Hamilton's Method of Apportionment in Politics

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  • 0:02 Intro to Hamilton's Method
  • 1:00 Definitions and Formulas
  • 2:22 Example for Additional Seats
  • 3:39 Example Problem
  • 6:26 Lesson Summary
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Lesson Transcript
Instructor: Maria Airth

Maria has a Doctorate of Education and over 20 years of experience teaching psychology and math related courses at the university level.

There are many different methods used to assign House of Representative voting seats to each state. In this lesson, we will explore Hamilton's Method of Apportionment.

Hamilton's Method

To begin, we will go back. In history, that is. The problem of apportionment started long ago when our country was just beginning. Apportionment is the method used to assign voting seats in the House of Representatives to each represented state. I'm sure you can imagine there are many ways that the government could have decided to divide the seats up between the states.

In 1792, a method proposed by Alexander Hamilton was adopted. The Hamilton Method called for assigning each state its Lower Quota. In the event that all seats available are not assigned, one additional seat is assigned to each state starting with the state with the highest fractional Standard Quota, until all seats are assigned.

That seems a bit confusing, but once we review the definitions and go through an example, I know that it will all be very clear to you. So let's get started.

Definitions and Formulas

The Hamilton Method of Apportionment requires a state's Lower Quota to be used to assign initial seats. What is a Lower Quota? To answer that, we need to work through the process to calculate a Lower Quota.

First, we have to determine the Standard Divisor, which is the total population divided by the number of available seats to be assigned. We can use the initials SD to stand for the Standard Divisor. Next, we find each state's Standard Quota, the state's population divided by the SD found in the first step. Use SQ to represent Standard Quota.

You can imagine that it is very rare for a Standard Quota calculation to come out as a whole number. It could happen, but it certainly wouldn't be common. This is where the Lower Quota comes in. The Lower Quota is the whole number portion of a Standard Quota. For example, if a state's SQ = 4.15, its Lower Quota is 4.

The Hamilton Method refers to using Lower Quotas for all states and then assigning additional seats starting with the highest fractional Standard Quotas. It might be easier to illustrate this with an example.

Example for Additional Seats

Let's assume that Pennsylvania (with an SQ of 4.243), Virginia (SQ of 5.16), and Maryland (SQ of 3.612) are the only states we have to consider in an election (maybe it is a tri-state area election or something like that). There are only 13 seats available. Based on Hamilton's Method each state initially gets its Lower Quota apportioned. So, Pennsylvania would receive 4 seats, Virginia 5, and Maryland 3. All the Lower Quotas add up to 12 seats. There is one more seat left. Which state should get it?

Well, when we remove the whole number portion of the Standard Quota, we are left with the decimal or fractional portion of each SQ. To decide which state gets more seats, we would order the decimal values from largest to smallest. Starting with the largest decimal, we assign one additional seat to each state until all the seats are assigned. In this case, after assigning one additional seat to the top fractional portion (which is Maryland), all the available seats have been assigned so the apportionment is complete.

Example Problem

Now that you understand the definitions, the procedures, and the calculations, let's try a problem from start to finish.

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