ABSTRACT

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.

part I|2 pages

Voting

chapter |2 pages

Introduction to Part I

chapter 1|20 pages

Two Candidates

chapter 2|20 pages

Social Choice Functions

chapter 3|18 pages

Criteria for Social Choice

chapter 4|18 pages

Which Methods Are Good?

chapter 5|14 pages

Arrow’s Theorem

chapter 6|28 pages

Variations on the Theme

chapter |4 pages

Notes on Part I

part II|2 pages

Apportionment

chapter |2 pages

Introduction to Part II

chapter 7|16 pages

Hamilton’s Method

chapter 8|22 pages

Divisor Methods

chapter 9|18 pages

Criteria and Impossibility

chapter 10|10 pages

The Method of Balinski and Young

chapter 11|14 pages

Deciding among Divisor Methods

chapter |6 pages

Notes on Part II

part III|2 pages

Conflict

chapter |2 pages

Introduction to Part III

chapter 13|18 pages

Strategies and Outcomes

chapter 14|18 pages

Chance and Expectation

chapter 15|18 pages

Solving Zero-Sum Games

chapter 16|22 pages

Conflict and Cooperation

chapter 17|18 pages

Nash Equilibria

chapter 18|20 pages

The Prisoner’s Dilemma

chapter |4 pages

Notes on Part III

part IV|2 pages

The Electoral College

chapter |2 pages

Introduction to Part IV

chapter 19|20 pages

Weighted Voting

chapter 20|14 pages

Whose Advantage?

chapter |4 pages

Notes on Part IV