2001;
159 pp;
Softcover

MSC: Primary 91; 00;

Print ISBN: 978-0-8218-2847-2

Product Code: ELECT

List Price: $30.00

AMS Member Price: $24.00

MAA Member Price: $27.00

**Electronic ISBN: 978-1-4704-2487-9
Product Code: ELECT.E**

List Price: $28.00

AMS Member Price: $22.40

MAA Member Price: $25.20

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# Chaotic Elections! A Mathematician Looks at Voting

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*Donald G. Saari*

What does the 2000 U.S. presidential election have in common with
selecting a textbook for a calculus course in your department? Was Ralph
Nader's influence on the election of George W. Bush greater than the now-famous
chads? In

This expository book shows how mathematics can help to identify and
characterize a disturbingly large number of paradoxical situations that result
from the choice of a voting procedure. Moreover, rather than being able to
dismiss them as anomalies, the likelihood of a dubious election result is
surprisingly large. These consequences indicate that election
outcomes—whether for president, the site of the next Olympics, the chair
of a university department, or a prize winner—can differ from what the
voters really wanted. They show that by using an inadequate voting procedure,
we can, inadvertently, choose badly. To add to the difficulties, it turns out
that the mathematical structures of voting admit several strategic
opportunities, which are described.

Finally, mathematics also helps identify positive results: By using
mathematical symmetries, we can identify what the phrase “what the voters
really want” might mean and obtain a unique voting method that satisfies
these conditions.

Saari's book should be required reading for anyone who wants to
understand not only what happened in the presidential election of
2000, but also how we can avoid similar problems from appearing
anytime any group is making a choice using a voting procedure. Reading
this book requires little more than high school mathematics and an
interest in how the apparently simple situation of voting can lead to
surprising paradoxes.

#### Readership

Students, general mathematical audience, political scientists, economists, physical scientists, engineers interested in decision theory.

#### Reviews & Endorsements

Take a look at this interesting book. It will cause you to reexamine ranking and voting methods that you may have come to rely on.

-- Math Horizons

The book presents a very clear picture of how the author views the central issues of voting theory and provides an excellent entrée into his work.

-- Zentralblatt MATH

This exceedingly timely and lively book is a mostly non-technical, highly personalized account of author Don Saari's views on and contributions to voting theory and practice. It has perhaps as many surprises and subplots as the extraordinary 2000 United States presidential election … Some of the surprises are mathematical ones, such as the robustness of the various paradoxes that pervade voting theory. The relevance of chaotic dynamics to these matters is intriguing and gives the book title a delightful double meaning … written with flair and imagination, making it entertaining and interesting to read … Saari has written an original, topical, and enjoyable book combining thoughtful social commentary with interesting and accessible mathematics. Read it and read it soon so that you can expand your mathematical horizons, upgrade your civic awareness, and sparkle at social events.

-- MAA Online

#### Table of Contents

# Table of Contents

## Chaotic Elections! A Mathematician Looks at Voting

- Cover Cover11 free
- Title iii4 free
- Copyright iv5 free
- Contents vii8 free
- Preface ix10 free
- Chapter 1. A Mess of an Election 116 free
- Chapter 2. Voter Preferences, or the Procedure? 3348
- Chapter 3. Chaotic Election Outcomes 6984
- Chapter 4. How to Be Strategic 91106
- Chapter 5. What Do the Voters Want? 109124
- Chapter 6. Other Procedures; Other Assumptions 137152
- Bibliography 153168
- Index 157172
- Back Cover Back Cover1175