Studies in Economic Theory

Geometry of Voting

Authors: Saari, Donald G.

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  • ISBN 978-3-642-48644-9
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About this book

Over two centuries of theory and practical experience have taught us that election and decision procedures do not behave as expected. Instead, we now know that when different tallying methods are applied to the same ballots, radically different outcomes can emerge, that most procedures can select the candidate, the voters view as being inferior, and that some commonly used methods have the disturbing anomaly that a winning candidate can lose after receiving added support. A geometric theory is developed to remove much of the mystery of three-candidate voting procedures. In this manner, the spectrum of election outcomes from all positional methods can be compared, new flaws with widely accepted concepts (such as the "Condorcet winner") are identified, and extensions to standard results (e.g. Black's single-peakedness) are obtained. Many of these results are based on the "profile coordinates" introduced here, which makes it possible to "see" the set of all possible voters' preferences leading to specified election outcomes. Thus, it now is possible to visually compare the likelihood of various conclusions. Also, geometry is applied to apportionment methods to uncover new explanations why such methods can create troubling problems.

Table of contents (4 chapters)

  • From an Election Fable to Election Procedures

    Saari, Donald G.

    Pages 1-26

  • Geometry for Positional and Pairwise Voting

    Saari, Donald G.

    Pages 27-145

  • From Symmetry to the Borda Count and Other Procedures

    Saari, Donald G.

    Pages 147-228

  • Many Profiles; Many New Paradoxes

    Saari, Donald G.

    Pages 229-354

Buy this book

eBook $109.00
price for USA (gross)
  • ISBN 978-3-642-48644-9
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $139.00
price for USA
  • ISBN 978-3-642-48646-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Geometry of Voting
Authors
Series Title
Studies in Economic Theory
Series Volume
3
Copyright
1994
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin ยท Heidelberg
eBook ISBN
978-3-642-48644-9
DOI
10.1007/978-3-642-48644-9
Softcover ISBN
978-3-642-48646-3
Series ISSN
1431-8849
Edition Number
1
Number of Pages
XVII, 372
Topics