The Mathematics Of Politics Second Edition

Author : E. Arthur Robinson,Daniel H. Ullman
Publisher : CRC Press
Page : 440 pages
File Size : 43,7 Mb
Release : 2016-11-18
Category : Mathematics
ISBN : 9781498798907

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The Mathematics of Politics, Second Edition by E. Arthur Robinson,Daniel H. Ullman Pdf

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.

Author : E. Arthur Robinson,Daniel Ullman
Publisher : Unknown
Page : 128 pages
File Size : 41,5 Mb
Release : 2017
Category : Political science
ISBN : 1315366673

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The Mathematics of Politics by E. Arthur Robinson,Daniel Ullman Pdf

Author : Alan D. Taylor,Allison M. Pacelli
Publisher : Springer Science & Business Media
Page : 378 pages
File Size : 47,5 Mb
Release : 2009-12-29
Category : Social Science
ISBN : 9780387776439

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Mathematics and Politics by Alan D. Taylor,Allison M. Pacelli Pdf

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

Author : Jonathan K. Hodge,Richard E. Klima
Publisher : American Mathematical Soc.
Page : 238 pages
File Size : 51,6 Mb
Release : 2018-10-01
Category : Elections
ISBN : 9781470442873

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The Mathematics of Voting and Elections: A Hands-On Approach by Jonathan K. Hodge,Richard E. Klima Pdf

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.

Author : E. Arthur Robinson, Jr.,Daniel H. Ullman
Publisher : CRC Press
Page : 477 pages
File Size : 55,6 Mb
Release : 2010-12-09
Category : Business & Economics
ISBN : 9781439891179

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A Mathematical Look at Politics by E. Arthur Robinson, Jr.,Daniel H. Ullman Pdf

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.

Author : Jeff Gill
Publisher : Cambridge University Press
Page : 449 pages
File Size : 49,7 Mb
Release : 2006-04-24
Category : Mathematics
ISBN : 9780521834261

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Essential Mathematics for Political and Social Research by Jeff Gill Pdf

"More than ever before, modern social scientists require a basic level of mathematical literacy, yet many students receive only limited mathematical training prior to beginning their research careers. This textbook addresses this dilemma by offering a comprehensive, unified introduction to the essential mathematics of social science. Throughout the book the presentation builds from first principles and eschews unnecessary complexity. Most importantly, the discussion is thoroughly and consistently anchored in real social science applications, with more than 80 research-based illustrations woven into the text and featured in end-of-chapter exercises. Students and researchers alike will find this first-of-its-kind volume to be an invaluable resource."--BOOK JACKET.

Author : Gordon Tullock
Publisher : Ann Arbor : University of Michigan Press
Page : 200 pages
File Size : 44,5 Mb
Release : 1967
Category : Mathematics
ISBN : UOM:39015002397258

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Toward a Mathematics of Politics by Gordon Tullock Pdf

Author : Will H. Moore,David A. Siegel
Publisher : Princeton University Press
Page : 450 pages
File Size : 45,8 Mb
Release : 2013-08-11
Category : Political Science
ISBN : 9780691159171

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A Mathematics Course for Political and Social Research by Will H. Moore,David A. Siegel Pdf

Political science and sociology increasingly rely on mathematical modeling and sophisticated data analysis, and many graduate programs in these fields now require students to take a "math camp" or a semester-long or yearlong course to acquire the necessary skills. Available textbooks are written for mathematics or economics majors, and fail to convey to students of political science and sociology the reasons for learning often-abstract mathematical concepts. A Mathematics Course for Political and Social Research fills this gap, providing both a primer for math novices in the social sciences and a handy reference for seasoned researchers. The book begins with the fundamental building blocks of mathematics and basic algebra, then goes on to cover essential subjects such as calculus in one and more than one variable, including optimization, constrained optimization, and implicit functions; linear algebra, including Markov chains and eigenvectors; and probability. It describes the intermediate steps most other textbooks leave out, features numerous exercises throughout, and grounds all concepts by illustrating their use and importance in political science and sociology. Uniquely designed and ideal for students and researchers in political science and sociology Uses practical examples from political science and sociology Features "Why Do I Care?" sections that explain why concepts are useful Includes numerous exercises Complete online solutions manual (available only to professors, email david.siegel at duke.edu, subject line "Solution Set") Selected solutions available online to students

