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.

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An accessible exposition of social choices such as selecting a winning competitor, or dividing up resources.

About the Author

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.