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Ch 7: The Mathematics of Voting

About This Chapter

Watch online video lessons to learn about preference ballots, the Borda count method, Arrow's impossibility theorem and more. Each lesson is accompanied by a short quiz you can use to check your understanding of these math topics.

The Mathematics of Voting - Chapter Summary and Learning Objectives

Let our experienced instructors show you why the mathematics of voting are about more than just counting the nods in favor of a particular candidate. We'll introduce you to several methods used to measure voter preferences along with the mathematical criteria used to compare them. You can also learn how each of these voting systems is constructed though video lessons designed to teach you about:

  • Types of election ballots
  • Differences between voting methods
  • Voting system criteria
  • Arrow's impossibility theorem

Video Objectives
What Are Preference Ballots and Preference Schedules? Learn what preference ballots are and why they differ from linear ballots. Find out how they're used to create preference schedules.
The Plurality Method in Elections Explore the ins and outs of this voting method by studying such concepts as majority rule, the Condorcet criterion and strategic voting.
The Borda Count Method in Elections Examine the steps required to implement this system of voting.
The Plurality-with-Elimination Election Method Learn how this method differs from the plurality method. Discover some aspects of the monotonicity criterion.
The Pairwise Comparison Method in Elections Find out what the pairwise comparison method entails. Learn what's required to meet the independence of irrelevant alternatives criterion.
Ranking Candidates: Recursive & Extended Ranking Methods Compare recursive and extended methods for ranking candidates.
Arrow's Impossibility Theorem & Its Use in Voting Discover how Arrow's impossibility theorem is applied to voting methods.

7 Lessons in Chapter 7: The Mathematics of Voting
What Are Preference Ballots and Preference Schedules?

1. What Are Preference Ballots and Preference Schedules?

Preference voting is not the most commonly used form of voting in the United States. Even so, it is very interesting and has its place in our society. This lesson reviews preference ballots and schedules.

The Plurality Method in Elections

2. The Plurality Method in Elections

The plurality method of voting is the most common form of voting in the U.S. The basic principle is that the candidate with the most votes wins; however, there really is more to it than that.

The Borda Count Method in Elections

3. The Borda Count Method in Elections

Have you ever wondered how a winner is determined when you must rank the choices in a voting scenario? This lesson covers the Borda count method of determining a winner in preferential elections.

The Plurality-with-Elimination Election Method

4. The Plurality-with-Elimination Election Method

When a run-off is needed in an election, do all the voters have to return to the polls? In the plurality with elimination election method, the run-off can happen instantly. This lesson explains how.

The Pairwise Comparison Method in Elections

5. The Pairwise Comparison Method in Elections

The pairwise comparison method in elections is a method of comparing candidates to each other in head-to-head contests. This lesson reviews the pairwise comparison method.

Ranking Candidates: Recursive & Extended Ranking Methods

6. Ranking Candidates: Recursive & Extended Ranking Methods

If you have ever wondered who would come in second place in an election (or third or fourth), this lesson will give you two ways - the recursive and extended methods - to determine just that information.

Arrow's Impossibility Theorem & Its Use in Voting

7. Arrow's Impossibility Theorem & Its Use in Voting

This lesson reviews Arrow's Impossibility Theorem, which states that there is no preferential voting method that adheres to reasonable fairness principles. An example is used to illustrate his theorem.

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