Mathematics of Social Choice

Voting, Compensation, and Division

Häftad, Engelska, 2009

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Beskrivning

How do you select a winner from a field of candidates? How do you rank a field of candidates? How do you share a divisible resource like a cake, or an indivisible one like a pet or a house? These are the questions addressed in this fun and accessible book that takes an entertaining look 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 mathematics majors as well as students whose only mathematical background is elementary algebra. Material geared toward more sophisticated readers can be skipped without any loss of continuity. The book includes many elementary and usually simple, but rigorous mathematical proofs appropriate for beginning mathematics majors. Students will also find appendices with background material on set notation, logic, and mathematical induction and solutions to many of the homework exercises.

Produktinformation

Utgivningsdatum:2009-12-30
Mått:451 x 451 x 645 mm
Vikt:482 g
Format:Häftad
Språk:Engelska
Antal sidor:256
Förlag:Society for Industrial & Applied Mathematics,U.S.
ISBN:9780898716955

Utforska kategorier

Tillämpad matematik inom Naturvetenskap och teknik

Mer om författaren

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.

Innehållsförteckning

PrefacePart I: Voting: Chapter 1: Winner selectionChapter 2: Rule of the majorityChapter 3: Election spoilersChapter 4: The Smith setChapter 5: Smith-fairness and the no-weak-spoiler criterionChapter 6: Schulze’s beatpath methodChapter 7: MonotonicityChapter 8: Elections with many or few votersChapter 9: Irrelevant comparisons and the Muller–Satterthwaite theoremChapter 10: Strategic voting and the Gibbard–Satterthwaite theoremChapter 11: Winner selection versus rankingChapter 12: Irrelevant alternatives and Arrow’s theoremPart II: Compensation: Chapter 13: Fairness and envy-freenessChapter 14: Pareto-optimality and equitabilityChapter 15: Equality, equitability, and Knaster’s procedurePart III: Division: Chapter 16: Envy-free, Pareto-optimal, and equitable cake cuttingChapter 17: “I cut, you choose” for three: Steinhaus’s methodChapter 18: Hall’s marriage theoremChapter 19: “I cut, you choose” for more than three: Kuhn’s methodsChapter 20: The method of Selfridge and ConwayChapter 21: The geometry of Pareto-optimal division between two peopleChapter 22: The adjusted winner method of Brams and TaylorChapter 23: Conflict resolution using the adjusted winner methodChapter 24: The effect of dishonesty on the adjusted winner methodChapter 25: Proportional allocationChapter 26: Dividing a piecewise homogeneous cake among N>2 peoplePart IV: Appendices: Appendix A: SetsAppendix B: LogicAppendix C: Mathematical inductionAppendix D: Solutions to selected exercisesIndex.