for the Huntington-Hill method.




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