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Mathematics of Social Choice: Voting, Compensation, and Division

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Christoph Börgers


2010 / xii + 245 pages / Softcover / ISBN: 978-0-898716-95-5 / List Price $41.00 / SIAM Member Price $28.70 / Order Code OT119

Keywords: social choice theory, theory of voting methods, fair division, mathematics in the social sciences, applications of elementary mathematics


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.

The text is divided into three parts:

  • The first part 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: Voting, Compensation, and Division 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.

This book is primarily addressed to readers without a high-level mathematical background, such as college students majoring in subjects other than mathematics and advanced high school students. However, some material appropriate for more sophisticated readers is included in small print, and makes the text appealing to undergraduate mathematics majors interested in learning about applications of mathematics in the social sciences. 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.

About the Author
Christoph Bö¬örgers is a Professor in the Department of Mathematics at Tufts University.

ISBN: 9780898716955

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