- Hardcover: 240 pages
- Publisher: Princeton University Press; 1st edition (April 4, 2010)
- Language: English
- ISBN-10: 0691139946
- ISBN-13: 978-0691139944
- Product Dimensions: 6.1 x 1.1 x 9.3 inches
- Shipping Weight: 1 pounds (View shipping rates and policies)
- Average Customer Review: 4 customer reviews
- Amazon Best Sellers Rank: #1,646,356 in Books (See Top 100 in Books)
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Numbers Rule: The Vexing Mathematics of Democracy, from Plato to the Present 1st Edition
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"Mathematicians, economists, and political theorists have made their own attempts to elucidate the math of voting, and figure out better electoral systems. The story of these efforts is told in Numbers Rule. . . . Timely."--Anthony Gottlieb, New Yorker
"Clear and energetic. . . Szpiro charts this history selectively and with the use of major characters to render vivid a story of rival systems, which can easily degenerate into equations. He is a mathematician and uses tables to illustrate his arguments: but these are accessible to simple understanding. He is also a journalist and thus can tell a story."--John Lloyd, Financial Times
"Although voting problems manifest subtle mathematical complexities, Szpiro is an excellent communicator of mathematical concepts with a nimble ability to sidestep technical jargon. . . . An interesting, selective introduction into the complexities of voting reform."--Donald G. Saari, Times Higher Education
"A history of social choice theory, with much more detail (yet still readable) than one is used to receiving on this topic. I liked this book very much."--Tyler Cowen, Marginal Revolution
"I knew from reading Martin Gardner's columns that every voting system you can devise will occasionally turn up paradoxical results. . . . Szpiro walks you through the whole subject with very few equations."--John Derbyshire, National Review
"Engaging storytelling . . . for a reader who is primarily interested in learning some of the historical context of the characters who have contributed to the mathematics of social choice theory, it is hard to imagine a better book."--Darren Glass, MAA Reviews
"In Numbers Rule, mathematician and journalist Szpiro presents a refreshingly different presentation of the mathematics of voting and apportionment. . . . The mathematical content is not trivial, and it is well written, very clear, and should be accessible to readers with an understanding of arithmetic and a willingness to play with numbers."--Choice
"Highly entertaining. . . . Anybody who has ever decried election results will be fascinated in Szpiro's accessible explanations of the paradoxes and enigmas that occur in all methods of election, from electing a pope in Rome, to apportionment of seats in the Congress by our founding fathers to ensure justice for all, even the minority."--Phil Semler, Sacramento Book Review>
"The author skillfully placed the development and evolution of the Social Choice theories in a broad historical context. The book shines in weaving the emergent math theories with historical circumstances. . . . [E]njoyable and informative."--Alexander Bogomolny, Cut the Knot
"Szpiro's book is a highly recommended good read on the history of the problems, which could illuminate a seminar series on the issues."--Ron Johnston, Environment and Planning
"It is an excellent addition to a growing body of literature that aims to convey ideas from the mathematical sciences to general audiences. Moreover, Szpiro's book is unique among other offerings in the mathematical social sciences in that it focuses on the historical development of the field. The narrative is engaging, witty, and easy to read."--Jonathan K. Hodge, Notices of the AMS
"George Szpiro's Numbers Rule does not break any new ground in the field of social choice theory, but it is probably the most entertaining book one is likely to find on the subject. . . . [A]ll social choice theorists should read this book. . . .Szpiro's book is ideally suited to be a supplementary reading for graduate classes in social choice theory."--Justin Buchler, Public Choice
From the Back Cover
"'Which candidate is the people's choice?' It's a simple question, and the answer is anything but. In Numbers Rule, George Szpiro tells the amazing story of the search for the fairest way of voting, deftly blending history, biography, and political skullduggery. Everyone interested in our too-fallible elections should read this book."--William Poundstone, author of Gaming the Vote: Why Elections Aren't Fair (and What We Can Do about It)
"Writing a book for a general audience on voting and electoral systems is a daunting task, but Szpiro succeeds admirably. He completely avoids technical jargon and focuses on the most important scholars and results in the field. This book fills a gap in the existing literature."--Hannu Nurmi, author of Voting Procedures under Uncertainty
"Numbers Rule focuses on key figures in the development of democracy and on the mathematics of voting, elections, and apportionment that they developed. Szpiro pays particular attention to the paradoxes that arise, and discusses them through examples."--Steven J. Brams, New York University
"Numbers Rule is very thoroughly researched and quite well written. The story Szpiro tells is both important and interesting. The most significant contribution this book makes is in the detailed history that it presents. It will have broad appeal."--Alan D. Taylor, coauthor of Mathematics and Politics
Top customer reviews
This book is highly readable and hits all the highlights. The exposition of the period from 1200-1450 was particularly interesting to me, since it is much less known than the relatively well-known French period.
If you have any interest in learning about why voting and apportionment are not straightforward, and want a readable, history-oriented book on approaches to these problems, I highly recommend this book.
Szpiro describes how democracies from ancient Greece to the twenty-first century have dealt with the issues involved in making representation and elections as just as humanly possible. He describes how methods used to choose between multiple candidates progressed from those used to elect abbesses in the Middle Ages to those used in France in the eighteenth century, and shows the odd effects that can result when a third candidate is inserted into a previously two-man race.
This book was, appropriately enough, released in a year ending in '0', given that 2010 is a census year--the task of congressional apportionment will begin again soon. Szpiro recounts the intense debates between advocates of different apportionment methods in the early years of the republic and recalls many of the conflicts in later decades between states over the final representative apportioned. The author describes many of the mathematical issues that result, including the Alabama, New State, and Population Paradoxes--he shows mathematically how a state can, incredibly, lose a representative when the size of the House of Representatives is increased by one.
One trail that Szpiro did not go down involves the effect of an increase in the size of the House on presidential elections. Many people over the years have called for an increase of the size of the House of Representatives to anywhere from 600 to 1000 seats--in very rare instances this would be enough to change the result of an extremely close presidential election. Had the House contained, say, 870 seats instead of the 435 that it actually contained for the 2000 election, Al Gore would have won even without carrying Florida.
Szpiro reports the opinions of mathematicians concerning whether multi-candidate elections and congressional apportionments can ever be made completely fair, and provides brief biographical sketches of many of the mathematicians who dealt with these problems. The author closes by discussing election problems encountered in recent decades in Switzerland, France, and Israel.
"Numbers Rule" is a great study of the mechanics needed to put democracy in place and shows that they are not foolproof--one is reminded of Winston Churchill's assertion that "Democracy is the worst form of government, except for all those other forms that have been tried from time to time."
I should note that while I have verified that the problem I describe above appears in both the Kindle app for the PC and the Kindle app for the iPad, I do not know if it also shows up on the screens of devices made by Amazon.
Although I found parts of the first chapter rather boring (i.e., analysis of Plato's views as translated from his writings), the pace rapidly picks up with each succeeding chapter, quickly making the book hard to put down. I found the inclusion of biographical appendices on several key individuals, as well as the couple of mathematical appendices, to very nicely complement the main text. This book can be enjoyed by anyone, especially those concerned about the fairness of our election process.