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Math 106: Contemporary Math9 chapters | 106 lessons

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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 quota rule refers to the strict use of calculated quotas in apportionment. If a method of apportionment allows a state to have more (or fewer) seats than its quotas determine, then the method is said to be in violation of the quota rule.

When talking about state representation in Congress, the **quota rule** refers to a method of apportioning voting seats that relies on upper and lower quotas. This seems really complicated, but if we break it down a bit, it becomes easier to understand. **Apportionment** is literally the portion of representatives each state receives. Can you see how the word 'portion' is right there inside ap*portion*ment? That makes it really easy to remember.

So, we are really just talking about portioning out representatives. Why is that important? Well, let's look at this family having a dinner:

Their ages range from really small children through teens and adults. There is a limited amount of food to go around, so how should they decide how much food each person gets? Should they all get an equal amount?

It seems obvious that the smallest children would not need as much food as the teenagers and adults. And, honestly, the adults probably don't need as much as the teenagers do, either.

So, would it be fair to give the teenagers the largest portions, the adults' portions slightly smaller and the younger children the smallest portions instead of equal shares for all? Yes, that would probably be fair.

That is also how the House of Representatives apportions out its voting seats to the states. However, instead of age, populations are used to determine each state's proper portion of seats in the House; that is their quota.

Obviously, the most important thing about the quota rule is finding out the actual quota of seats each state should be apportioned. To do this, first we need to find the standard divisor.

To get the **standard divisor (or SD)**, you divide the country's total population by the number of seats available.

Consider the U.S.A. We would take the total population (which is about 319 million) and divide by the number of seats in the House, which is 435. This gives us an SD of around 733,333.

The **standard quota (SQ)** sets the actual number of voting representatives for each state by dividing the state's population by the SD.

To really illustrate how apportionment uses population, let's look at two states that are about the same size geographically, but drastically different in population: Florida and Idaho.

Assuming a population of 19.89 million for Florida, what is the state's quota?

SQ = 19890000/733333 = 27.1227

Well, the state quota, based on what we've just learned, is the state's population divided by the standard divisor, which would come out to about 27.12. Whereas, for Idaho there is only a population of 1.64 million, giving an SQ of only 2.24, rounded up.

You can see how much population size impacts standard quotas when you compare these two states.

But, did you notice that neither of these standard quotas is a whole number? A state could not send a fraction of a person to Congress, so how do they determine an actual number of representatives?

You might round the number down. That would be called its **lower quota**.

Or, you could round the number up, finding the state's **upper quota**.

Each method of apportionment deals with this issue differently. If you are interested in finding out how each does it, please review the other lessons in this chapter.

Determining if the quota rule has been violated is actually quite easy. If any state is apportioned fewer seats than its lower quota, or more seats than its upper quota, then the quota rule has been violated.

Of the major apportionment methods, Hamilton, Jefferson, Adams, Webster, and Huntington-Hill, only the Hamilton Method satisfies the quota rule because it is the only method that determines seat allocation strictly based on upper or lower quotas.

Let's try an example.

You are in charge of organizing dinners for a local service club in your community. There are six families in your club and all have different ideas about what should be served each week. Some of the families are very large (with as many as ten people in the family), and one is just a single person. You've decided to create a committee to vote on the meal plans, but you don't want to be overwhelmed, so you are going to keep the committee to only 6 people.

Since there are 6 family groups, you decide to let each family group choose one representative to be on the committee.

Does this satisfy the quota rule of apportionment?

NO! The number of voting seats apportioned was not based on the standard quota for each group. In this scenario, we are not given the total number of people in the club, but it is clear that some family groups are much larger (or, more populous) than others. This would indicate that those groups should have a larger quota of seats than the smaller groups.

So, this lesson reviewed a single aspect of **apportionment**. Apportionment is the portioning out of voting seats in a governing body. Apportionment methods that depend on upper and lower quotas to determine seat allocation are said to satisfy the **quota rule**.

The first step in finding a state's quota is to determine the **standard divisor (SD)**. This is calculated with the formula: total population / number of seats available. The SD is then used to calculate the **standard quota (SQ)** with the formula state population / SD.

**Upper and lower quotas** refer to the whole number resulting from rounding a fractional SQ either up or down. Each method deals with this calculation individually, so there is no one right way to round in apportionment.

Finally, we learned that, of the main methods of apportionment, only the Hamilton Method satisfies the quota rule, because it is the only method that determines seat allocation strictly based on upper or lower quotas.

Thanks for joining me for this lesson on the quota rules.

Upon completing this lesson, you should be able to:

- Define apportionment and upper and lower quotas
- Describe the quota rule
- Recall how to calculate a state's quota
- Explain why the Hamilton Method satisfies the quota rule

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Math 106: Contemporary Math9 chapters | 106 lessons

- The Problem of Apportionment in Politics 7:13
- Hamilton's Method of Apportionment in Politics 7:30
- The Quota Rule in Apportionment in Politics 6:54
- Jefferson's Method of Apportionment in Politics 12:20
- Adams' Method of Apportionment in Politics 9:41
- Webster's Method of Apportionment in Politics 8:47
- Huntington-Hill Method of Apportionment in Politics 10:14
- Balinski & Young's Impossibility Theorem & Political Apportionment 7:27
- Go to The Mathematics of Apportionment

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