Mathematics and Politics

Strategy, Voting, Power and Proof

Author: Alan D. Taylor

Publisher: Springer Science & Business Media

ISBN: 1461225124

Category: Mathematics

Page: 284

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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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The Mathematics of Politics

Author: E. Arthur Robinson,Daniel H. Ullman

Publisher: CRC Press

ISBN: 1498798888

Category: Mathematics

Page: 459

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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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Formal Theories of Politics

Mathematical Modelling in Political Science

Author: P. E. Johnson

Publisher: Elsevier

ISBN: 1483297748

Category: Political Science

Page: 210

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Formal Theories of Politics demonstrates the role of formal mathematical models in political science, and aims to convey a sense of the questions and methods which govern the political science research agenda. While there is still much interest in empirical patterns of voting behaviour and public opinion data, there has been substantial growth in emphasis on mathematical theory as a technique for the derivation of testable hypotheses. Topics discussed include: optimal candidate strategies and equilibria in competitive elections; voting agendas and parliamentary procedure in the multidimensional events; revolution, repression and inequality as outputs of dynamics systems. The mathematical techniques are widely varied, including game theory, functional analysis, differential equations, expert systems, stochastic processes and statistical models.
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Internationalisation and Globalisation in Mathematics and Science Education

Author: Bill Atweh,Angela Calabrese Barton,Marcelo C. Borba,Noel Gough,Christine Keitel-Kreidt,Catherine Vistro-Yu,Renuka Vithal

Publisher: Springer Science & Business Media

ISBN: 140208790X

Category: Education

Page: 542

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This book aims to develop theoretical frameworks of the phenomena of internationalisation and globalisation and identify related ethical, moral, political and economic issues facing mathematics and science educators. It provides a wide representation of views some of which are not often represented in international publications. This is the first book to deal with issues of globalisation and internationalisation in mathematics and science education.
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Political Psychology

Situations, Individuals, and Cases

Author: David Patrick Houghton

Publisher: Routledge

ISBN: 1135855498

Category: Political Science

Page: 296

View: 6602

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What shapes political behavior more: the situations in which individuals find themselves, or the internal psychological makeup—beliefs, values, and so on—of those individuals? This is perhaps the leading division within the psychological study of politics today. This text provides a concise, readable, and conceptually-organized introduction to the topic of political psychology by examining this very question. Using this situationism-dispositionism framework—which roughly parallels the concerns of social and cognitive psychology—this book focuses on such key explanatory mechanisms as behaviorism, obedience, personality, groupthink, cognition, affect, emotion, and neuroscience to explore topics ranging from voting behavior and racism to terrorism and international relations. Houghton's clear and engaging examples directly challenge students to place themselves in both real and hypothetical situations which involve intense moral and political dilemmas. This highly readable text will provide students with the conceptual foundation they need to make sense of the rapidly changing and increasingly important field of political psychology.
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Applying Fuzzy Mathematics to Formal Models in Comparative Politics

Author: Terry D. Clark,Jennifer M. Larson,John N. Mordeson,Joshua D. Potter,Mark J. Wierman

Publisher: Springer Science & Business Media

ISBN: 3540774602

Category: Computers

Page: 214

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This book explores the intersection of fuzzy mathematics and the spatial modeling of preferences in political science. Beginning with a critique of conventional modeling approaches predicated on Cantor set theoretical assumptions, the authors outline the potential benefits of a fuzzy approach to the study of ambiguous or uncertain preference profiles. While crisp models assume that ambiguity is a form of confusion emerging from imperfect information about policy options, the authors argue instead that some level of ambiguity is innate in human preferences and social interaction. What fuzzy mathematics offers the researcher, then, is a precise tool with which he can model the inherently imprecise dimensions of nuanced empirical reality. Moving beyond the limited treatment fuzzy methodologies have received in extant political science literature, this book develops single- and multidimensional models of fuzzy preference landscapes and characterizes the surprisingly high levels of stability that emerge from interactions between players operating within these models. The material presented makes it a good text for a graduate seminar in formal modeling. It is also suitable as an introductory text in fuzzy mathematics for graduate and advanced undergraduate students.
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The Mathematics of Voting and Elections

A Hands-on Approach

Author: Jonathan K. Hodge

Publisher: American Mathematical Soc.

