Mathematics of social choice : voting, compensation, and division / Christoph Börgers.

Format:

Book

Author/Creator:

Börgers, Christoph.

Contributor:

Society for Industrial and Applied Mathematics.

Language:

English

Subjects (All):

Voting--Mathematical models.

Elections--Mathematical models.

Social choice--Mathematical models.

Physical Description:

1 electronic text (xi, 245 p. : ill.) : digital file.

Place of Publication:

Philadelphia, Pa. : Society for Industrial and Applied Mathematics (SIAM, 3600 Market Street, Floor 6, Philadelphia, PA 19104), 2010.

Language Note:

English

System Details:

Mode of access: World Wide Web.

System requirements: Adobe Acrobat Reader.

Summary:

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.

Contents:

Pt. 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.

Pt. II. Compensation. 13. Fairness and envy-freeness

14. Pareto-optimability and equitability

15. Equality, equitability and Knaster's procedure.

Pt. 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.

pt. IV. Appendices: A. Sets

B. Logic

C. Mathematical induction

D. Solutions to selected exercises.

Notes:

Includes index.

Description based on title page of print version.

ISBN:

0-89871-762-0

Publisher Number:

OT119 siam

OT119 SIAM