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.

Alan D. Taylor is the Marie Louise Bailey Professor of Mathematics at Union College, where he has been since receiving his Ph.D. from Dartmouth College in 1975. His research interests have included logic and set theory, finite and infinitary combinatorics, simple games, and social choice theory. He is the author of Mathematics and Politics: Strategy, Voting, Power and Proof, and coauthor of Fair Division: From Cake-Cutting to Dispute Resolution and The Win-Win Solution: guaranteeing Fair Shares to Everybody (both with Steven J. Brams) and Simple Games: Desirability Relations, Trading, and Pseudoweightings (with William S. Zwicker).