I. The Hamilton Apportionment Method
The Hamilton Apportion Method (also “Hamilton/Vinton Method”, US Census Bureau, 2014) sets the divisor as the proportion of the total population per house seat. After the population for each of the 10 states has been divided by the divisor (5,321.9), the whole number of the quotient is kept and the decimal dropped. This will result in a discrepancy: less than 100 house seats. The first surplus seat is assigned to the state with the largest fraction after the original division. The next is assigned to the state with the second-largest fraction and so on. The process continues until all missing house seats are allocated.

Table 1: First Allocation after Following the Hamilton Method
State Population Quotient First Allocation Leftover Decimal Seats Apportioned
1 15,475 2.9 2 0.9 3
2 35,644 6.7 6 0.7 7
3 98,756 18.6 18 0.6 19
4 88,346 16.6 16 0.6 16
5 369 0.1 0 0.1 0
6 85,663 16.1 16 0.1 16
7 43,427 8.2 8 0.2 8
8 84,311 15.8 15 0.8 16
9 54,730 10.3 10 0.3 10
10 25,467 4.8 4 0.8 5
TOTAL 532,188 100.0 95.0 5.0 100.0 Divisor 5,321.9

The average constituency of each state is 53,219. One notes that:
• The decision-making process of allocating the five remaining seats beginning with those that have the larger fractions is straightforward enough beginning with states #1, 8, 10, 2 and 3. However, state #4 had exactly the same fraction as #3 but failed to receive any more unallocated seats because the remainder of five had run out.
• Unhappily, the Hamilton procedure leaves state #5 unrepresented.
II. Absolute and Relative Unfairness
On the basis that the nationwide average is 5,322 constituents, those displaying negative numbers for “Absolute Unfairness” below are more poorly represented (Pirnot, 2013).
Table 2: Absolute Unfairness vs. National Average
State Population Present Seats Apportioned Average