The Mathematics of Politics

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 satisfactory way? This is where mathematics meets politics.

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.