Elections with Statistics

Understanding Elections through Statistics

Polling, Predicting, and Testing

Overview

[Book Cover] To achieve my goals in this book, I decided on as broad an audience as I could. To be clear, this is not a graduate-level textbook. My audience is those who have had some experience with statistics. This exposure could be from an advanced high school course or an introductory college course in statistics. It may also come from extensive experience in employment, such as through professional journalism covering elections and polls.

Thus, I envision this book to be accessible to those who have already had an introduction to statistical thinking in terms of the ideas behind hypothesis testing. This means having an exposure to test statistics and the p-value. The point of the book is to obtain a better understanding of elections, from the polls to the predictions to the testing. This requires some mathematics. However, the amount of mathematics required depends on the goals of the reader. The more you want to understand polling, the more mathematics you must learn and use. However, one can obtain a sound understanding of polls and elections without a full mathematical treatment.

In short, I try to make the mathematics self-contained. This allows you to skip over it without losing the fundamental points of the book. However, working through the mathematics will aid in understanding the assumptions behind elections.

Information on purchasing this book can be found at Amazon, at Barnes and Noble, at Routledge, and at Taylor & Francis.

 

 

 

 

Table of Contents

The following provides the table of contents for the first edition. For additional information, please see the book at the official Taylor & Francis site.

 

 

Preface

Acknowledgements

About the Author

Part I: Estimating Electoral Support

This book opens with a thorough examination of techniques for estimating a candidate’s current electoral support, both now and in the future. The mathematics are based on the binomial and the normal distributions, and the assumption that the data collected are representative of the population.

Chapter 1: Polling 101

1.1. Simple Random Sampling

1.2. One Estimator of μ: The Sample Proportion

1.3. Reasonable Values of μ

1.4. A Second Estimator of μ: Agresti-Coull

1.5. SRS Without Replacement

1.6. Conclusion

1.7. Extensions

1.8. Chapter Appendix

Chapter 2: Polling 399

2.1. Stratified Sampling

2.2. The Mathematics of Estimating μ

2.3. Confidence Intervals

2.4. Conclusion

2.5. Extensions

2.6. Chapter Appendix

Chapter 3: Combining Polls

3.1. Simple Averaging of Polls

3.2. Weighted Averaging of Polls

3.3. Averaging of Polls over Time

3.4. Looking Ahead

3.5. South Korean 2017 Presidential Election

3.6. Conclusion

3.7. Extensions

3.8. Chapter Appendix

Chapter 4: In-Depth Analysis: Brexit 2016

4.1. Knowing Your Data

4.2. Combining the Polls

4.3. Discussion: What Went Wrong?

4.4. Conclusion

Part II: Testing Election Results

Here, we start the second half of the book. In the first part, we focused on examining methods for estimating the support level for a candidate, either currently or in the future. This relied heavily on the binomial and normal distributions. As the first part progressed, layer after layer of complication were added. In many cases, questions were raised and not answered. The second part of this book focuses on testing the election — and the electoral system — for fairness. Not surprisingly, the ability to test for unfairness relies on data. The more information available, the better we are able to test.

Chapter 5: Digit Tests

5.1. History

5.2. The Benford Test

5.3. The Generalized Benford Test

5.4. Using the Generalized Benford Distribution

5.5. Conclusion

5.6. Extensions

5.7. Chapter Appendix

Chapter 6: Differential Invalidation

6.1. Differential Invalidation

6.2. Regression Modeling

6.3. Examining Côte d'Ivoire

6.4. Conclusion

6.5. Extensions

6.6. Chapter Appendix

Chapter 7: Considering Geography

7.1. Detecting Spatial Correlation

7.2. The Spatial Lag Model

7.3. Casetti’s Spatial Expansion Model (SEM)

7.4. Geographically Weighted Regression

7.5. The Spatial Lagged Expansion Method

7.6. Conclusion

7.7. Extensions

7.8. Chapter Appendix

Chapter 8: In-Depth Analysis: Sri Lanka since 1994

8.1. Differential Invalidation

8.2. Methods and Data

8.3. Results by Election

8.4. Discussion

8.5. Conclusion

Bibliography

Index