About This Chapter
Below is a sample breakdown of the mathematics of voting chapter into a 5-day school week. Based on the pace of your course, you may need to adapt the lesson plan to fit your needs.
|Day||Topics||Key Terms and Concepts Covered|
|Monday||Ballots and schedules||Linear ballot, preference ballots, preference schedule, transitive properties of a voter's preference, and the connection between candidate elimination and relative preferences|
|Tuesday||Methods in elections: Part I||The plurality method, majority rule, majority criterion, plurality candidate, majority candidate, Condorcet criterion, the borda count method, and the advantages and disadvantages to these methods|
|Wednesday||Methods in elections: Part II||The plurality-with-elimination method, the monotonicity criterion, the pairwise comparison method, the independence-of-irrelevant-alternatives criterion, steps for methodology implementation, and related formulas|
|Thursday||Ranking Candidates||Extended vs. recursive ranking methods|
|Friday||Arrow's Impossibility Theorem||Pareto efficiency, no dictators, and independence of irrelevant alternatives|
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.
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.
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.
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.
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.
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.
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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