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Mathematics of Social Choice

Mathematics of Social Choice
Voting, Compensation, and Division

$42.99 (P)

  • Date Published: January 2010
  • availability: This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial & Applied Mathematics for availability.
  • format: Paperback
  • isbn: 9780898716955

$ 42.99 (P)
Paperback

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About the Authors
  • Mathematics of Social Choice is a fun and accessible book that looks at the choices made by groups of people with different preferences, needs, and interests. Divided into three parts, the text first examines voting methods for selecting or ranking candidates. A brief second part addresses compensation problems wherein an indivisible item must be assigned to one of several people who are equally entitled to ownership of the item, with monetary compensation paid to the others. The third part discusses the problem of sharing a divisible resource among several people. Mathematics of Social Choice can be used by undergraduates studying mathematics and students whose only mathematical background is elementary algebra. More advanced material can be skipped without any loss of continuity. The book can also serve as an easy introduction to topics such as the Gibbard–Satterthwaite theorem, Arrow's theorem, and fair division for readers with more mathematical background.

    • Suitable for non-mathematics undergraduates, but with appendices to deepen understanding
    • Also serves to introduce new mathematicians to topics such as the Gibbard–Satterthwaite theorem, Arrow's theorem and fair division
    • Includes homework exercises, complete with solutions at the back
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    Product details

    • Date Published: January 2010
    • format: Paperback
    • isbn: 9780898716955
    • length: 184 pages
    • dimensions: 255 x 176 x 13 mm
    • weight: 0.46kg
    • availability: This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial & Applied Mathematics for availability.
  • Table of Contents

    Preface
    Part I. Voting:
    1. Winner selection
    2. Rule of the majority
    3. Election spoilers
    4. The Smith set
    5. Smith-fairness and the no-weak-spoiler criterion
    6. Schulze's beatpath method
    7. Monotonicity
    8. Elections with many or few voters
    9. Irrelevant comparisons and the Muller–Satterthwaite theorem
    10. Strategic voting and the Gibbard–Satterthwaite theorem
    11. Winner selection versus ranking
    12. Irrelevant alternatives and Arrow's theorem
    Part II. Compensation:
    13. Fairness and envy-freeness
    14. Pareto-optimability and equitability
    15. Equality, equitability and Knaster's procedure
    Part III. Division:
    16. Envy-free, Pareto-optimal, and equitable cake cutting
    17. 'I cut, you choose' for three: Steinhaus' method
    18. Hall's marriage theorem
    19. 'I cut, you choose' for more than three: Kuhn's methods
    20. The method of Selfridge and Conway
    21. The geometry of Pareto-optimal division between two people
    22. The adjusted winner method of Brams and Taylor
    23. Conflict resolution using the adjusted winner method
    25. Proportional allocation
    26. Dividing a piecewise homogeneous cake among N>2 people
    Part IV: Appendices: A. Sets
    B. Logic
    C. Mathematical induction
    D. Solutions to selected exercises
    Index.

  • Author

    Christoph Börgers, Tufts University, Massachusetts
    Christoph Börgers 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.

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