# M3 A1 Lasa2 the Apportionment Problem Essay example

659 Words Nov 11th, 2014 3 Pages
M3_Assignment 1: LASA 2: The Apportionment Problem
Argosy University
General Education Mathematics | MAT109 A05
November 8, 2014

Abstract
This essay determine how 100 congressional seats should be divided among the 10 states of the union. The number of seats in a state should (in any fair distribution) be proportional to its ratio in the population. Therefore rounding according to some (acceptable) rule should be applied.

Below you will see the table showing the Hamilton method of apportionment to determine the number of seats each state would receive.

Hamilton Method (Named for Alexander Hamilton) Implementing this method is a three-step procedure.
1) Calculate each state's representation and round each one down.
2)
The Huntington-Hill Method is a modified version of the Webster method, but it uses a slightly different rounding method. While 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, it will be allocated an additional seat. This method will almost always result in the desired number of seats which helps to avoid an Alabama Paradox.
Apportionment can achieve both a fair and unfair representation giving the research I have done on this assignment. It also depends on the apportionment method in which is used that also plays a factor in your results.
For optimal fairness measures I believe that the Huntington-Hill method displays the most fairness. Giving the example that ai and Pi are the number of seats for state i and its population, respectively. Then I would look at the measurements by the given fairness formula.
• For the measure |ai - aj(Pi/Pj)| Adams method is optimal.
• For the measure |Pj/aj-Pi/ai| Dean's method is optimal.
• For the measure |(ai/aj)(Pi/Pj)-1| Huntington-Hill is optimal.
• For the measure |ai/Pi - aj/Pj| Webster is optimal.
• For the measure |ai(Pj/Pi) - aj| Jefferson's method is optimal.

As you can see, it might not be obvious that these seemingly similar measures of absolute fairness would give rise to such different methods to