Mathematics and Politics

Strategy, Voting, Power and Proof

Author: Alan D. Taylor

Publisher: Springer Science & Business Media

ISBN: 1461225124

Category: Mathematics

Page: 284

View: 4862

interest in a particular application, however, often depends on his or hergeneralinterestintheareainwhichtheapplicationistakingplace. My experience at Union College has been that there is a real advan tage in having students enter the course knowing thatvirtually all the applications will focus on a single discipline-in this case, political science. The level ofpresentation assumes no college-level mathematicalor social science prerequisites. The philosophy underlying the approach we have taken in this book is based on the sense that we (mathemati cians)havetendedtomaketwoerrorsinteachingnonsciencestudents: wehaveoverestimatedtheircomfortwithcomputationalmaterial,and we have underestimated their ability to handle conceptual material. Thus, while there is very little algebra (and certainly no calculus) in our presentation, we have included numerous logical arguments that students in the humanitiesand the socialscienceswill find accessible, but not trivial. The book contains five main topics: a m.odel of escalation, game theoretic models of international conflict, yes-no voting systems, political power, and social choice. The first partofthe text is made up of a single chapter devoted to each topic. The second part of the text revisits each topic, again with a single chapter devoted to each. The organizationofthe bookisbasedonpedagogicalconsiderations, with the material becoming somewhat more sophisticated as one moves through the ten chapters. On the other hand, within any given chap terthere is little reliance on material from earlierchapters, except for those devoted to the same topic.
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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: 3021

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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Mathematics and Politics

Strategy, Voting, Power, and Proof

Author: Alan D. Taylor,Allison M. Pacelli

Publisher: Springer Science & Business Media

ISBN: 0387776451

Category: Social Science

Page: 364

View: 3857

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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Mathematics and Politics

Strategy, Voting, Power and Proof

Author: Alan D. Taylor

Publisher: Springer Science & Business Media

ISBN: 9780387943916

Category: Mathematics

Page: 284

View: 3410

interest in a particular application, however, often depends on his or hergeneralinterestintheareainwhichtheapplicationistakingplace. My experience at Union College has been that there is a real advan tage in having students enter the course knowing thatvirtually all the applications will focus on a single discipline-in this case, political science. The level ofpresentation assumes no college-level mathematicalor social science prerequisites. The philosophy underlying the approach we have taken in this book is based on the sense that we (mathemati cians)havetendedtomaketwoerrorsinteachingnonsciencestudents: wehaveoverestimatedtheircomfortwithcomputationalmaterial,and we have underestimated their ability to handle conceptual material. Thus, while there is very little algebra (and certainly no calculus) in our presentation, we have included numerous logical arguments that students in the humanitiesand the socialscienceswill find accessible, but not trivial. The book contains five main topics: a m.odel of escalation, game theoretic models of international conflict, yes-no voting systems, political power, and social choice. The first partofthe text is made up of a single chapter devoted to each topic. The second part of the text revisits each topic, again with a single chapter devoted to each. The organizationofthe bookisbasedonpedagogicalconsiderations, with the material becoming somewhat more sophisticated as one moves through the ten chapters. On the other hand, within any given chap terthere is little reliance on material from earlierchapters, except for those devoted to the same topic.
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Mathematics and Democracy

Designing Better Voting and Fair-Division Procedures

Author: Steven J. Brams

Publisher: Princeton University Press

ISBN: 1400835593

Category: Science

Page: 392

View: 8848

Voters today often desert a preferred candidate for a more viable second choice to avoid wasting their vote. Likewise, parties to a dispute often find themselves unable to agree on a fair division of contested goods. In Mathematics and Democracy, Steven Brams, a leading authority in the use of mathematics to design decision-making processes, shows how social-choice and game theory could make political and social institutions more democratic. Using mathematical analysis, he develops rigorous new procedures that enable voters to better express themselves and that allow disputants to divide goods more fairly. One of the procedures that Brams proposes is "approval voting," which allows voters to vote for as many candidates as they like or consider acceptable. There is no ranking, and the candidate with the most votes wins. The voter no longer has to consider whether a vote for a preferred but less popular candidate might be wasted. In the same vein, Brams puts forward new, more equitable procedures for resolving disputes over divisible and indivisible goods.
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Mathematics of Social Choice

Voting, Compensation, and Division

Author: Christoph Bo”rgers

Publisher: SIAM

ISBN: 0898717620

Category: Elections

Page: 245

View: 1769

Mathematics of Social Choice is a fun and accessible book that looks at the choices made by groups of people with different preferences, needs, and interests. Divided into three parts, the text first examines voting methods for selecting or ranking candidates. A brief second part addresses compensation problems wherein an indivisible item must be assigned to one of several people who are equally entitled to ownership of the item, with monetary compensation paid to the others. The third part discusses the problem of sharing a divisible resource among several people. Mathematics of Social Choice can be used by undergraduates studying mathematics and students whose only mathematical background is elementary algebra. More advanced material can be skipped without any loss of continuity. The book can also serve as an easy introduction to topics such as the Gibbard-Satterthwaite theorem, Arrow's theorem, and fair division for readers with more mathematical background.
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Numbers Rule

The Vexing Mathematics of Democracy, from Plato to the Present

Author: George G. Szpiro

Publisher: Princeton University Press

ISBN: 9781400834440

Category: Mathematics

Page: 240

View: 6666

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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Chaotic Elections!

