Mathematics of social choice : voting, compensation, and division
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
eBook, English, 2010
Society for Industrial and Applied Mathematics (SIAM, 3600 Market Street, Floor 6, Philadelphia, PA 19104), Philadelphia, Pa., 2010
1 online resource (xi, 245 pages) : illustrations
9780898717624, 0898717620
694086409
Print version:
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
Includes index
English
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