Geometry of Voting

  • Donald G. Saari

Part of the Studies in Economic Theory book series (ECON.THEORY, volume 3)

Table of contents

  1. Front Matter
    Pages i-xvi
  2. Donald G. Saari
    Pages 27-145
  3. Donald G. Saari
    Pages 229-354
  4. Back Matter
    Pages 355-374

About this book

Introduction

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.

Keywords

Apportionment Methods Entscheidungstheorie Gruppenentscheidung Manipulation Präferenzordnung Voting Voting Theory decision theory organization organizations social choice value-at-risk

Authors and affiliations

  • Donald G. Saari
    • 1
  1. 1.Department of MathematicsNorthwestern UniversityEvanstonUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-48644-9
  • Copyright Information Springer-Verlag Berlin Heidelberg 1994
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-48646-3
  • Online ISBN 978-3-642-48644-9
  • Series Print ISSN 1431-8849
  • About this book