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

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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
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The Win-Win Solution

Guaranteeing Fair Shares to Everybody

Author: Steven J. Brams,Alan D. Taylor

Publisher: W. W. Norton & Company

ISBN: 9780393320817

Category: Business & Economics

Page: 177

View: 4683

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Offers a technique that is not only fair, but also guarantees that both parties walk away with as much of the "win-win" potential as possible.
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Power, Voting, and Voting Power: 30 Years After

Author: Manfred J Holler,Hannu Nurmi

Publisher: Springer Science & Business Media

ISBN: 3642359299

Category: Business & Economics

Page: 762

View: 4011

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The developments over a thirty-year time span in the study of power, especially voting power, are traced in this book, which provides an up-to-date overview of applications of n-person game theory to the study of power in multimember bodies. Other theories that shed light on power distribution (e.g. aggregation theory) are treated as well. The book revisits the themes discussed in the well-known 1982 publication "Power, Voting and Voting Power" (edited by Manfred J. Holler). Thirty years later this essential topic has been taken up again and many of the authors from its predecessor participate here again in discussing the state-of-the-art, demonstrating the achievements of three decades of intensive research, and pointing the way to key issues for future work.
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Fair Division

From Cake-Cutting to Dispute Resolution

Author: Steven J. Brams,Alan D. Taylor

Publisher: Cambridge University Press

ISBN: 9780521556446

Category: Business & Economics

Page: 272

View: 2926

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Cutting a cake, dividing up the property in an estate, determining the borders in an international dispute - such problems of fair division are ubiquitous. Fair Division treats all these problems and many more through a rigorous analysis of a variety of procedures for allocating goods (or 'bads' like chores), or deciding who wins on what issues, when there are disputes. Starting with an analysis of the well-known cake-cutting procedure, 'I cut, you choose', the authors show how it has been adapted in a number of fields and then analyze fair-division procedures applicable to situations in which there are more than two parties, or there is more than one good to be divided. In particular they focus on procedures which provide 'envy-free' allocations, in which everybody thinks he or she has received the largest portion and hence does not envy anybody else. They also discuss the fairness of different auction and election procedures.
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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: 8819

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A highly accessible book offering a new interpretation and resolution of Arrow's and Sen's theorems.
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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: 2339

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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.
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The Geometry of Efficient Fair Division

Author: Julius B. Barbanel

Publisher: Cambridge University Press

ISBN: 9781139444392

Category: Mathematics

Page: N.A

View: 7755

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What is the best way to divide a 'cake' and allocate the pieces among some finite collection of players? In this book, the cake is a measure space, and each player uses a countably additive, non-atomic probability measure to evaluate the size of the pieces of cake, with different players generally using different measures. The author investigates efficiency properties (is there another partition that would make everyone at least as happy, and would make at least one player happier, than the present partition?) and fairness properties (do all players think that their piece is at least as large as every other player's piece?). He focuses exclusively on abstract existence results rather than algorithms, and on the geometric objects that arise naturally in this context. By examining the shape of these objects and the relationship between them, he demonstrates results concerning the existence of efficient and fair partitions.
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Chaotic Elections!

A Mathematician Looks at Voting

Author: Donald Saari

Publisher: American Mathematical Soc.

ISBN: 9780821886168

Category: Political Science

Page: 159

View: 2415

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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.
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