Social Choice and the Mathematics of Manipulation [Hardcover]

A mathematical look at why it is impossible to devise a completely unmanipulable voting system, first published in 2005.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.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.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.1. Introduction; 2. The GibbardSatterthwaite theorem; 3. Additional results for single-valued elections; 4. The DugganSchwartz 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. ...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 lÓ3