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Numbers Rule:
The Vexing Mathematics of Democracy, from Plato to the Present
George G. Szpiro

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 democratic institutions.

In a sweeping narrative that combines history, biography, and mathematics, George Szpiro details the fascinating lives and big ideas of great minds such as Plato, Pliny the Younger, Ramon Llull, Pierre Simon Laplace, Thomas Jefferson, Alexander Hamilton, John von Neumann, and Kenneth Arrow, among many others. Each chapter in this riveting book tells the story of one or more of these visionaries and the problem they sought to overcome, like the Marquis de Condorcet, the eighteenth-century French nobleman who demonstrated that a majority vote in an election might not necessarily result in a clear winner. Szpiro takes readers from ancient Greece and Rome to medieval Europe, from the founding of the American republic and the French Revolution to today's high-stakes elective politics. He explains how mathematical paradoxes and enigmas can crop up in virtually any voting arena, from electing a class president, a pope, or prime minister to the apportionment of seats in Congress.

Numbers Rule describes the trials and triumphs of the thinkers down through the ages who have dared the odds in pursuit of a just and equitable democracy.

George G. Szpiro, PhD, is a mathematician and journalist. He covers Israel and the Middle East for the Swiss daily newspaper Neue Zürcher Zeitung, for which he also writes an award-winning monthly column on mathematics. His books include Poincaré's Prize: The Hundred-Year Quest to Solve One of Math's Greatest Puzzles (Dutton).


"'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

I am a journalist for the Swiss daily "Neue Zürcher Zeitung" and its weekly Sunday edition "NZZ am Sonntag". My beat is Israel and the Middle East. But because I was trained as a mathematician I also do science reporting. On this web site I also present my previous books "Kepler's Conjecture" and "Secret Life of Numbers"

My wife is a sculptor and you are welcome to visit her website here.

Buy Poincare's Prize at Amazon


Poincaré's Prize

The Hundred-Year Quest to Solve One of Math's Greatest Puzzles

Secret Life of Numbers

50 Easy Pieces on How Mathematicians Work And Think

Kepler's conjecture

How Some of the Greatest Minds in History Helped Solve One of the Oldest Math Problems in the World

Neue Zürcher Zeitung

The NZZ is based in Zurich, Switzerland. It is considered one of the leading German-language newspapers, has a circulation of about 160,000 and is read also in Germany, Austria and other countries. Founded in 1780 it is one of the world's oldest newspapers. Until 1969 the NZZ published three different editions a day!.

NZZ am Sonntag

On March 17, 2002 the Neue Zürcher Zeitung started a Sunday paper, named "NZZ am Sonntag." I have a monthly column on mathematics, and also write about other science subjects.

Hard Science

My research articles are not available on line. You may check them out below, and if you are interested in one or more of them please drop me a line.

About George Szpiro
Contact Info
E-Mail: 'my first name spelt backwards' at 'this website' dot 'com'

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