Mathematics and Politics

Strategy, Voting, Power, and Proof

Author: Alan D. Taylor,Allison M. Pacelli

Publisher: Springer Science & Business Media

ISBN: 0387776435

Category: Social Science

Page: 364

View: 2069

As a text for an undergraduate mathematics course for nonmajors, Mathematics and Politics requires no prerequisites in either area while the underlying philosophy involves minimizing algebraic computations and focusing instead on some conceptual aspects of mathematics in the context of important real-world questions in political science. Five major topics are covered including a model of escalation, game theoretic models of international conflict, yes-no voting systems, political power, and social choice. Each topic is discussed in an introductory chapter and revisited in more depth in a later chapter. This new edition has added co-author, Allison Pacelli, and two new chapters on "Fairness" and "More Fairness." The examples and the exercises have been updated and enhanced throughout. Reviews from first edition: This book is well written and has much math of interest. While it is pitched at a non-math audience there is material here that will be new and interesting to the readers... -Sigact News For mathematicians, Taylor's book shows how the social sciences make use of mathematical thinking, in the form of axiomatic systems, and offers a chance to teach this kind of thinking to our students. - The College Mathematics Journal The writing is crisp and the sense of excitement about learning mathematics is seductive. The political conflict examples are well thought out and clear. -Michael C. Munger

Glück, Logik und Bluff

Mathematik in Spiel — Methoden, Ergebnisse und Grenzen

Author: Jörg Bewersdorff

Publisher: Springer-Verlag

ISBN: 3663108139

Category: Mathematics

Page: 357

View: 1303

Glück, Logik und Bluff - drei Begriffe, die abhängig vom Charakter eines Gesellschaftsspieles Wege zum Gewinn weisen. Eng damit verbunden sind drei mathematische Theorien: Die Wahrscheinlichkeitsrechung erlaubt es, die Gewinnchancen in Glücksspielen zu kalkulieren. Von Algorithmen, wie sie auch Schachcomputern zugrundeliegen, handelt die Theorie der kombinatorischen Spiele. Ganz andere Optimierungsansätze, nämlich solche aus der mathematischen Spieltheorie, sind gefragt, wenn Mitspieler wie bei Kartenspielen unterschiedliche Informationsstände über den erreichten Spielstand haben. Anhand vielfältiger (Bei-) Spiele werden Teile der drei Theorien vorgestellt.

The Measurement of Voting Power

Theory and Practice, Problems and Paradoxes

Author: Dan S. Felsenthal,Moshé Machover

Publisher: Edward Elgar Pub


Category: Political Science

Page: 322

View: 7871

'To say that this book is excellent would be an understatement. It is really remarkable. Not only would it help people using power indices to redirect their analysis, but it could also incite game theorists in general to reconsider the bad opinion they have of cooperative game theory (must I say that there are several texts that exist on game theory in which cooperative game theory is hardly mentioned?). In brief, it is very highly recommended to social choice theorists, game theorists (and mathematical economists using game theory), and mathematically-inclined political scientists.' - Maurice Salles, Social Choice and Welfare 'The history of the power indices goes back more than fifty years and is told accurately and completely, for the first time, in this volume. More important, Felsenthal and Machover elucidate the conceptual foundations of the power indices, discover new paradoxes to which the various indices are vulnerable, and draw important lessons, using empirical cases, about the proper measurement and interpretation of voting power.' - Steven Brams, New York University, US 'Dan Felsenthal and Moshe Machover have been writing stimulating and important papers on the voting power indices for several years. This book collects them together and adds new material. It is both mathematically rigorous and politically important. It will become a required reference for anyone working on weighted voting games, whether in US legislatures or the European Union.' - Iain McLean, Nuffield College, Oxford University, UK 'This book pulls no punches in exposing confusions in the orthodox approach to voting power. Its clarity and good sense point the way to a better founded theory.' - Ken Binmore, University College London, UK


Author: Alʹbert Nikolaevich Shiri︠a︡ev,Hans Jürgen Engelbert

Publisher: N.A


Category: Probabilities

Page: 592

View: 8949


Decisions and Elections

Explaining the Unexpected

Author: Donald G. Saari,Donald G. (University of California Saari, Irvine)

Publisher: Cambridge University Press

ISBN: 9780521004046

Category: Business & Economics

Page: 240

View: 3304

A highly accessible book offering a new interpretation and resolution of Arrow's and Sen's theorems.


