Understanding Elections through Statistics: Polling, Prediction, and Testing

by Ole J. Forsberg

Overview

Elections are random events. From individuals deciding whether to vote, to people deciding for whom to vote, to election authorities deciding what to count, the outcomes of competitive democratic elections are rarely known until election day…or beyond. Understanding Elections through Statistics: Polling, Prediction, and Testing explores this random phenomenon from two points of view: predicting the election outcome using opinion polls and testing the election outcome using government-reported data.

Written for those with only a brief introduction to statistics, this book takes you on a statistical journey from how polls are taken to how they can—and should—be used to estimate current popular opinion. Once an understanding of the election process is built, we turn toward testing elections for evidence of unfairness. While holding elections has become the de facto proof of government legitimacy, those electoral processes may hide a dirty little secret of the government illicitly ensuring a favorable election outcome.

This book includes these features designed to make your statistical journey more enjoyable:

• Vignettes of elections, including maps, to provide concrete bases for the material
• In-chapter cues to help one avoid the heavy math—or to focus on it
• End-of-chapter problems designed to review and extend that which was covered in the chapter
• Many opportunities to turn the power of the R statistical environment to the enclosed election data files, as well as to those you find interesting

From these features, it is clear the audience for this book is quite diverse. This text provides mathematics for those interested in mathematics, but also offers detours for those who just want a good read and a deeper understanding of elections.

Author

Ole J. Forsberg holds PhDs in both political science and statistics. He currently teaches mathematics and statistics in the Department of Mathematics at Knox College in Galesburg, IL.

Product Details

ISBN-13:	9781032684536
Publisher:	CRC Press
Publication date:	10/10/2024
Series:	Chapman & Hall/CRC Statistics in the Social and Behavioral Sciences
Edition description:	2nd ed.
Pages:	356
Product dimensions:	6.12(w) x 9.19(h) x (d)

About the Author

Ole J. Forsberg, BS, MAT, MA, MSE, PhDd, is an Assistant Professor of Mathematics-Statistics at Knox College in Galesburg, IL. He received a PhD in Political Science at the University of Tennessee–Knoxville in 2006, concentrating in International Relations, War, and Terrorism. After finishing his dissertation, Dr Forsberg began a deeper investigation of the statistical techniques he used. As a result of that embarrassment, Dr Forsberg began statistical studies at the Johns Hopkins University (MSE, 2010) and concluded them with a PhD in Statistics from Oklahoma State University in 2014. His dissertation explored and applied applications of statistical techniques to testing elections for violations of the “free and fair” democratic claim. His research agenda lies in extending and applying statistical methods to modeling elections and testing the results for evidence of bias in election results.

Table of Contents

Preface ix

Acknowledgments xiii

About the Author xv

Part I Estimating Electoral Support 1

1 Polling 101 3

1.1 Simple Random Sampling 5

1.2 One Estimator of π: The Sample Proportion 6

1.3 Reasonable Values of π 12

1.4 A Second Estimator of π: Agresti-Coull 21

1.5 SRS without Replacement 26

1.6 Conclusion 28

1.7 Extensions 29

1.8 Chapter Appendix 30

2 Polling 399 33

2.1 Stratified Sampling 35

2.2 The Mathematics of Estimating π 38

2.3 Confidence Intervals 49

2.4 Conclusion 52

2.5 Extensions 53

2.6 Chapter Appendix 54

3 Combining Polls 57

3.1 Simple Averaging of Polls 59

3.2 Weighted Averaging of Polls 61

3.3 Averaging of Polls over Time 64

3.4 Looking Ahead 70

3.5 South Korean 2017 Presidential Election 73

3.6 Conclusion 77

3.7 Extensions 78

3.8 Chapter Appendix 79

4 In-Depth Analysis: Brexit 2016 83

4.1 Knowing Your Data 85

4.2 Combining the Polls 89

4.3 Discussion: What Went Wrong? 90

4.4 Conclusion 92

Part II Testing Election Results 94

5 Digit Tests 95

5.1 History 97

5.2 The Benford Test 99

5.3 The Generalized Benford Test 108

5.4 Using the Generalized Benford Distribution 112

5.5 Conclusion 119

5.6 Extensions 120

5.7 Chapter Appendix 121

6 Differential Invalidation 125

6.1 Differential Invalidation 127

6.2 Regression Modeling 132

6.3 Examining Côte d'Ivoire 141

6.4 Conclusion 143

6.5 Extensions 144

6.6 Chapter Appendix 145

7 Considering Geography 149

7.1 Detecting Spatial Correlation 151

7.2 The Spatial Lag Model 158

7.3 Casetti's Spatial Expansion Model (SEM) 161

7.4 Geographically Weighted Regression 164

7.5 The Spatial Lagged Expansion Method 169

7.6 Conclusion 172

7.7 Extensions 173

7.8 Chapter Appendix 174

8 In-Depth Analysis: Sri Lanka since 1994 177

8.1 Differential Invalidation 179

8.2 Methods and Data 179

8.3 Results by Election 182

8.4 Discussion 192

8.5 Conclusion 193

Bibliography 195

Index 207

Editorial Reviews

"This unique book, by an author who is both a Statistician and Political Scientist, discusses the statistical theory of two important aspects of elections. The first half is an in-depth introduction to the classical statistical theory of polling, including estimators, confidence intervals, and stratified sampling. It comes complete with snippets of R code and many concrete examples, including two cases that challenged pollsters: the 2016 US presidential election and the 2016 Brexit vote. The second half concerns statistical methods for after the fact detection of fraudulent elections. It includes an in-depth treatment of methods based on the Benford distribution, but also methods based on classical regression analysis. Again numerous pieces of R code and concrete examples are provided."
- E. Arthur Robinson, Jr., Professor of Mathematics, George Washington University

"This book has multiple layers that provides flexibility in its use. It makes polling and the statistical issues understandable for those who have little knowledge of statistics beyond the elementary course material. It includes enough of the mathematical underpinnings so that a student wishing to delve deeper into the material has that opportunity. It treats the material with cleverness and wryness that transforms the topic, usually thought of as "dry" by many people, into an interesting and compelling read. The use of maps and real-world examples help make the issues relevant and practical. It should be required reading for anyone studying political science and polling/elections, or anyone with a methodological background wishing to understand these topics at a greater depth."
- Mark Payton, Rocky Vista University

 

"The book contains a list of 145 most recent references and a detailed index. Many exercises and appendices with mathematical derivations are given at the end of chapters. Numerous R scripts are presented throughout the whole monograph, providing ready-to-run or make-it-yourself tools for practical implementation of all the techniques. The book can be interesting not only to students in political sciences and statistical methods but to a wider audience interested to understand the results and checkup fairness of elections."
- Stan Lipovetsky, Technometrics January 2021

From the Publisher