Social Choice and the Mathematics of Manipulation (Outlooks)

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9780521008839: Social Choice and the Mathematics of Manipulation (Outlooks)

Honesty in voting is not always the best policy. This is a book for mathematicians, political scientists, economists and philosophers who want to understand how it is impossible to devise a reasonable voting system in which voters can never gain by submitting a disingenuous ballot. The book requires no prerequisites except a willingness to follow rigorous mathematical arguments.

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Honesty in voting, it turns out, is not always the best policy. This is a book for mathematicians, political scientists, economists and philosophers who want to understand the sense in which it is impossible to devise a reasonable voting system in which voters can never gain by submitting a disingenuous ballot. With the exception of the last chapter, the book is completely self-contained, and requires no prerequisites except a willingness to follow rigorous mathematical arguments.

Review:

"...until recently there has been a problem facing mathematicians who are interested in learning about [the mathematics of elections]...I am pleased to say that this is no longer the case, as Alan D. Taylor's recently released Social Choice and the Mathematics of Manipulation fits this bill perfectly."
MAA Reviews, Darren Glass

"[T]his book is a little gem. It will be especially prized by those who need to understand voting systems and how they can be manipulated by individual voters."
Mathematics Today

"Taylor's book gives an excellent overview of many results stemming from Gibbard's and Satterthwaite's original analysis...The general organization of the book is excellent. This is truly a wonderful book and it can be recommended to mathematicians looking for applications in the social sciences" - Marice Salles

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Alan D. Taylor
Published by Cambridge University Press (2005)
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Book Description Cambridge University Press, 2005. Softcover. Book Condition: New. First edition. Honesty in voting, it turns out, is not always the best policy. Indeed, in the early 1970s, Allan Gibbard and Mark Satterthwaite, building on the seminal work of Nobel laureate Kenneth Arrow, proved that with three or more alternatives there is no reasonable voting system that is non-manipulable; voters will always have an opportunity to benefit by submitting a disingenuous ballot. The ensuing decades produced a number of theorems of striking mathematical naturality that dealt with the manipulability of voting systems. This book presents many of these results from the last quarter of the twentieth century, especially the contributions of economists and philosophers, from a mathematical point of view, with many new proofs. The presentation is almost completely self-contained, and requires no prerequisites except a willingness to follow rigorous mathematical arguments. Mathematics students, as well as mathematicians, political scientists, economists and philosophers will learn why it is impossible to devise a completely unmanipulable voting system. Contents 1. Introduction 2. The Gibbard-Satterthwaite theorem 3. Additional results for single-valued elections 4. The Duggan-Schwartz theorem 5. Additional results for multi-valued elections 6. Ballots that rank sets 7. Elections with outcomes that are lotteries 8. Elections with variable agendas References Index. Printed Pages: 187. Bookseller Inventory # 11835

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Book Description Cambridge University Press, 2005. Softcover. Book Condition: New. First edition. Honesty in voting, it turns out, is not always the best policy. Indeed, in the early 1970s, Allan Gibbard and Mark Satterthwaite, building on the seminal work of Nobel laureate Kenneth Arrow, proved that with three or more alternatives there is no reasonable voting system that is non-manipulable; voters will always have an opportunity to benefit by submitting a disingenuous ballot. The ensuing decades produced a number of theorems of striking mathematical naturality that dealt with the manipulability of voting systems. This book presents many of these results from the last quarter of the twentieth century, especially the contributions of economists and philosophers, from a mathematical point of view, with many new proofs. The presentation is almost completely self-contained, and requires no prerequisites except a willingness to follow rigorous mathematical arguments. Mathematics students, as well as mathematicians, political scientists, economists and philosophers will learn why it is impossible to devise a completely unmanipulable voting system. Contents 1. Introduction 2. The Gibbard-Satterthwaite theorem 3. Additional results for single-valued elections 4. The Duggan-Schwartz theorem 5. Additional results for multi-valued elections 6. Ballots that rank sets 7. Elections with outcomes that are lotteries 8. Elections with variable agendas References Index. Printed Pages: 187. Bookseller Inventory # 11835

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Book Description CAMBRIDGE UNIVERSITY PRESS, United Kingdom, 2005. Paperback. Book Condition: New. Language: English . Brand New Book ***** Print on Demand *****. Honesty in voting, it turns out, is not always the best policy. Indeed, in the early 1970s, Allan Gibbard and Mark Satterthwaite, building on the seminal work of Nobel laureate Kenneth Arrow, proved that with three or more alternatives there is no reasonable voting system that is non-manipulable; voters will always have an opportunity to benefit by submitting a disingenuous ballot. The ensuing decades produced a number of theorems of striking mathematical naturality that dealt with the manipulability of voting systems. This 2005 book presents many of these results from the last quarter of the twentieth century, especially the contributions of economists and philosophers, from a mathematical point of view, with many new proofs. The presentation is almost completely self-contained, and requires no prerequisites except a willingness to follow rigorous mathematical arguments. Mathematics students, as well as mathematicians, political scientists, economists and philosophers will learn why it is impossible to devise a completely unmanipulable voting system. Bookseller Inventory # AAV9780521008839

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Book Description CAMBRIDGE UNIVERSITY PRESS, United Kingdom, 2005. Paperback. Book Condition: New. Language: English . Brand New Book ***** Print on Demand *****.Honesty in voting, it turns out, is not always the best policy. Indeed, in the early 1970s, Allan Gibbard and Mark Satterthwaite, building on the seminal work of Nobel laureate Kenneth Arrow, proved that with three or more alternatives there is no reasonable voting system that is non-manipulable; voters will always have an opportunity to benefit by submitting a disingenuous ballot. The ensuing decades produced a number of theorems of striking mathematical naturality that dealt with the manipulability of voting systems. This 2005 book presents many of these results from the last quarter of the twentieth century, especially the contributions of economists and philosophers, from a mathematical point of view, with many new proofs. The presentation is almost completely self-contained, and requires no prerequisites except a willingness to follow rigorous mathematical arguments. Mathematics students, as well as mathematicians, political scientists, economists and philosophers will learn why it is impossible to devise a completely unmanipulable voting system. Bookseller Inventory # AAV9780521008839

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