Author: N.A

Publisher: N.A


Category: Asia

Page: N.A

View: 2294


Chaotic Elections!

A Mathematician Looks at Voting

Author: Donald Saari

Publisher: American Mathematical Soc.

ISBN: 9780821886168

Category: Political Science

Page: 159

View: 5124

What does the 2000 U.S. presidential election have in common with selecting a textbook for a calculus course in your department? Was Ralph Nader's influence on the election of George W. Bush greater than the now-famous chads? In Chaotic Elections!, Don Saari analyzes these questions, placing them in the larger context of voting systems in general. His analysis shows that the fundamental problems with the 2000 presidential election are not with the courts, recounts, or defective ballots, but are caused by the very way Americans vote for president. This expository book shows how mathematics can help to identify and characterize a disturbingly large number of paradoxical situations that result from the choice of a voting procedure. Moreover, rather than being able to dismiss them as anomalies, the likelihood of a dubious election result is surprisingly large. These consequences indicate that election outcomes--whether for president, the site of the next Olympics, the chair of a university department, or a prize winner--can differ from what the voters really wanted. They show that by using an inadequate voting procedure, we can, inadvertently, choose badly. To add to the difficulties, it turns out that the mathematical structures of voting admit several strategic opportunities, which are described. Finally, mathematics also helps identify positive results: By using mathematical symmetries, we can identify what the phrase ``what the voters really want'' might mean and obtain a unique voting method that satisfies these conditions. Saari's book should be required reading for anyone who wants to understand not only what happened in the presidential election of 2000, but also how we can avoid similar problems from appearing anytime any group is making a choice using a voting procedure. Reading this book requires little more than high school mathematics and an interest in how the apparently simple situation of voting can lead to surprising paradoxes.

Ökonomische Theorie der Demokratie

Author: Anthony Downs

Publisher: Mohr Siebeck

ISBN: 9783165290523

Category: Business & Economics

Page: 303

View: 4193

English summary: It was Anthony Downs' objective to create a model dealing with voter and government behavior. In order to do so, he established goals which governments, parties and lobbyists as well as the voters can pursue. To motivate all those concerned, he introduced the self-interest axiom and called for rationality in order to attain these goals. With the help of marginal analysis, each voter determines his/her party differential, which will help to determine each voter's choice at the ballot box and to decide which party's rule will give him/her greater utility in the future. Downs describes how crucial the concept of ideology is to his theory. He maintains that a two-party democracy could not provide stable and effective government unless there is a large measure of ideological consensus amongst its citizens, and that political parties encouraged voters to be irrational by remaining vague and ambiguous. German description: Anthony Downs' inzwischen klassisches Demokratie-Modell des Wahler- und Regierungsverhaltens orientiert sich an der okonomischen Theorie. Er nimmt an, dass politische Parteien und Wahler in der Verfolgung bestimmter, deutlich spezifizierter Ziele optimal handeln. So treffen die Wahler unter Ungewissheit uber den Wahlvorgang und die zukunftige Regierungsbildung ihre Wahl nach dem mutmasslichen Nutzen. Die Regierung versucht, mit Hilfe der Manipulation des Budgets ihre Wiederwahl zu erreichen.Ideologien der Parteien auf der einen Seite, Interessengruppen auf der anderen stellen den Wahlern bzw. der Regierung Informationen zur rationalen Entscheidungsfindung zur Verfugung. Dabei wird deutlich, dass Mehrparteiensysteme und Verhaltniswahlrecht jedes Wahl-Kalkul unlosbar werden lassen. Auf die weiteren Folgerungen fur Demokratie-Forschung und -Verstandnis geht Downs im letzten Teil seines Werkes ausfuhrlich ein.

