Social Choice and the Mathematics of Manipulation
Social Choice and the Mathematics of Manipulation Honesty in voting, it turns out, is not always the best policy. The ensuing decades produced a number of theorems of striking mathematical naturality…
Specifikacia Social Choice and the Mathematics of Manipulation
Social Choice and the Mathematics of Manipulation
Honesty in voting, it turns out, is not always the best policy. The ensuing decades produced a number of theorems of striking mathematical naturality that dealt with the manipulability of voting systems. 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 presentation is almost completely self-contained, and requires no prerequisites except a willingness to follow rigorous mathematical arguments. 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. Mathematics students, as well as mathematicians, political scientists, economists and philosophers will learn why it is impossible to devise a completely unmanipulable voting system.
Proof and the Art of Mathematics
Proof and the Art of Mathematics