The Mathematics of Voting and Elections: A Hands-on Approach, 2nd Edition
by Jonathan K. Hodge (Author), Richard E. Klima (Author)

About the Author
Jonathan K. Hodge: Grand Valley State University, Allendale, MI
Richard E. Klima: Appalachian State University, Boone, NC

About this book
The Mathematics of Voting and Elections: A Hands-On Approach, Second Edition, is an inquiry-based approach to the mathematics of politics and social choice. The aim of the book is to give readers who might not normally choose to engage with mathematics recreationally the chance to discover some interesting mathematical ideas from within a familiar context, and to see the applicability of mathematics to real-world situations. Through this process, readers should improve their critical thinking and problem solving skills, as well as broaden their views of what mathematics really is and how it can be used in unexpected ways. The book was written specifically for nonmathematical audiences and requires virtually no mathematical prerequisites beyond basic arithmetic. At the same time, the questions included are designed to challenge both mathematical and non-mathematical audiences alike. More than giving the right answers, this book asks the right questions. The book is fun to read, with examples that are not just thought-provoking, but also entertaining. It is written in a style that is casual without being condescending. But the discovery-based approach of the book also forces readers to play an active role in their learning, which should lead to a sense of ownership of the main ideas in the book. And while the book provides answers to some of the important questions in the field of mathematical voting theory, it also leads readers to discover new questions and ways to approach them. In addition to making small improvements in all the chapters, this second edition contains several new chapters. Of particular interest might be Chapter 12 which covers a host of topics related to gerrymandering.

Brief contents
Chapter 1. What’s So Good About Majority Rule? 1
    The Mayor of Stickeyville 1
    Anonymity, Neutrality, and Monotonicity 3
    Majority Rule and May’s Theorem 5
    Quota Systems 6
    Back to May’s Theorem 8
    Questions for Further Study 10
    Answers to Starred Questions 12
Chapter 2. Le Pen, Nader, and Other Inconveniences 15
    The Plurality Method 17
    The Borda Count 18
    Preference Orders 20
    Back to Borda 22
    May’s Theorem Revisited 23
    Questions for Further Study 25
    Answers to Starred Questions 30
Chapter 3. Back into the Ring 33
    Condorcet Winners and Losers 35
    Sequential Pairwise Voting 38
    Instant Runoff 42
    Putting It All Together 45
    Questions for Further Study 46
    Answers to Starred Questions 49
Chapter 4. Trouble in Democracy 53
    Independence of Irrelevant Alternatives 54
    Arrow’s Theorem 58
    Pareto’s Unanimity Condition 63
    Concluding Remarks 65
    Questions for Further Study 65
    Answers to Starred Questions 68
Chapter 5. Explaining the Impossible 71
    Proving Arrow’s Theorem 72
    Potential Solutions 79
    Concluding Remarks 85
    Questions for Further Study 86
    Answers to Starred Questions 88
Chapter 6. Gaming the System 91
    Strategic Voting 92
    The Gibbard-Satterthwaite Theorem 93
    Proving the Gibbard-Satterthwaite Theorem 95
    Concluding Remarks 101
    Questions for Further Study 102
    Answers to Starred Questions 103
Chapter 7. One Person, One Vote? 105
    Weighted Voting Systems 106
    Dictators, Dummies, and Veto Power 109
    Swap Robustness 110
    Trade Robustness 113
    Questions for Further Study 115
    Answers to Starred Questions 118
Chapter 8. Calculating Corruption 121
    The Banzhaf Power Index 122
    The Shapley-Shubik Power Index 125
    Banzhaf Power in Psykozia 128
    A Splash of Combinatorics 130
    Shapley-Shubik Power in Psykozia 133
    Questions for Further Study 135
    Answers to Starred Questions 138
Chapter 9. The Ultimate College Experience 143
    The Electoral College 144
    The Winner-Take-All Rule 146
    Some History 148
    in the Electoral College 149
    Swing Votes and Perverse Outcomes 153
    Alternatives to the Electoral College 157
    Questions for Further Study 158
    Answers to Starred Questions 162
Chapter 10. Trouble in Direct Democracy 163
    Even More Trouble 165
    The Separability Problem 166
    Binary Preference Matrices 168
    Testing for Separability 169
    Some Potential Solutions 173
    Questions for Further Study 179
    Answers to Starred Questions 182
Chapter 11. Proportional (Mis)representation 185
    The U.S. House of Representatives 186
    Hamilton’s Apportionment Method 187
    Jefferson’s Apportionment Method 190
    Webster’s Apportionment Method 195
    Three Apportionment Paradoxes 196
    Hill’s Apportionment Method 198
    Another Impossibility Theorem 200
    Concluding Remarks 201
    Questions for Further Study 202
    Answers to Starred Questions 205
Chapter 12. Choosing Your Voters 207
    Gerrymandering 209
    Rules for Redistricting 214
    Geometry and Compactness 215
    Partisan Symmetry 218
    The Efficiency Gap 221
    Concluding Remarks 223
    Questions for Further Study 224
    Answers to Starred Questions 227
Bibliography 229
Index 233

Series: Mathematical World (Book 30)
Pages: 238 pages
Publisher: American Mathematical Society; 2 edition (October 1, 2018)
Language: English
ISBN-10: 1470442876
ISBN-13: 978-1470442873