Understanding elections through statistics by Ole J. Forsberg, CRC press, Taylor & Francis group, boca Raton, FL, 2020, 225 pp., $69.95, ISBN 978-0367895372

This book offers a good introduction to some statistical methods used in elections. It has two parts. The first part contains four chapters that cover estimation methods for polls. The main technical problem is the estimation of the proportion of the population holding a particular preference in voting. The analytic core of the problem is binomial distribution and the sampling and estimation procedures center around this distribution. As in the real world there are always complications. Various remedies are provided to address these complications. The author has done a great job of introducing the critical concepts and considerations in both the problem formulation and solution. For example, when introducing the importance of weighting in deriving the estimate of the poll, the author pretends to write a press release of his poll result on the issue of gender fairness in the military. It is clear that if a different source of demographics statistics is used, the poll result is quite different. Examples as such are quite useful for readers to understand the subject matter and its complexity. The second part of the book covers a few techniques to detect frauds and anomalies by examining the election results. Some techniques build on an interesting premise that humans are bad at mimicking randomness. This echoes what Fisher (1958) had said, “if one tries to think of numbers at random, one thinks of numbers very far from at random.” The Benford test is introduced in detail, including its history and its interesting applications in analyzing election data to detect anomaly based on the distributions of the leading digits reported by different precincts. The differential invalidation and some regression models are introduced as well. Spatial correlations could be modeled by using the geographical information in the data. The book concludes with a detailed discussion on data from Sri Lanka since 1994. This is a useful book that can help a broad range of readers to appreciate the power of statistics in understanding the election process from an analytic and scientific perspective. On top of the techniques introduced in the book, there are anecdotes and comments and insights that can enrich the reading experience. E.g., as in the preface the statement from a Nicaraguan leader “Indeed, you won the elections, but I won the count.” or the comment in the end of Chapter 4 “as with many things in statistics, increasing quality in one area tends to reduce quality in another.” Statistical techniques in this book are tightly bonded with the contexts and the backgrounds of their application. After reading the book, I appreciate the book has helped me understand a complex problem in a complex world. Not everything is what it appears to be, but we can equip ourselves with sufficient knowledge and useful tools to help us look at the data in every angle and really feel the data as it is.