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Mathematics and Democracy: Designing Better Voting and Fair-Division Procedures

Mathematics and Democracy: Designing Better Voting and Fair-Division Procedures [Kindle Edition]

Steven J. Brams

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Product Description


"Showing how social-choice theory and game theory could make political and social institutions more democratic, Brams uses mathematical analysis to develop new procedures that could enable voters to better express their preferences."--Times Higher Education

"The image on the cover of Mathematics and Democracy shows four people pulling on two ropes. If they all pull, the knot will jam. The book's contents show, on the contrary, that sometimes mathematics and game theory can unjam the problems of voting."--Iain McLean, Science

"In seven chapters, Brams proposes and dissects a range of, often very elegant, fair division procedures pertaining to different situations. . . . Brams strengthens his arguments with a wealth of real-life examples, from US elections to the 1978 peace negotiations between Israel and Egypt. The mathematical results are amply illustrated with easy-to-follow examples. . . . If you're interested in democracy, then this book makes eye-opening reading, and if you're planning on wielding power at some point in the future, then it should be compulsory!"--Marianne Freiberger, +Plus Magazine

"Mathematics and Democracy is rich in analyses of historical cases. . . . Read Mathematics and Democracy: You will learn of the vast number of voting options that have been mooted, and you will easily conclude that any proposed change, however minor, will arouse fury in some constituency somewhere."--Philip J. Davis, SIAM News

"Increasingly, mathematicians are finding interesting problems in social science, a development that the previous books of Steven J. Brams helped to catalyze. Mathematics and Democracy, based on a selection of Brams's (mostly co-authored) papers, will add to his influence."--D. Marc Kilgour, Mathematical Reviews

"Since the math is elementary and the problems familiar, the book can be read both by political scientists not allergic to formal reasoning and by amateurs of mathematics interested in politics. Voting practitioners and designers will be delighted to find thorough discussions of less-known methods. All of them will find the book an interesting introduction to the fascinating subfield of mathematically oriented political science that analyzes and invents constructive institutional solutions to social dilemmas."--Marek Kaminski, Political Science Quarterly

Product Description

Voters today often desert a preferred candidate for a more viable second choice to avoid wasting their vote. Likewise, parties to a dispute often find themselves unable to agree on a fair division of contested goods. In Mathematics and Democracy, Steven Brams, a leading authority in the use of mathematics to design decision-making processes, shows how social-choice and game theory could make political and social institutions more democratic. Using mathematical analysis, he develops rigorous new procedures that enable voters to better express themselves and that allow disputants to divide goods more fairly.

One of the procedures that Brams proposes is "approval voting," which allows voters to vote for as many candidates as they like or consider acceptable. There is no ranking, and the candidate with the most votes wins. The voter no longer has to consider whether a vote for a preferred but less popular candidate might be wasted. In the same vein, Brams puts forward new, more equitable procedures for resolving disputes over divisible and indivisible goods.

Product details

  • Format: Kindle Edition
  • File Size: 3771 KB
  • Print Length: 392 pages
  • Publisher: Princeton University Press (17 Dec 2007)
  • Sold by: Amazon Media EU S.à r.l.
  • Language: English
  • ASIN: B004M17EKC
  • Text-to-Speech: Enabled
  • X-Ray:
  • Amazon Bestsellers Rank: #732,467 Paid in Kindle Store (See Top 100 Paid in Kindle Store)
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Most Helpful Customer Reviews on (beta) 3.5 out of 5 stars  4 reviews
4 of 4 people found the following review helpful
4.0 out of 5 stars welcome addition to voting rules literature 9 July 2009
By Jason P. Sorens - Published on
I enjoyed this book. Brams does provide mathematical proofs of his propositions in the chapter appendices, but overall, this is a fairly accessible and wide-ranging overview of Brams' current thinking on voting rules and fair-division procedures. One of the most interesting contributions of this book is the development of ranked approval voting systems, which combine many of the attractive features of Condorcet voting and simple approval voting. Brams also develops ways to implement proportional representation outside the party-list context, useful for professional societies, corporate boards, etc. seeking to elect multiple positions at once.

I highly recommend this book to lay readers seeking to learn about the state of the art in normative voting-rule theory. With any luck, it will advance the cause of reform of voting rules in single-winner, political elections.
1 of 1 people found the following review helpful
4.0 out of 5 stars An interesting addition to the literature 15 Mar 2011
By Bruce R. Gilson - Published on
Format:Paperback|Verified Purchase
This book continues Prof. Brams' partiality toward Approval Voting, a system he did not invent but of which he has been one of the strongest partisans. However, to his credit, he has actually admitted in this book that Approval Voting is not a panacea and there might be better ones "in certain circumstances." William Poundstone's book, "Gaming the Vote," actually discusses a system I prefer: Range Voting (also known as Score Voting). This being said, I generally think this to be a valuable new book: it discusses some modifications of Approval Voting that look like improvements, and analyzes some of the good and bad points of various voting systems. You should read it, but take Brams' well-known bias toward Approval Voting into account when reading.
5.0 out of 5 stars Get the First Printing 10 Aug 2012
By Christopher Grant - Published on
While in many ways the second printing resembles the first printing, the actual printing of the text is noticeably less crisp and legible in the second printing than in the first printing. (See the samples I've uploaded to Customer Images.) The degradation of the quality is consistent throughout; e.g., every "3" in the second printing has its lower stroke nearly disconnected from the rest of the character.

If you're the sort of person who, say, can't see any difference in the printing in a mass-market paperback and in its hardback counterpart, or if you can see the difference but don't care, then the shortcomings of the second printing won't matter to you. For the rest of you, I suggest that you buy your copy of this book somewhere where you can inspect the quality of the printing beforehand.
6 of 22 people found the following review helpful
1.0 out of 5 stars Neither Fish nor Fowl 17 Feb 2008
By PST - Published on
This is neither a book on mathematics, nor a book for the generally interested reader: The mathematics it contains is very simple, yet incomplete. A math book on this level should certainly define Nash equilibria, to mention just one deficiency.
It is not a book for general reading, as it is simply too boring!

I have no idea, as to who might be the target audience of such a book.

This is a pity, as the subject is both interesting and important.

I read another book by Prof. Brams: Fair Division: from Cake Cutting to Dispute Resolution, which was far better, so I hope, this this was a one time mistake by Prof. Brams.
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