MAT109 | General Education Mathematics
By J.J. Johnson III
As a consensus officer in a newly democratic nation, I have been assigned to determine how 100 congressional seats should be divided among 10 states of union with varying populations. In this paper, I will be demonstrating how I used to Hamilton method of appropriation to determine the number of seats each state should receive as well as the average constituency. I will also explain the absolute and relative unfairness of this method while further looking into how this method helps avoid the Alabama Paradox, thus being the best way to achieve fair representation.
As shown in the table I have attached, I first found the total population of the union I am representing. I was then able to find the percentage of representation each state held, which allowed me to determine the number of seats based on their individual population. However, after determining that number, I did find I had 5 seat left that I still had to assign. Using this method, I found the integer and fractional part to each percentage, which allowed me to assign the rest of the seats, as show in the table.
To explain why I feel this is the best method to use, I need to demonstrate the absolute and relative unfairness of this method and how it avoids the Alabama Paradox. Absolute unfairness is the difference in average constituencies while relative unfairness considers the size of constituencies in calculating absolute unfairness. One disturbing issue is the distribution is State 5 who representation didn’t change due to its population being smaller than other states. This is an apportionment scheme which appears extremely unfair, but can be calculated. We need to take into consideration that the largest average constituency is 5486.4 for State 3, the absolute unfairness between State 3 and State 5 is:Absolute unfairness = State 3 average constituency – State 5 average constituency= 5486.4 – 0= 5486.4By exposing the unfairness values shown above, there is a serious flaw within the distribution, which is signifying that we need a different way to calculate these circumstance.
As if the new state lines were drawn between states 5 (359 current population) and 6 (85663 population).Should the boundaries or population change in a state then at the next meeting of the house of representation the representation will be reviewed and it will be determined if there should be a change in representation for that particular state. Some things that can cause population to increase are things like, immigration and migration and baby booming. Things that can cause a population to decrease are things like again immigration and migration, deaths, and natural disasters. State boundaries don’t change often and they hardly ever change for diplomatic reasons, if a state boundary changes its for reasons like if a natural disaster breaks off a piece of the state or if the boundaries are naturally occurring like a river and the river changes...