Fair Representation

Meeting the Ideal of One Man, One Vote

Author: Michel L. Balinski,H. Peyton Young

Publisher: Brookings Institution Press

ISBN: 9780815716341

Category: Political Science

Page: 192

View: 6520

The issue of fair representation will take center stage as U.S. congressional districts are reapportioned based on the 2000 Census. Using U.S. history as a guide, the authors develop a theory of fair representation that establishes various principles for translating state populations—or vote totals of parties—into a fair allocation of congressional seats. They conclude that the current apportionment formula cheats the larger states in favor of the smaller, contrary to the intentions of the founding fathers and compromising the Supreme Court's "one man, one vote" rulings. Balinski and Young interweave the theoretical development with a rich historical account of controversies over representation, and show how many of these principles grew out of political contests in the course of United States history. The result is a work that is at once history, politics, and popular science. The book—updated with data from the 1980 and 1990 Census counts—vividly demonstrates that apportionment deals with the very substance of political power.

Prague Economic Papers

Author: N.A

Publisher: N.A


Category: Czechoslovakia

Page: N.A

View: 540

Quarterly journal of economic theory and policy.

Professor Stewarts mathematische Schätze

Author: Ian Stewart

Publisher: Rowohlt Verlag GmbH

ISBN: 3644017115

Category: Mathematics

Page: 432

View: 1308

Was war noch mal die Catalan’sche Vermutung? Und woher kommt eigentlich das Wurzelsymbol? Was hat die Zahl Pi mit dem Sternenhimmel zu tun? Wer erfand das Gleichheitszeichen? Der britische Matheguru Ian Stewart breitet in diesem Band Schätze aus, die er in Jahrzehnten gesammelt hat: über 180 interessante Matherätsel, Lösungen, Spiele, Tricks, Geschichten, Anekdoten und Logeleien. Zudem ist Stewarts Schatztruhe mit interessanten historischen Exkursen angereichert, zum Beispiel einer kurzen Einführung in das Rechnen der Maya und der alten Ägypter und auch in die Vergangenheit unseres eigenen Rechnens: Wer erfand das Gleichheitszeichen – und warum? Ein Buch zum Blättern und Stöbern, zum Spaßhaben und Dazulernen, für Laien und für Fortgeschrittene.

The new Wigmore

a treatise on evidence : expert evidence

Author: David H. Kaye,David E. Bernstein,Jennifer L. Mnookin,Richard D. Friedman

Publisher: N.A

ISBN: 9780735593534

Category: Law

Page: 806

View: 843


A Mathematical Mosaic

Patterns & Problem Solving

Author: Ravi Vakil

Publisher: Brendan Kelly Pub

ISBN: 9781895997286

Category: Mathematics

Page: 288

View: 6784

Ravi Vakil, described in the San Francisco Chronicle as “a legend in the world of math competitions” has finally released his long-awaited second edition of A Mathematical Mosaic: Patterns & Problem Solving. Regarded by many as a seminal book in the field of mathematics competitions, the first edition of A Mathematical Mosaic has received wide acclaim from mathematics teachers, professors and the mathematics community at large. In a review in The Mathematics Teacher, high school teacher John Cocharo wrote, “Without a doubt, this book is a must for any library, teacher's reference or student's amusement.” André Toom in his review in the Mathematical Monthly observed, “[A Mathematical Mosaic] speaks in an interesting and understandable way about number theory, combinatorics, game theory, geometry, and calculus, to say nothing about magic tricks, puzzles and other digressions. What is most important is that whenever Vakil starts to discuss something, he never leaves the reader without a piece of exact, rigorous knowledge.”


Führungsstrategien der CDU-Vorsitzenden Angela Merkel im innerparteilichen Machtgeflecht 2000-2004

Author: Hajo Schumacher

Publisher: N.A


Category: Women prime ministers

Page: 321

View: 8264


Rational Politics

Decisions, Games, and Strategy

Author: Steven J. Brams

Publisher: N.A


Category: Political Science

Page: 233

View: 3957