A Mathematician Looks at Voting

Author: Donald Saari

Publisher: American Mathematical Soc.

ISBN: 9780821886168

Category: Political Science

Page: 159

View: 9452

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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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: 2720

Fair Division, unlike most research on fairness in the social sciences and mathematics, is devoted solely to the analysis of constructive procedures for actually dividing things up and resolving disputes, including indivisible items or issues, such as the marital property in a divorce or sovereignty in an international dispute.
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The Mathematics of Politics, Second Edition

Author: E. Arthur Robinson,Daniel H. Ullman

Publisher: CRC Press

ISBN: 149879890X

Category: Mathematics

Page: 477

View: 747

It is because mathematics is often misunderstood, it is commonly believed it has nothing to say about politics. The high school experience with mathematics, for so many the lasting impression of the subject, suggests that mathematics is the study of numbers, operations, formulas, and manipulations of symbols. Those believing this is the extent of mathematics might conclude mathematics has no relevance to politics. This book counters this impression. The second edition of this popular book focuses on mathematical reasoning about politics. In the search for ideal ways to make certain kinds of decisions, a lot of wasted effort can be averted if mathematics can determine that finding such an ideal is actually impossible in the first place. In the first three parts of this book, we address the following three political questions: (1) Is there a good way to choose winners of elections? (2) Is there a good way to apportion congressional seats? (3) Is there a good way to make decisions in situations of conflict and uncertainty? In the fourth and final part of this book, we examine the Electoral College system that is used in the United States to select a president. There we bring together ideas that are introduced in each of the three earlier parts of the book.
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The Mathematics of Voting and Elections: A Hands-On Approach: Second Edition

Author: Jonathan K. Hodge,Richard E. Klima

Publisher: American Mathematical Soc.

ISBN: 1470442876

Category: Elections

Page: 238

View: 2204

The Mathematics of Voting and Elections: A Hands-On Approach, Second Edition, is an inquiry-based approach to the mathematics of politics and social choice. The aim of the book is to give readers who might not normally choose to engage with mathematics recreationally the chance to discover some interesting mathematical ideas from within a familiar context, and to see the applicability of mathematics to real-world situations. Through this process, readers should improve their critical thinking and problem solving skills, as well as broaden their views of what mathematics really is and how it can be used in unexpected ways. The book was written specifically for non-mathematical audiences and requires virtually no mathematical prerequisites beyond basic arithmetic. At the same time, the questions included are designed to challenge both mathematical and non-mathematical audiences alike. More than giving the right answers, this book asks the right questions. The book is fun to read, with examples that are not just thought-provoking, but also entertaining. It is written in a style that is casual without being condescending. But the discovery-based approach of the book also forces readers to play an active role in their learning, which should lead to a sense of ownership of the main ideas in the book. And while the book provides answers to some of the important questions in the field of mathematical voting theory, it also leads readers to discover new questions and ways to approach them. In addition to making small improvements in all the chapters, this second edition contains several new chapters. Of particular interest might be Chapter 12 which covers a host of topics related to gerrymandering.
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Social Choice and the Mathematics of Manipulation

Author: Alan D. Taylor

Publisher: Cambridge University Press

ISBN: 9780521008839

Category: Mathematics

Page: 176

View: 3153

A mathematical look at why it is impossible to devise a completely unmanipulable voting system, first published in 2005.
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The Mathematics of Elections and Voting

Author: W.D. Wallis

Publisher: Springer

ISBN: 3319098101

Category: Mathematics

Page: 96

View: 8132

This title takes an in-depth look at the mathematics in the context of voting and electoral systems, with focus on simple ballots, complex elections, fairness, approval voting, ties, fair and unfair voting, and manipulation techniques. The exposition opens with a sketch of the mathematics behind the various methods used in conducting elections. The reader is lead to a comprehensive picture of the theoretical background of mathematics and elections through an analysis of Condorcet’s Principle and Arrow’s Theorem of conditions in electoral fairness. Further detailed discussion of various related topics include: methods of manipulating the outcome of an election, amendments, and voting on small committees. In recent years, electoral theory has been introduced into lower-level mathematics courses, as a way to illustrate the role of mathematics in our everyday life. Few books have studied voting and elections from a more formal mathematical viewpoint. This text will be useful to those who teach lower level courses or special topics courses and aims to inspire students to understand the more advanced mathematics of the topic. The exercises in this text are ideal for upper undergraduate and early graduate students, as well as those with a keen interest in the mathematics behind voting and elections.
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A Mathematical Look at Politics

