# Ch 8: The Mathematics of Apportionment

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
• Several different methods of apportionment
• Balanski and Young's impossibility theorem

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
Chapter Practice Exam
Test your knowledge of this chapter with a 30 question practice chapter exam.
Not Taken
Practice Final Exam
Test your knowledge of the entire course with a 50 question practice final exam.
Not Taken

### Earning College Credit

Did you know… We have over 200 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.