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# Tikaya Final Maths Assignment.Doc

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Math’s Assignment

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Date

Abstract

This assignment will determine how 100 seats should be divided among the ten states. The number of seats in a state should be fairly distributed and in proportion to the ratio of population. The rounding off rule will be applied.

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

The Standard Divisor= Total Population/Number of seats

In our case the total population= 15475+35644+98756+88346+369+85663+43427+84311+54730+25467 Divided by 100(The number of seats)

=532188/100 which is equal to 5321.88

Therefore the standard quota= State Population/Standard Divisor

Calculated as follows for each individual states

|States |State Pop/Std Divisor |Standard Quota |Lower Quota |
|1 |15475/5321.88 |2.9 |2 |
|2 |35644/5321.88 |6.7 |7 |
|3 |98756/5321.88 |18.5 |19 |
|4 |88346/5321.88 |16.6 |17 |
|5 |369/5321.88 |0.1 |1 |
|6 |85663/5321.88 |16.1 |16 |
|7 |43427/5321.88 |8.1 |8 |
|8 |84311/5321.88 |15.8 |16 |
|9 |54730/5321.88 |10.2 |10 |
|10 |25467/5321.88 |4.7 |4 |

Therefore the number of seats each state will receive is per the table above, using the lower quota method which allocates the remaining seats after removing decimals to the state whose decimal places were largest until reaching the desired total of 100. In our case the states were 3, 4 and 8.

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.

The Average Constituency for each state is calculated by taking;

Population of State divided by the Number of representative for the states.

|States |Population of state/No of Representative for state |Average Constituency |
|1 |15475/2 |7737.5 |
|2 |35644/7 |5092 |
|3 |98756/19 |5197.7 |
|4 |88346/17 |5196.8 |
|5 |369/0.1 |3690 |
|6 |85663/16 |5353.9 |
|7 |43427/8 |5428.4 |
|8 |84311/16 |5269.4 |
|9 |54730/10 |5437 |
|10 |25467/4 |6366.8 |

3. Calculate the absolute and relative unfairness of this apportionment.

The Absolute Unfairness is calculated as follows

Larger Average Constituency- Smaller Average Constituency

In our case the larger average constituency=7737.5

While smaller average constituency=3690

Therefore absolute unfairness= 7737.5-3690 which is equal to 4047.5

The relative unfairness is calculated as follows

Absolute unfairness/Smaller average constituency for two states

The smaller average constituency for two states= Two smaller states/2 =3690+5092/2

Which is equal to 8782/2 = 4391

Therefore relative unfairness = 4047.5/4391 which is equal to 0.92

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.

The changes in the state boundaries could affect the balance of the congress representation because when the population increases, it will influence the total representative results as it’s evident in the preceding results above. In essence, no state that gains population gives up a seat even though there is no much change.

5. How and why could an Alabama Paradox occur?

An Alabama Paradox occurs when there is an increase in the available number of items that causes a particular group to lose an item or a seat. The Alabama Paradox occurs in the preceding circumstances even though the population remains exactly the same. In essence, if the seats to be apportioned increase, then the state will be forced to lose the seat.

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

Apportionment is the fair division process that is used to divide identical and indivisible objects among units that may be entitled to unequal shares. The Huntington-Hill apportionment method helps to avoid the Alabama Paradox by fixing the number of seats and applying the Quota rule. The method assigns a state it’s lower quota if the fractional part of its standard allowance is less than the geometric mean. The same is applied to an upper quota when if the usual allowance is greater than the geometric mean of two whole numbers. The method, therefore, solves the Alabama Paradox by apportionment and giving each number of seats equal to the lower or upper quota.

7. Based on 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 is only a half battle of achieving fair representation. It’s imperative to note that states use the census for the redistributing of their congressional districts after the appointments have been made. However, the U.S Constitution specifies that the seats in the House of Representative are divided according to the proportion of states populations. From my experience of solving this problem, I feel that apportionment is the best way to achieve fair representation because seats are allocated according to the population. This is the method of equal proportions.

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

The other method that can be used to obtain adequate representation is the Webster’s method. The method is nearly unbiased even though it favors larger states but only in very minimal circumstances. The method is the least biased and is the most proportionally and accurate of any apportionment method to be used in the Congress.