apportionment final paper

8/11/2019 Apportionment Final Paper

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Apportionment 2

Apportionment: Analyzing the Different Methods That Accompany It

When studying the apportionment process, it is interesting to begin with its history and

how it had continued to change over time. Anyone beginning to study the different

apportionment methods will truly be shocked at how little the data really varies in the end. The

Malapportionment section of this project does well at laying out the information in an organized

way that can easily be read and understood by anyone who may be lacking an understanding of

the apportionment process. However, before seeing the results of the malapportionment section,

one should first try to see where the changes in the apportionment method have been over the

years and what may have caused them. The focus of this apportionment method should be on the

span between 1790 and the mid twentieth century, when the hill method had finally been adopted

and implemented up until present day.

Analyzing Each Method and its Place in History

With the first census being introduced in 1790, Congress could be seen looking to

support the less populated states by adopting Hamiltons method. Hamiltons method involved

rounding down each quotient (determined by dividing the total amount of house seats into the

states population) and then focusing on the fraction that was left was subtracting the new,

rounded down whole number from the original quotient. After determining the amount of

representation lost from rounding down, the fractions were then ranked. By taking the new

amount of representation and subtracting it by the desired amount of seats, one could then

designate an additional seat to the ranked fractions that fell equal to or under that number.

Smaller states that had been underrepresented with only one representative were now being

provided an additional one under this method. However, after becoming victim to Americas first

veto from Washington, Congress turned to Jeffersons method, which is completely opposite of


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Apportionment 4

mean. It erases that unfair bias we see with Websters method of only rounding up at .5 and

allows states that fall just below that mark a chance to also get rounded up. Its flaw comes

with the larger states that dont round up if below that .5 mark unlike the smaller states

that do have a better chance at rounding up. With this all occurring in-between that

timeframe of 1790-1940, Congress finally settles on the Hill method. Like Deans Method,

the Hill method incorporates a mean to compare with the quotient, however Hill chooses to

use the Geometric mean, which is determined by the following equation:

xy

With X and Y representing the same values used in the Dean method, this mean provides will

always provide a higher number than the Harmonic mean, which allows for less of a favoring

towards smaller states that can be seen with the Dean method.

Resulting Malapportionment Statistics

After determining the apportionment for each method, one should then move to focus on

the malapportionment statistics. This provides easy access to data such as the mean deviation and

voter equivalency ratio that becomes vital when determining which method should ultimately be

used. Using Table 1, one should be able to see right away that the Jefferson method is in no way

appropriate to implement as the apportionment method. With Hawaii being completely

underrepresented with only one representative acting for almost 1.4 million people and

Wyoming being overrepresented with one representative only acting for under 600,000 people,

we see that this method gives an outstanding Voter Equivalency Ratio of 2.41. The Percentage

Mean Absolute Deviation of 14.82% only verifies that this method has no place in a modern

America and should excluded from the ongoing analysis of the other methods, which all contain

relatively close data. With only five methods to analyze now, one should continue on the path of


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focusing on older apportionment methods. While each of methods may benefit one category of

apportionment, the focus should lie on a method that is solid as a whole, even if other methods

should better numbers in certain categories. This becomes true with the Adams method, which

shows the lowest Voter Equivalency Ratio at 1.66. However, this is only between the most and

least represented and when the Mean Absolute Deviation is viewed, it can be seen coming in at a

much higher number than the remaining four methods. Hamilton comes in at the exact opposite,

which makes sense, seeing that it required states to round their quotients up instead of down.

This means that one should now see a higher Voter Equivalency Ratio, but a lower mean of

deviation. The Adams and Hamilton Methods show their strengths and weaknesses in completely

opposite categories. There is really no argument for Websters method seeing that it doesnt

compete in any category, which may explain why it was never implemented into apportioning

seats. One should come to the conclusion that the mean divisor methods that the Jefferson,

Hamilton, Adams, and Webster methods use to apportion seats show too great of a bias. This

will leave either the Dean Method or Hill Method, which instead use mean divisor methods to

eliminate any obvious signs of bias to either these larger or smaller states. When comparing these

two methods, one will first notice that while the state of Montana is overrepresented with the

Dean method, it is underrepresented with the Hill method. As stated before, this can only mean

that the Geometric mean in the Hill method is larger than the quotient versus the Harmonic mean

in the Dean method, which is smaller than the quotient. While the Voter Equivalency Ratio

comes in smaller with the Hill method at 1.76, the Dean method provides both a smaller

percentage mean of deviation (6.11%) and also has a drastically lower max deviation percentage

(30.16%). The Hill method shows a percentage mean of deviation at 6.15%, which is only

slightly larger than that of the Dean method.


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Apportionment 6

Table 1


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Apportionment 7

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