ISBN: 9780821872628

Category: Mathematics

Page: 226

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The Mathematics of Voting and Elections: A Hands-on Approach will help you discover answers to these and many other questions. Easily accessible to anyone interested in the subject, the book requires virtually no prior mathematical experience beyond basic arithmetic, and includes numerous examples and discussions regarding actual elections from politics and popular culture.
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Critical Mathematics Education

Theory, Praxis and Reality

Author: Paul Ernest,Bharath Sriraman,Nuala Ernest

Publisher: IAP

ISBN: 1681232618

Category: Education

Page: 357

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Mathematics is traditionally seen as the most neutral of disciplines, the furthest removed from the arguments and controversy of politics and social life. However, critical mathematics challenges these assumptions and actively attacks the idea that mathematics is pure, objective, and value?neutral. It argues that history, society, and politics have shaped mathematics—not only through its applications and uses but also through molding its concepts, methods, and even mathematical truth and proof, the very means of establishing truth. Critical mathematics education also attacks the neutrality of the teaching and learning of mathematics, showing how these are value?laden activities indissolubly linked to social and political life. Instead, it argues that the values of openness, dialogicality, criticality towards received opinion, empowerment of the learner, and social/political engagement and citizenship are necessary dimensions of the teaching and learning of mathematics, if it is to contribute towards democracy and social justice. This book draws together critical theoretic contributions on mathematics and mathematics education from leading researchers in the field. Recurring themes include: The natures of mathematics and critical mathematics education, issues of epistemology and ethics; Ideology, the hegemony of mathematics, ethnomathematics, and real?life education; Capitalism, globalization, politics, social class, habitus, citizenship and equity. The book demonstrates the links between these themes and the discipline of mathematics, and its critical teaching and learning. The outcome is a groundbreaking collection unified by a shared concern with critical perspectives of mathematics and education, and of the ways they impact on practice.
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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: 4326

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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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Reviving Ancient Chinese Mathematics

Mathematics, History and Politics in the Work of Wu Wen-Tsun

Author: Jiri Hudecek

Publisher: Routledge

ISBN: 1134468253

Category: History

Page: 210

View: 636

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Twentieth-century China has been caught between a desire to increase its wealth and power in line with other advanced nations, which, by implication, means copying their institutions, practices and values, whilst simultaneously seeking to preserve China’s independence and historically formed identity. Over time, Chinese philosophers, writers, artists and politicians have all sought to reconcile these goals and this book shows how this search for a Chinese way penetrated even the most central, least contested area of modernity: science. Reviving Ancient Chinese Mathematics is a study of the life of one of modern China’s most admired scientific figures, the mathematician Wu Wen-Tsun. Negotiating the conflict between progress and tradition, he found a path that not only ensured his political and personal survival, but which also brought him renown as a mathematician of international status who claimed that he stood outside the dominant western tradition of mathematics. Wu Wen-Tsun’s story highlights crucial developments and contradictions in twentieth -century China, the significance of which extends far beyond the field of mathematics. On one hand lies the appeal of radical scientific modernity, "mechanisation" in all its forms, and competitiveness within the international scientific community. On the other is an anxiety to preserve national traditions and make them part of the modernisation project. Moreover, Wu’s intellectual development also reflects the complex relationship between science and Maoist ideology, because his turn to history was powered by his internalisation of certain aspects of Maoist ideology, including its utilitarian philosophy of science. This book traces how Wu managed to combine political success and international scientific eminence, a story that has wider implications for a new century of increasing Chinese activity in the sciences. As such, it will be of great interest to students and scholars of Chinese history, the history of science and the history and philosophy of mathematics.
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