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Social Choice and the Mathematics of Manipulation

1 rating: 5.0
A book by Alan D. Taylor

"...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 recently released Social Choice and the Mathematics … see full wiki

Author: Alan D. Taylor
Publisher: Cambridge University Press
1 review about Social Choice and the Mathematics of Manipulation

The best resource around for learning how voting systems can be used and manipulated

  • Mar 19, 2007
Most Americans were shocked in 2000 to learn that voting is an inexact science. This is something that mathematicians have known since Kenneth Arrow published his impossibility theorem in 1950. That theorem states that no voting system based on ranked preferences can possibly meet a set of selected criteria when there are three or more alternatives. This idea was expanded on by Allan Gibbard and Mark Satterwaite, who proved that with three or more alternatives, there is no reasonable voting system that cannot be manipulated. In other words, it is always possible for voters to benefit by casting a disingenuous vote. In this book, Taylor sets down the mathematical foundations for these results as well as presenting several additional theorems that show additional aspects of the problem.
The results are certainly counter-intuitive, after all how is it possible for someone to gain by voting against themselves? However, it is possible and such issues have a great deal of relevance when social choices are made via some form of extended ballot. The mathematics is occasionally hard to follow, there were times when I really had to slow down and pick my way through the theorems. Nevertheless, most of the notation is that of set theory and predicate calculus, so if you understand that, you can wend your way through the book.
It is well worth reading, voting theory is a fascinating topic to explore and Taylor has written the best book available that will blaze your trail.

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