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# The Mathematics of Politics

DOI link for The Mathematics of Politics

The Mathematics of Politics book

# The Mathematics of Politics

DOI link for The Mathematics of Politics

The Mathematics of Politics book

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## 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.

## TABLE OF CONTENTS

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 12|14 pages

#### History of Apportionment in the United States

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