Mathematics of Social Choice

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.