Mathematics of Social Choice : Voting, Compensation, and Division

ISBN-10: 0898716950

ISBN-13: 9780898716955

Edition: 2010

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Book details

Copyright year: 2010
Publisher: Society for Industrial and Applied Mathematics
Binding: Paperback
Pages: 250
Size: 7.00" wide x 10.00" long x 0.50" tall
Weight: 1.276
Language: English

Christoph B�rgers has been a Professor in the Department of Mathematics at Tufts University since 1994. He has also worked at the University of Michigan and at the IBM T. J. Watson Research Center. He received his PhD from New York University.

Preface
Voting
Winner selection
Rule of the majority
Election spoilers
The Smith set
Smith-fairness and the no-weak-spoiler criterion
Schulze's beatpath method
Monotonicity
Elections with many or few voters
Irrelevant comparisons and the Muller-Satterthwaite theorem
Strategic voting and the Gibbard-Satterthwaite theorem
Winner selection versus ranking
Irrelevant alternatives and Arrow's theorem
Compensation
Fairness and envy-freeness
Pareto-optimability and equitability
Equality, equitability and Knaster's procedure
Division
Envy-free, Pareto-optimal, and equitable cake cutting
'I cut, you choose' for three: Steinhaus' method
Hall's marriage theorem
'I cut, you choose' for more than three: Kuhn's methods
The method of Selfridge and Conway
The geometry of Pareto-optimal division between two people
The adjusted winner method of Brams and Taylor
Conflict resolution using the adjusted winner method
Proportional allocation
Dividing a piecewise homogeneous cake among N>2 people
Appendices
Sets
Logic
Mathematical induction
Solutions to selected exercises
Index
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