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Basic Geometry of Voting : Basic Geometry of Voting - Donald G. Saari

Basic Geometry of Voting

Basic Geometry of Voting

Paperback Published: 18th September 1995
ISBN: 9783540600640
Number Of Pages: 300

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A surprise is how the complexities of voting theory can be explained and resolved with the comfortable geometry of our three-dimensional world. This book is directed toward students and others wishing to learn about voting, experts will discover previously unpublished results. As an example, a new profile decomposition quickly resolves two centuries old controversies of Condorcet and Borda, demonstrates, that the rankings of pairwise and other methods differ because they rely on different information, casts series doubt on the reliability of a Condorcet winner as a standard for the field, makes the famous Arrow`s Theorem predictable, and simplifies the construction of examples. The geometry unifies seemingly disparate topics as manipulation, monotonicity, and even the apportionment issues of the US Supreme Court.

From an Election Fable to Election Proceduresp. 1
An Electoral Fablep. 2
The Moral of the Talep. 8
From Aristotle to "Fast Eddie"p. 15
What Kind of Geometry?p. 21
Geometry for Positional And Pairwise Votingp. 29
Ranking Regionsp. 30
Profiles and Election Mappingsp. 38
The Problem With Condorcetp. 45
Why Can't an Organization Be More Like a Person?p. 45
Geometry of Pairwise Votingp. 56
Black's Single-Peakednessp. 71
Arrow's Theoremp. 83
Positional Voting And the BCp. 101
Positional Voting Methodsp. 101
What a Difference a Procedure Makes; Several Different Outcomesp. 110
Positional Versus Pairwise Votingp. 125
Profile Decompositionp. 140
From Aggregating Pairwise Votes to the Borda Countp. 154
The Other Positional Voting Methodsp. 168
Multiple Voting Schemesp. 178
Other Election Proceduresp. 190
Other Voting Issuesp. 201
Weak Consistency: The Sum of the Partsp. 201
From Involvement and Monotonicity to Manipulationp. 215
Gibbard-Satterthwaite and Manipulable Proceduresp. 231
Proportional Representationp. 242
House Monotone Methodsp. 263
Notesp. 285
Referencesp. 291
Indexp. 297
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9783540600640
ISBN-10: 3540600647
Series: Basic Geometry of Voting
Audience: General
Format: Paperback
Language: English
Number Of Pages: 300
Published: 18th September 1995
Publisher: Springer-Verlag Berlin and Heidelberg Gmbh & Co. Kg
Country of Publication: DE
Dimensions (cm): 23.55 x 15.55  x 1.93
Weight (kg): 0.48

Earn 294 Qantas Points
on this Book