# [EM] New Book by Donald Saari: "Chaotic Elections! A Mathematician Looks at Voting"

Steve Barney BARNES99 at vaxa.cis.uwosh.edu
Thu Mar 22 11:02:33 PST 2001

http://www.ams.org/bookstore-getitem/item=ELECT

"Chaotic Elections! A Mathematician Looks at Voting"
Donald G. Saari, University of California, Irvine, CA

Not yet published.
Expected publication date is May 4, 2001

Description

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 Chaotic Elections!, Don Saari
analyzes these questions, placing them in the larger context of voting
systems in general. His analysis shows that the fundamental problems
with the 2000 presidential election are not with the courts, recounts or
defective ballots, but are caused by the very way Americans vote for
president.

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
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

Contents

A mess of an election
Voter preferences, or the procedure?
Chaotic election outcomes
How to be strategic
What do the voters want?
Other procedures; other assumptions
Bibliography
Index

Details:

Publisher: American Mathematical
Society
Distributor: American Mathematical
Society
Publication Year: 2001
ISBN: 0-8218-2847-9
Paging: 159 pp.
Binding: Softcover
List Price: \$23
Institutional Member Price: \$18
Individual Member Price: \$18
Order Code: ELECT