Jefferson's Method of Apportionment in Politics

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  • 0:02 Jefferson's Method
  • 1:45 Definitions & Calculations
  • 5:58 Example
  • 8:41 Second Example
  • 10:35 Lesson Summary
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Lesson Transcript
Instructor: Maria Airth

Maria has a Doctorate of Education and over 15 years of experience teaching psychology and math related courses at the university level.

The Jefferson Method of Apportionment is just one of many different methods of apportionment. In this lesson, we will review the Jefferson Method using examples to solidify the concepts.

Jefferson's Method

Congratulations! You have been elected president of the United States of America! As your first act in office, you have decided to help middle school students all over the U.S. by consolidating the states into just three, easy to remember states. No more memorizing 50 states and capitals. You have, aptly, named these new states Stars, White Stripe, and Red Stripe (the stars and stripes, for short).

Well, these new states need to have representation in your Congress. You've decided to use the Jefferson Method of Apportionment to assign seats to each state. This method of apportionment was used by the U.S. Congress from 1790 to 1840.

But, how do you do that? To understand the Jefferson Method of Apportionment, you must first understand that apportionment is dividing, or portioning, the total number of voting seats in a body of government between entities. So, what we are doing is deciding how many votes each state will have.

In Jefferson's Method of Apportionment, each state is assigned a lower quota of seats. If the lower quota equals the total to be assigned, you are finished. But, if the lower quota does not match the seats to be assigned, you must modify the standard divisor until the modified quotas for the states does equal the total to be assigned. I may have just mentioned some terms that you may not be familiar with. Let's define those now.

Definitions and Calculations

In Jefferson's Method, we first have to find the lower quota. To do this, we start at the very beginning with determining a standard divisor by dividing the total population by the number of seats to assign. For example, if the total population is 1,200, the number of seats is 12, then the standard Divisor = 1,200 / 12 = 100.

We use the standard divisor to get the standard quota, the number of seats each state should get. This is calculated by dividing the population of the state by the standard divisor. That makes a bit of sense; the divisor divides everything, and the quota is the number of seats calculated using the divisor.

Earlier, we got a standard divisor of 100, so let's assume we have a state with 120 people. That means that the standard quota = 120 / 100 = 1.2. Notice that the quota is not a whole number. It would not be possible to occupy two-tenths of a seat for voting purposes, so we need to find a method to change that decimal into a whole number.

The nearest whole numbers to 1.2 are 1 and 2. It's pretty obvious that the lower whole number is referred to as the lower quota and the higher whole number is called the upper quota.

So, so far we have:

  • Standard divisor (SD): the population / seats, and that's the number to divide with
  • Standard quota (SQ): state population / standard divisor, which is the raw fractional result after using the divisor
  • Lower quota (LQ): the closest, smaller whole number to the standard quota
  • Upper quota (UQ): the closest, larger whole number to the standard quota

It would be great if all the lower quotas of any Jefferson Method procedure added up to the correct number of seats, but that really doesn't happen often. So, we have to go back to the beginning and change the original standard divisor. This creates a modified divisor (MD). You can use trial and error to change the divisor however you like; just make sure you always make it less than the original standard divisor.

Now that you have chosen a new modified divisor, you use the same calculations as before to come up with a modified quota (MQ) and the same criteria to determine the modified lower quota. Continue modifying the divisor until your calculations result in modified lower quotas that sum to equal your desired number of seats exactly.

This second run through on the procedure has added three new terms to our list:

  • Modified divisor (MD): a number smaller than the original standard divisor, picked through trial and error
  • Modified quota (MQ): the quota as calculated using the modified divisor
  • Modified lower quota (MLQ): the closest smaller whole number to the modified quota

Can you see how each of these is directly related to its standard counterpart? To return to our example from before, the lower quota was 1. What if we had decided to have two seats in the House? This is where the modification of the divisor comes in. Our original standard divisor of 100 led to a final result of having too few seats apportioned. No problem; we can just make up a new modified divisor smaller than 100. If the modified divisor = 50, then the modified quota = 120 / 50 = 2.4. Here, the modified lower quota = 2, and that is the correct total number of seats, so we're done now.

It might sound a bit suspicious to be modifying numbers just because we want to, but remember, as long as every state's population is being divided by the same divisor, they are all being treated the same. It comes down to needing to apportion all the seats within the calculation without just giving seats away after the fact.

Example

Let's return to your dilemma of apportioning out voting seats in the House of Representatives to your three newly formed states. There are about 320 million people in the U.S. We'll assume that Stars has 120 million of these, White Stripe has 75 million, and Red Stripe has 125 million. You decide that you would be happy with 500 voting seats. So, using Jefferson's Method of Apportionment, how many seats does each state receive?

Well, we start with finding our standard divisor. 320,000,000 / 500 = 640,000. Now we find our standard quotas for each state by dividing each state population by the standard divisor.

Stars = 120,000,000 / 640,000 = 187.5

White Stripe = 75,000,000 / 640,000 = 117.18

Red Stripe = 125,000,000/ 640,000 = 195.3

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