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.
"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
Table of Contents:
CHAPTER ONE: THE ANTI-DEMOCRAT 1
CHAPTER TWO: THE LETTER WRITER 22
CHAPTER THREE: THE MYSTIC 33
CHAPTER FOUR: THE CARDINAL 50
CHAPTER FIVE: THE OFFICER 60
CHAPTER SIX: THE MARQUIS 73
CHAPTER SEVEN: THE MATHEMATICIAN 89
CHAPTER EIGHT: THE OXFORD DON 100
CHAPTER NINE: THE FOUNDING FATHERS 119
CHAPTER TEN: THE IVY LEAGUERS 134
CHAPTER ELEVEN: THE PESSIMISTS 165
CHAPTER TWELVE: THE QUOTARIANS 187
CHAPTER THIRTEEN: THE POSTMODERNS 202
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