The Problem of Apportionment in Politics

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  • 0:01 Illustrative Introduction
  • 1:52 Apportionment Problem Defined
  • 2:32 Applicable Definitions
  • 3:12 Formula for Seats by State
  • 5:36 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.

This lesson discusses the problem of apportionment. It deals with how to fairly give each state its portion of representation in the government. Terms will be defined and an example will be used to illustrate the problem.

Illustrative Introduction

Before we get into definitions in this lesson, I'd like to take a moment to illustrate the concepts that we'll be discussing. So, let's pretend that you are in charge of supplying three dog shelters with food and supplies. You must decide how many resources each shelter receives, and you must do it fairly.

In looking at the shelters, you notice the largest shelter is over twice as big as the next closest in size, and about seven times bigger than the smallest. Well, that makes it easy doesn't it?

Just divide up the food so that the largest gets more than half of the resources, the medium size should get about ¾ of the remaining resources and the smallest should get what is left. Fair! Right?

WRONG! When you look closer, you see that the actual number of animals at each shelter is not relative to the size of the buildings. In fact, the largest building only houses a small number of dogs. The smallest has over 20 times as many dogs as the largest. In fact, even though the medium sized building is half as big as the largest, it actually houses the most number of dogs. So, the supplies should be rearranged to take into account the populations at each shelter, right?

Well, that isn't really fair either. The largest building has the capacity for more and must maintain a much bigger building even if there aren't as many dogs there. That requires resources. But, the smallest must maintain more actual dogs, thus needs extra resources, too.

Another problem is that each shelter is part of the group, and as such, they each feel they should get equal resources.

Hmm. What should you do?

The Apportionment Problem Defined

And there you have it: the apportionment problem is the problem of fairly dividing resources, taking into consideration both size and population.

You can remember what it means by just looking at the word: apportionment has the word portion right inside it. What is a portion? It is an appropriate amount.

Now let's apply the concept to government representation. In this case, resources refer to seats in Congress, and we are concerned about fairly portioning out those seats to states in light of both the states' sizes and populations.

Applicable Definitions

There are 50 States in the United States of America. For apportionment purposes, when we say state we are talking about one of these already existing and recognized states (not territories).

Population refers to the number of residents in a state. This is determined through the Census Bureau.

Finally, seats refers to the available positions for voting representatives in a body of government. There are 435 seats in the House of Representatives, and the seats are apportioned using a mathematical formula based on the populations of each state.

Formula for Seats by State

In the U.S., the problem of apportionment has been addressed differently in the two houses of voting representatives. Each state is given two seats in the Senate. However, the seats in the House of Representatives are apportioned using a mathematical formula to account for each state's population.

To determine how many seats each state should receive, first a standard divisor must be established. This is the total population divided by the number of seats available. In the year 2012, there were approximately 314 million people in the USA. With 435 seats available in Congress, that means:

SD= 314,000,000 / 435 = (approx.) 0.733

Now we have the divisor: there should be one seat for every 733,000 people. To determine the number of actual seats per state, or the standard quota, we divide the state population by the SD. The calculation looks like this: SQ = State population / SD

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