Social Choice and the Mathematics of Manipulation

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.