This book focuses on mathematical reasoning about politics. People commonly believe mathematics has nothing to say about politics. The high school experience suggests mathematics is the study of numbers, operations, formulas, and manipulations of symbols. Those who, from this experience, conclude mathematics has no relevance to politics will not find much in this book they regard as mathematics. A lot of wasted effort can be averted if mathematics is used to determine whether some decisions are actually impossible in the first place. Is it possible to create methods to vote, methods to apportion, and methods to make decisions in a