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

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

George G. Szpiro

Language: English

Pages: 240

ISBN: 0691139946

Format: PDF / Kindle (mobi) / ePub


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.

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Was not to be a successful experiment either. Dionysius II, jealous of his more capable uncle, sent Dion into exile. Plato himself was ill prepared for the intrigues at the court of Syracuse and with his friend gone, he remained without a protector. This was not an enviable situation for a sixty-year-old philosopher to be in. Plato took the wise course of action and left Syracuse. Back in Athens, he returned to the Academy that he had founded twenty years earlier. Six years later, Plato was again.

Club and the health club to the nursery it is obvious that the majority wants a cafeteria.” Nobody bothers to find out whether the nursery would have bested the cafeteria if a direct vote had been taken. And this is how the personnel director can have her way. 80 THE MARQUIS Hence with good reason the deeply troubled Condorcet feared that the paradox poses great dangers. Since ignorant masses could be manipulated by corrupt politicians and charlatans he decided that the people had to be.

After having being assured that the Lee’s Reader would concern himself only with experimental findings. The committee meeting was set for Thursday, December 18. On the Friday preceding the meeting, Dodgson attended an oral examination of candidates and then spent the rest of the day on various chores. In the eve103 CHAPTER EIGHT ning it occurred to him to investigate the subject of the upcoming decision. It turned out to be much more complicated than he had initially expected. With great.

Laboratories, scientists in private companies—work outside the framework of government to ensure their independence. So essential has the academy’s service to government become that over the years Congress and the White House have repeatedly issued legislation and executive orders that reaffirm its unique role. In contrast to the American Political Science Association the NAS did take up the gauntlet. A commission was created that was to decide on the best method to use for apportionment. The.

Way and therefore was the most acceptable. Nevertheless, the whole affair left a bad taste because on the theoretical level the question had not been settled at all. One could not get rid of the arbitrariness to which the mathematical imprecision of the rounding process gives rise. It was only partly tongue-incheek that some wags suggested explicitly introducing randomness into the apportionment method. They proposed a roulette-based method to distribute fractional seats. The width of each cell.

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