It is because mathematics is often misunderstood, it is commonly believed it has nothing to say about politics. The high school experience with mathematics, for so many the lasting impression of the subject, suggests that mathematics is the study of numbers, operations, formulas, and manipulations of symbols. Those believing this is the extent of mathematics might conclude mathematics has no relevance to politics. This book counters this impression. The second edition of this popular book focuses on mathematical reasoning about politics. In the search for ideal ways to make certain kinds of decisions, a lot of wasted effort can be averted if mathematics can determine that finding such an ideal is actually impossible in the first place. In the first three parts of this book, we address the following three political questions: (1) Is there a good way to choose winners of elections? (2) Is there a good way to apportion congressional seats? (3) Is there a good way to make decisions in situations of conflict and uncertainty? In the fourth and final part of this book, we examine the Electoral College system that is used in the United States to select a president. There we bring together ideas that are introduced in each of the three earlier parts of the book.

What Ralph Nader's spoiler role in the 2000 presidential election tells us about the American political system. Why Montana went to court to switch the 1990 apportionment to Dean's method. How the US tried to use game theory to win the Cold War, and why it didn't work. When students realize that mathematical thinking can address these sorts of pressing concerns of the political world it naturally sparks their interest in the underlying mathematics. A Mathematical Look at Politics is designed as an alternative to the usual mathematics texts for students in quantitative reasoning courses. It applies the power of mathematical thinking to problems in politics and public policy. Concepts are precisely defined. Hypotheses are laid out. Propositions, lemmas, theorems, and corollaries are stated and proved. Counterexamples are offered to refute conjectures. Students are expected not only to make computations but also to state results, prove them, and draw conclusions about specific examples. Tying the liberal arts classroom to real-world mathematical applications, this text is more deeply engaging than a traditional general education book that surveys the mathematical landscape. It aims to instill a fondness for mathematics in a population not always convinced that mathematics is relevant to them.

It is because mathematics is often misunderstood, it is commonly believed it has nothing to say about politics. The high school experience with mathematics, for so many the lasting impression of the subject, suggests that mathematics is the study of numbers, operations, formulas, and manipulations of symbols. Those believing this is the extent of mathematics might conclude mathematics has no relevance to politics. This book counters this impression. The second edition of this popular book focuses on mathematical reasoning about politics. In the search for ideal ways to make certain kinds of decisions, a lot of wasted effort can be averted if mathematics can determine that finding such an ideal is actually impossible in the first place. In the first three parts of this book, we address the following three political questions: (1) Is there a good way to choose winners of elections? (2) Is there a good way to apportion congressional seats? (3) Is there a good way to make decisions in situations of conflict and uncertainty? In the fourth and final part of this book, we examine the Electoral College system that is used in the United States to select a president. There we bring together ideas that are introduced in each of the three earlier parts of the book.