Author: E. Arthur Robinson, Jr.,Daniel H. Ullman

Publisher: CRC Press

ISBN: 1439891176

Category: Business & Economics

Page: 477

View: 1939

What Ralph Nader's spoiler role in the 2000 presidential election tells us about the American political system. Why Montana went to court to switch the 1990 apportionment to Dean’s method. How the US tried to use game theory to win the Cold War, and why it didn’t work. When students realize that mathematical thinking can address these sorts of pressing concerns of the political world it naturally sparks their interest in the underlying mathematics. A Mathematical Look at Politics is designed as an alternative to the usual mathematics texts for students in quantitative reasoning courses. It applies the power of mathematical thinking to problems in politics and public policy. Concepts are precisely defined. Hypotheses are laid out. Propositions, lemmas, theorems, and corollaries are stated and proved. Counterexamples are offered to refute conjectures. Students are expected not only to make computations but also to state results, prove them, and draw conclusions about specific examples. Tying the liberal arts classroom to real-world mathematical applications, this text is more deeply engaging than a traditional general education book that surveys the mathematical landscape. It aims to instill a fondness for mathematics in a population not always convinced that mathematics is relevant to them.
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Chance, Strategy, and Choice

An Introduction to the Mathematics of Games and Elections

Author: Samuel Bruce Smith

Publisher: Cambridge University Press

ISBN: 1107084520

Category: Business & Economics

Page: 352

View: 8970

Games and elections are fundamental activities in society with applications in economics, political science, and sociology. These topics offer familiar, current, and lively subjects for a course in mathematics. This classroom-tested textbook, primarily intended for a general education course in game theory at the freshman or sophomore level, provides an elementary treatment of games and elections. Starting with basics such as gambling, zero-sum and combinatorial games, Nash equilibria, social dilemmas, and fairness and impossibility theorems for elections, the text then goes further into the theory with accessible proofs of advanced topics such as the Sprague–Grundy theorem and Arrow's impossibility theorem. • Uses an integrative approach to probability, game, and social choice theory • Provides a gentle introduction to the logic of mathematical proof, thus equipping readers with the necessary tools for further mathematical studies • Contains numerous exercises and examples of varying levels of difficulty • Requires only a high school mathematical background.
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Tweeting to Power

The Social Media Revolution in American Politics

Author: Jason Gainous,Kevin M. Wagner

Publisher: Oxford University Press

ISBN: 0199965072

Category: Business & Economics

Page: 190

View: 1795

Using theory and data, Gainous and Wagner illustrate how online social media is bypassing traditional media and creating new forums for the exchange of political information and campaigning.
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Democratic Reason

Politics, Collective Intelligence, and the Rule of the Many

Author: Hélène Landemore

Publisher: Princeton University Press

ISBN: 0691155658

Category: Business & Economics

Page: 279

View: 5444

Individual decision making can often be wrong due to misinformation, impulses, or biases. Collective decision making, on the other hand, can be surprisingly accurate. In Democratic Reason, Hélène Landemore demonstrates that the very factors behind the superiority of collective decision making add up to a strong case for democracy. She shows that the processes and procedures of democratic decision making form a cognitive system that ensures that decisions taken by the many are more likely to be right than decisions taken by the few. Democracy as a form of government is therefore valuable not only because it is legitimate and just, but also because it is smart. Landemore considers how the argument plays out with respect to two main mechanisms of democratic politics: inclusive deliberation and majority rule. In deliberative settings, the truth-tracking properties of deliberation are enhanced more by inclusiveness than by individual competence. Landemore explores this idea in the contexts of representative democracy and the selection of representatives. She also discusses several models for the "wisdom of crowds" channeled by majority rule, examining the trade-offs between inclusiveness and individual competence in voting. When inclusive deliberation and majority rule are combined, they beat less inclusive methods, in which one person or a small group decide. Democratic Reason thus establishes the superiority of democracy as a way of making decisions for the common good.
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Affective Intelligence and Political Judgment

Author: George E. Marcus,W. Russell Neuman,Michael MacKuen

Publisher: University of Chicago Press

ISBN: 9780226504681

Category: Philosophy

Page: 199

View: 8948

This work draws on research in neuroscience, physiology, and experimental psychology to conceptualize habit and reason as two mental states that interact in a delicate, highly functional balance controlled by emotion. It sheds light on a range of political behaviour, including party identification.
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Gaming the Vote

Why Elections Aren't Fair (and What We Can Do About It)

Author: William Poundstone

Publisher: Macmillan

ISBN: 9780809048922

Category: Political Science

Page: 352

View: 2482

Offers a critical assessment of fundamental flaws in the American electoral system, looking at how a minor "spoiler" candidate can affect the election by taking enough votes away from the most popular candidate to tip the election to another, and proposes a simple but fair solution designed to transform the electoral system.
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Building Red America

The New Conservative Coalition and the Drive for Permanent Power

Author: Thomas B. Edsall

Publisher: Basic Books

ISBN: 0465018165

Category: Political Science

Page: 320

View: 6832

This is a masterful-and disturbing-work of political journalism that challenges all of us to wake up and take heed
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