Author : Steven J. Brams
Publisher : Courier Corporation
Page : 338 pages
File Size : 51,6 Mb
Release : 2013-01-17
Category : Mathematics
ISBN : 9780486143637

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Game Theory and Politics by Steven J. Brams Pdf

DIVMany illuminating and instructive examples of the applications of game theoretic models to problems in political science appear in this volume, which requires minimal mathematical background. 1975 edition. 24 figures. /div

Author : George Szpiro
Publisher : Princeton University Press
Page : 240 pages
File Size : 51,6 Mb
Release : 2020-11-03
Category : History
ISBN : 9780691209081

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Numbers Rule by George Szpiro Pdf

The author takes the general reader on a tour of the mathematical puzzles and paradoxes inherent in voting systems, such as the Alabama Paradox, in which an increase in the number of seats in the Congress could actually lead to a reduced number of representatives for a state, and the Condorcet Paradox, which demonstrates that the winner of elections featuring more than two candidates does not necessarily reflect majority preferences. Szpiro takes a roughly chronological approach to the topic, traveling from ancient Greece to the present and, in addition to offering explanations of the various mathematical conundrums of elections and voting, also offers biographical details on the mathematicians and other thinkers who thought about them, including Plato, Pliny the Younger, Pierre Simon Laplace, Thomas Jefferson, John von Neumann, and Kenneth Arrow.

Author : W.D. Wallis
Publisher : Springer
Page : 103 pages
File Size : 43,7 Mb
Release : 2014-10-08
Category : Mathematics
ISBN : 9783319098104

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The Mathematics of Elections and Voting by W.D. Wallis Pdf

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.

Author : John Stillwell
Publisher : CRC Press
Page : 312 pages
File Size : 51,6 Mb
Release : 2018-04-27
Category : Mathematics
ISBN : 9780429998034

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Yearning for the Impossible by John Stillwell Pdf

Yearning for the Impossible: The Surprising Truth of Mathematics, Second Edition explores the history of mathematics from the perspective of the creative tension between common sense and the "impossible" as the author follows the discovery or invention of new concepts that have marked mathematical progress. The author puts these creations into a broader context involving related "impossibilities" from art, literature, philosophy, and physics. This new edition contains many new exercises and commentaries, clearly discussing a wide range of challenging subjects.

Author : Jonathan K. Hodge,Richard E. Klima
Publisher : Unknown
Page : 255 pages
File Size : 43,9 Mb
Release : 2018
Category : POLITICAL SCIENCE
ISBN : 147044982X

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The Mathematics of Voting and Elections by Jonathan K. Hodge,Richard E. Klima Pdf

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 ca.

Author : Eric Gutstein,Bob Peterson
Publisher : Rethinking Schools
Page : 192 pages
File Size : 52,8 Mb
Release : 2005
Category : Mathematics
ISBN : 9780942961546

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Rethinking Mathematics by Eric Gutstein,Bob Peterson Pdf

In this unique collection, more than 30 articles show how to weave social justice issues throughout the mathematics curriculum, as well as how to integrate mathematics into other curricular areas. Rethinking Mathematics offers teaching ideas, lesson plans, and reflections by practitioners and mathematics educators. This is real-world math-math that helps students analyze problems as they gain essential academic skills. This book offers hope and guidance for teachers to enliven and strengthen their math teaching. It will deepen students' understanding of society and help prepare them to be critical, active participants in a democracy. Blending theory and practice, this is the only resource of its kind.

Author : Eric Steinhart
Publisher : Broadview Press
Page : 250 pages
File Size : 47,8 Mb
Release : 2017-11-21
Category : Philosophy
ISBN : 9781554813452

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More Precisely: The Math You Need to Do Philosophy - Second Edition by Eric Steinhart Pdf

More Precisely is a rigorous and engaging introduction to the mathematics necessary to do philosophy. Eric Steinhart provides lucid explanations of many basic mathematical concepts and sets out the most commonly used notational conventions. He also demonstrates how mathematics applies to fundamental issues in various branches of philosophy, including metaphysics, philosophy of language, epistemology, and ethics. This second edition adds a substantial section on decision and game theory, as well as a chapter on information theory and the efficient coding of information.