Mathematics of Social Choice Voting, Compensation, and Division

Name: Mathematics of Social Choice Voting, Compensation, and Division
Price: 38.69 USD
Availability: InStock
ISBN: 9780898716955

ISBN-10: 0898716950

ISBN-13: 9780898716955

Edition: 2010

Authors: Christoph Bï¿½rgers, Christoph Bï¿½rgers

List price: $45.00

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Book details

List price: $45.00
Copyright year: 2010
Publisher: Society for Industrial and Applied Mathematics
Publication date: 12/30/2009
Binding: Paperback
Pages: 256
Size: 7.00" wide x 10.00" long x 0.50" tall
Weight: 1.034
Language: English

Christoph Bï¿½rgers 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