Social choice and the mathematics of manipulation / Alan D. Taylor.
By: Taylor, Alan D
.
Contributor(s): Mathematical Association of America.
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Item type | Current library | Call number | Copy number | Status | Date due | Barcode | Item holds |
---|---|---|---|---|---|---|---|
General Lending | MTU Bishopstown Library Lending | 324.6015193 (Browse shelf(Opens below)) | 1 | Available | 00183619 |
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Enhanced descriptions from Syndetics:
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.
Includes bibliographical references (pages 167-171) and index.
Part one -- An introduction to social choice theory -- An introduction to manipulability -- Resolute voting rules -- Part two -- Non-resolute voting rules -- Social choice functions -- Ultrafilters and the infinite -- Part three -- More on resolute procedures -- More on non-resolute procedures -- Other election-theoretic contexts.
Table of contents provided by Syndetics
- 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
Author notes provided by Syndetics
Alan D. Taylor is Marie Louise Bailey Professor of Mathematics at Union College.(Bowker Author Biography)