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
(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
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.
Social Choice Functions
Criteria for Social Choice
Which Methods Are Good?
Variations on a Theme
Notes on Part I
Criteria and Impossibility
The Method of Balinski and Young
Deciding among Divisor Methods
History of Apportionment in the United States
Notes on Part II
Strategies and Outcomes
Chance and Expectation
Solving Zero-Sum Games
Conflict and Cooperation
The Prisoner’s Dilemma
Notes on Part III
IV THE ELECTORAL COLLEGE
Notes on Part IV
Solutions to Odd-Numbered Exercises and Problems