Chaotic Elections!: A Mathematician Looks at Voting

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American Mathematical Soc., Apr 3, 2001 - Political Science - 159 pages
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 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.
 

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User Review  - dougb56586 - LibraryThing

In this short book (152 pages), a Mathematics Professor explains how elections can often yield drastically different outcomes depending on which voting procedure is used, and further, that if a low ... Read full review

LibraryThing Review

User Review  - FPdC - LibraryThing

Of the two expository books by Saari on the mathematics of voting systems, this is clearly the more mathematically oriented , although it is not exactly a mathematical text, containing no proofs of ... Read full review

Contents

A Mess of an Election
1
1 Electoral College
4
2 Other procedures
17
Voter Preferences or the Procedure?
33
1 Some examples
34
2 Representation triangle and profiles
40
3 Procedure lines and elections
45
4 Approval or Cumulative voting?
53
2 Strategic voting
94
3 Debate and selecting amendments
100
4 Any relief?
102
5 Changing the outcome
103
What Do the Voters Want?
109
1 Breaking ties and cycles
110
2 Reversal effects
123
3 A profile coordinate system
129

5 More candidates toward Lincolns election
60
Chaotic Election Outcomes
69
1 Deanna had to withdraw
70
2 General results
72
3 Consequences
79
4 Chaotic notions for chaotic results
84
How to Be Strategic
91
1 Choice of a procedure
92
Other Procedures Other Assumptions
137
1 Beyond voting other aggregation methods
138
2 Apportioning congressional seats on a torus
143
3 Other procedures and other assumptions
148
4 Concluding comment
152
Bibliography
153
Index
157
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