Ch 8: The Mathematics of Apportionment

About This Chapter

Watch video lessons and learn about the mathematics of apportionment in politics. Measure your comprehension by challenging yourself to take each of the lesson quizzes.

The Mathematics of Apportionment - Chapter Summary and Learning Objectives

In politics, apportionment often involves determining the number of representatives in proportion to the number of constituents they represent. Problems arise when you have states or regions of varying sizes. You want everyone to have a fair say, so you have to use sophisticated equations to determine how to give smaller states or regions power without denying larger populations their power. In this chapter, the instructors will show you the various methods for apportionment in politics. After completing the videos, you should know more about the following:

  • Reasons why apportionment is a major issue
  • Rules about quotas
  • Several different methods of apportionment
  • Balanski and Young's impossibility theorem
  • Population paradoxes

Video Objective
The Problem of Apportionment in Politics Learn about apportionment problems as well as concepts that include upper and lower quotas.
Hamilton's Method of Apportionment in Politics Discover how to provide examples of the steps in Hamilton's method.
The Quota Rule in Apportionment in Politics Explain the quota rule.
The Alabama, New States and Population Paradoxes Discuss instances when these paradoxes may occur.
Jefferson's Method of Apportionment in Politics Learn to implement the Jefferson method by focusing on the use of lower quotas.
Adams' Method of Apportionment in Politics Explore the use of upper quotas and concerns about biases as you learn to solve apportionment problems using the Adams method.
Webster's Method of Apportionment in Politics Learn and provide examples of Webster's method, and explain why this method favors standard calculations.
Huntington-Hill Method of Apportionment in Politics Define the terms standard quota, standard divisor, lower and upper quotas, quota, modified divisor, and geometric mean. Explain why these terms are necessary to this method of apportionment.
Balanski and Young's Impossibility Theorem and Political Apportionment Discover the reasons why these individuals claim that no apportionment method satisfies the various rules associated with apportionment.

9 Lessons in Chapter 8: The Mathematics of Apportionment
Test your knowledge with a 30-question chapter practice test
The Problem of Apportionment in Politics

1. The Problem of Apportionment in Politics

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.

Hamilton's Method of Apportionment in Politics

2. Hamilton's Method of Apportionment in Politics

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.

The Quota Rule in Apportionment in Politics

3. The Quota Rule in Apportionment in Politics

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.

The Alabama, New States & Population Paradoxes

4. The Alabama, New States & Population Paradoxes

A paradox is a logical procedure that results in illogical outcomes. This lesson will review three paradoxes that are associated with population-based apportionment.

Jefferson's Method of Apportionment in Politics

5. Jefferson's Method of Apportionment in Politics

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.

Adams' Method of Apportionment in Politics

6. Adams' Method of Apportionment in Politics

In the 1830s, John Quincy Adams believed that the method of apportionment being used by Congress was biased. In this lesson, we review his method of apportionment.

Webster's Method of Apportionment in Politics

7. Webster's Method of Apportionment in Politics

Daniel Webster proposed his method of apportionment in the 1830s. It was adopted and used by the House of Representatives for many years. This lesson reviews his method.

Huntington-Hill Method of Apportionment in Politics

8. Huntington-Hill Method of Apportionment in Politics

The Huntington-Hill Method of Apportionment is the currently used method to assign each state its number of representative voting seats in the House of Representatives. This lesson reviews how to calculate this method.

Balinski & Young's Impossibility Theorem & Political Apportionment

9. Balinski & Young's Impossibility Theorem & Political Apportionment

The Balinski & Young Impossibility Theorem points out that there is no apportionment method that allows for the Quota Rule and does not allow any paradoxes to occur. This lesson investigates that statement.

Chapter Practice Exam
Test your knowledge of this chapter with a 30 question practice chapter exam.
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Practice Final Exam
Test your knowledge of the entire course with a 50 question practice final exam.
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