# The Mathematics of Elections and Voting

• W.D. Wallis
Textbook

1. Front Matter
Pages i-x
2. W. D. Wallis
Pages 1-2
3. W. D. Wallis
Pages 3-18
4. W. D. Wallis
Pages 19-32
5. W. D. Wallis
Pages 33-45
6. W. D. Wallis
Pages 47-58
7. W. D. Wallis
Pages 59-68
8. W. D. Wallis
Pages 69-77
9. W. D. Wallis
Pages 79-87
10. Back Matter
Pages 89-96

### Introduction

The Mathematics of Elections and Voting  takes an in-depth look at the mathematics in the context of voting and electoral systems, with focus on simple ballots, complex elections, fairness, approval voting, ties, fair and unfair voting, and manipulation techniques. The exposition opens with a sketch of the mathematics behind the various methods used in conducting elections. The reader is lead to a comprehensive picture of the theoretical background of mathematics and elections through an analysis of Condorcet’s Principle and Arrow’s Theorem of conditions in electoral fairness. Further detailed discussion of various related topics include: methods of manipulating the outcome of an election, amendments, and voting on small committees.

In recent years, electoral theory has been introduced into lower-level mathematics courses, as a way to illustrate the role of mathematics in our everyday life.  Few books have studied voting and elections from a more formal mathematical viewpoint.  This text will be useful to those who teach lower level courses or special topics courses and aims to inspire students to understand the more advanced mathematics of the topic. The exercises in this text are ideal for upper undergraduate and early graduate students, as well as those with a keen interest in the mathematics behind voting and elections. ​

### Keywords

Arrow’s Theorem Condorcet’s principle Elections majority rule plurality voting voting fairness

#### Authors and affiliations

• W.D. Wallis
• 1
1. 1.Department of MathematicsSouthern Illinois UniversityEvansvilleUSA

Industry Sectors
Pharma
Biotechnology