It is because mathematics is often misunderstood, it is commonlybelieved it has nothing to say about politics. The high schoolexperience with mathematics, for so many the lasting impressionof the subject, suggests that mathematics is the study of numbers,operations, formulas, and manipulations of symbols. Thosebelieving this is the extent of mathematics might concludemathematics has no relevance to politics. This book counters this impression.The second edition of this popular book focuses on mathematical reasoningabout politics. In the search for ideal ways to make certain kindsof decisions, a lot of wasted effort can be averted if mathematics can determine thatfinding such an ideal is actually impossible in the first place.In the first three parts of this book, we address the following threepolitical 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 anduncertainty?In the fourth and final part of this book, we examine the ElectoralCollege system that is used in the United States to select a president.There we bring together ideas that are introduced in each of the threeearlier parts of the book.