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Numbers Rule: The Vexing Mathematics of Democracy, from Plato to the Present
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Numbers Rule: The Vexing Mathematics of Democracy, from Plato to the Present

3.67  ·  Rating details ·  66 ratings  ·  12 reviews
Since the very birth of democracy in ancient Greece, the simple act of voting has given rise to mathematical paradoxes that have puzzled some of the greatest philosophers, statesmen, and mathematicians. Numbers Rule traces the epic quest by these thinkers to create a more perfect democracy and adapt to the ever-changing demands that each new generation places on our ...more
Hardcover, 226 pages
Published April 1st 2010 by Princeton University Press (first published March 1st 2010)
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Oct 27, 2017 rated it liked it  ·  review of another edition
Un buon libro per capire qualcosa in più su come i voti nei sistemi democratici si possano tradurre in seggi parlamentari, fra contraddizioni, sproporzioni e stranezze storiche che possono far sorridere
Aug 16, 2018 rated it really liked it
The Paradoxes of Democracy

This is a book about the mathematics of elections and the implications of different methods towards fairness. The progression of topics is both historical and biographical. Szpiro begins with an interesting discussion of Plato and examines the principles and merits behind the scheme proposed by "The Athenian Stranger" (a stand-in for Plato himself) in "The Laws". The presentation here was much more interesting than what I recall being taught, however the scheme is
Jan 20, 2013 rated it liked it
Shelves: nonfiction, school
Several chapters from this book were assigned reading in my course on Social Choice. I enjoyed those selections, so I decided to finish the remaining chapters. I find Szpiro's writing to be quite enjoyable despite the fact that the topic is predominantly mathematics. By adding the intrigue of politics, Szpiro is able to add many interesting anecdotes and tongue-in-cheek comments that make the reader chuckle. His particular pet-peeve seems to be the Bush-Gore election (it's given several mentions ...more
Jul 19, 2010 rated it it was amazing
[As always, I dont review books here that I read for work, except when I do. This is one of those exceptions. My full review can be found online at]


Given that individual members of society have their preferences, how should we aggregate them to figure out what society as a whole prefers?

How should we divide financial resources, pieces of cake, or congressional representation between people in a way that is as fair as possible?

Alex Chan
Aug 19, 2017 rated it it was amazing
Voting is a hard problem: how do you come to a group consensus between multiple options? And how do you divide representation between constituencies?

Lots of people have tried to answer these questions, and this book has an enjoyable and detailed account of their work and lives. Each chapter covers a key figure in the history of voting theory – such as Plato, Borda and Condorcet – and it does a good job of balancing the mathematics and the biography. I came away with a good sense of the
May 11, 2011 rated it liked it
As a math major who attended a college known for its political sciences, this book was right up my alley. But even more pertinently, I once devised a voting scheme to help my a cappella group select several songs. As it turns out, my method was similar to a system halfway between that of the medieval scholar Ramon Llull and a method by the famous 19th century author (and mathematician) Lewis Carroll. Reading this book years later, I learned that the system I had concocted was unfortunately ...more
Maurizio Codogno
May 14, 2013 rated it it was amazing
Shelves: divulgazione
Forse avete sentito parlare del teorema di Arrow, che dimostra matematicamente come - se vogliamo scegliere dei rappresentanti secondo un certo numero di regole assolutamente sensate - l'unica opzione possibile è avere un dittatore. Magari avete anche sentito parlare del paradosso dell'Alabama: suddividendo per stato in modo proporzionale i rappresentanti degli stati USA al Congresso e aumentando il numero di rappresentanti totali, era possibile che uno stato perdesse un seggio. Ma ci sono molte ...more
Ralph Orr
Dec 31, 2011 rated it really liked it
Shelves: democracy, history
A good introduction to the problem of fair proportional representation in democratic systems. The reader needs some comfort level with math.It explores the background to and the history behind how the United States apportions the House of Representatives in close conformity to the requirements of the Constitution, as as well as the impossibility of removing all ambiguities and weaknesses thereof. Beware three-or-more candidate elections. They are most prone to manipulation.
Jul 01, 2010 rated it it was ok
I generally like books on this topic, but this one missed the mark. The author spends at least as much time discussing the personal lives of the mathematicians and thinkers that came up with different voting schemes as he does discussing the "numbers", as advertised in the title. The stories themselves aren't very engaging, and the book failed to keep my attention and interest.
Dec 28, 2012 rated it liked it
Not what I was expecting: we find here the tale of Pliny's account of the eruption of Vesuvius and read about the medieval romances of Ramon Llull. Decision theory is touched upon in the most tangential fashion. Not that I mind: Szpiro's narratives are interesting and amusing, but the lead word in the title is hardly merited.
Mar 29, 2011 rated it liked it
Shelves: read-2013
Um livro sobre um tema muito interessante, fundamental para qualquer entendimento do processo democrático, mas que sofre pelo estilo demasiado pragmático do autor, principalmente os últimos capítulos o de o texto não está tão bem conseguido.
Ami Iida
May 21, 2015 rated it it was ok
Shelves: game-theory
This book describes a decent respect to election contents.
It applies for the game theory.
But sentence wrote lazy.
I want it to edit more.
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George G. Szpiro is an Israeli-Swiss applied mathematician and journalist, who has emerged as a writer of popular science books.