Börgers Christoph
Mathematics of social choice : voting, compensation, and division - USA SIAM 2010 - xi, 245 p
Part I: Voting
Chapter 1: Winner selection
Chapter 2: Rule of the majority
Chapter 3: Election spoilers
Chapter 4: The Smith set
Chapter 5: Smith-fairness and the no-weak-spoiler criterion
Chapter 6: Schulze s beatpath method
Chapter 7: Monotonicity
Chapter 8: Elections with many or few voters
Chapter 9: Irrelevant comparisons and the Muller Satterthwaite theorem
Chapter 10: Strategic voting and the Gibbard Satterthwaite theorem
Chapter 11: Winner selection versus ranking
Chapter 12: Irrelevant alternatives and Arrow s theorem
Part II: Compensation
Chapter 13: Fairness and envy-freeness
Chapter 14: Pareto-optimality and equitability
Chapter 15: Equality, equitability and Knaster's procedur
Part III: Division
Chapter 16: Envy-free, Pareto-optimal, and equitable cake cutting
Chapter 17: I cut, you choose for three: Steinhaus's method
Chapter 18: Hall s marriage theorem
Chapter 19: I cut, you choose for more than three: Kuhn s methods
Chapter 20: The method of Selfridge and Conway
Chapter 21: The geometry of Pareto-optimal division between two people
Chapter 22: The adjusted winner method of Brams and Taylor
Chapter 23: Conflict resolution using the adjusted winner method
Chapter 24: The effect of dishonesty on the adjusted winner method
Chapter 25: Proportional allocation
Chapter 26: Dividing a piecewise homogeneous cake among more than 2 people
Part IV: Appendices
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.
9780898716955
JF1001
Mathematics of social choice : voting, compensation, and division - USA SIAM 2010 - xi, 245 p
Part I: Voting
Chapter 1: Winner selection
Chapter 2: Rule of the majority
Chapter 3: Election spoilers
Chapter 4: The Smith set
Chapter 5: Smith-fairness and the no-weak-spoiler criterion
Chapter 6: Schulze s beatpath method
Chapter 7: Monotonicity
Chapter 8: Elections with many or few voters
Chapter 9: Irrelevant comparisons and the Muller Satterthwaite theorem
Chapter 10: Strategic voting and the Gibbard Satterthwaite theorem
Chapter 11: Winner selection versus ranking
Chapter 12: Irrelevant alternatives and Arrow s theorem
Part II: Compensation
Chapter 13: Fairness and envy-freeness
Chapter 14: Pareto-optimality and equitability
Chapter 15: Equality, equitability and Knaster's procedur
Part III: Division
Chapter 16: Envy-free, Pareto-optimal, and equitable cake cutting
Chapter 17: I cut, you choose for three: Steinhaus's method
Chapter 18: Hall s marriage theorem
Chapter 19: I cut, you choose for more than three: Kuhn s methods
Chapter 20: The method of Selfridge and Conway
Chapter 21: The geometry of Pareto-optimal division between two people
Chapter 22: The adjusted winner method of Brams and Taylor
Chapter 23: Conflict resolution using the adjusted winner method
Chapter 24: The effect of dishonesty on the adjusted winner method
Chapter 25: Proportional allocation
Chapter 26: Dividing a piecewise homogeneous cake among more than 2 people
Part IV: Appendices
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.
9780898716955
JF1001