A Mathematical Look At Politics

Author : E. Arthur Robinson, Jr.,Daniel H. Ullman
Publisher : CRC Press
Page : 0 pages
File Size : 43,9 Mb
Release : 2010-12-09
Category : Business & Economics
ISBN : 1439819831

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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 : E. Arthur Robinson,Daniel H. Ullman
Publisher : CRC Press
Page : 478 pages
File Size : 51,9 Mb
Release : 2016-11-18
Category : Mathematics
ISBN : 9781498798884

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The Mathematics of Politics 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, Jr.,Daniel H. Ullman
Publisher : CRC Press
Page : 477 pages
File Size : 53,6 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 : Sherif El-Helaly
Publisher : Springer
Page : 264 pages
File Size : 40,6 Mb
Release : 2019-05-21
Category : Mathematics
ISBN : 9783030147686

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The Mathematics of Voting and Apportionment by Sherif El-Helaly Pdf

This textbook contains a rigorous exposition of the mathematical foundations of two of the most important topics in politics and economics: voting and apportionment, at the level of upper undergraduate and beginning graduate students. It stands out among comparable books by providing, in one volume, an extensive and mathematically rigorous treatment of these two topics. The text’s three chapters cover social choice, yes-no voting, and apportionment, respectively, and can be covered in any order, allowing teachers ample flexibility. Each chapter begins with an elementary introduction and several examples to motivate the concepts and to gradually lead to more advanced material. Landmark theorems are presented with detailed and streamlined proofs; those requiring more complex proofs, such as Arrow’s theorems on dictatorship, Gibbard’s theorem on oligarchy, and Gärdenfors’ theorem on manipulation, are broken down into propositions and lemmas in order to make them easier to grasp. Simple and intuitive notations are emphasized over non-standard, overly complicated symbols. Additionally, each chapter ends with exercises that vary from computational to “prove or disprove” types. The Mathematics of Voting and Apportionment will be particularly well-suited for a course in the mathematics of voting and apportionment for upper-level undergraduate and beginning graduate students in economics, political science, or philosophy, or for an elective course for math majors. In addition, this book will be a suitable read for to any curious mathematician looking for an exposition to these unpublicized mathematical applications. No political science prerequisites are needed. Mathematical prerequisites (included in the book) are minimal: elementary concepts in combinatorics, graph theory, order relations, and the harmonic and geometric means. What is needed most is the level of maturity that enables the student to think logically, derive results from axioms and hypotheses, and intuitively grasp logical notions such as “contrapositive” and “counterexample.”

Author : P. E. Johnson
Publisher : Elsevier
Page : 225 pages
File Size : 44,5 Mb
Release : 2014-06-28
Category : Business & Economics
ISBN : 9781483297743

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Formal Theories of Politics by P. E. Johnson Pdf

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.

Author : Jordan Ellenberg
Publisher : Penguin Press
Page : 480 pages
File Size : 52,6 Mb
Release : 2014-05-29
Category : Mathematics
ISBN : 9781594205224

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How Not to Be Wrong by Jordan Ellenberg Pdf

A brilliant tour of mathematical thought and a guide to becoming a better thinker, How Not to Be Wrong shows that math is not just a long list of rules to be learned and carried out by rote. Math touches everything we do; It's what makes the world make sense. Using the mathematician's methods and hard-won insights-minus the jargon-professor and popular columnist Jordan Ellenberg guides general readers through his ideas with rigor and lively irreverence, infusing everything from election results to baseball to the existence of God and the psychology of slime molds with a heightened sense of clarity and wonder. Armed with the tools of mathematics, we can see the hidden structures beneath the messy and chaotic surface of our daily lives. How Not to Be Wrong shows us how--Publisher's description.

Author : E. Arthur Robinson,Daniel H. Ullman
Publisher : CRC Press
Page : 440 pages
File Size : 48,8 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 : Gordon Tullock
Publisher : Ann Arbor : University of Michigan Press
Page : 200 pages
File Size : 55,5 Mb
Release : 1967
Category : Mathematics
ISBN : UOM:39015002397266

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Toward a Mathematics of Politics by Gordon Tullock Pdf

Author : Anonim
Publisher : Unknown
Page : 0 pages
File Size : 43,7 Mb
Release : 1973
Category : Electronic
ISBN : OCLC:16251772

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Mathematical Approaches to Politics by Anonim Pdf

Author : Karl Wolfgang Deutsch,Antoine H. Stoetzel
Publisher : San Francisco : Jossey-Bass
Page : 498 pages
File Size : 53,7 Mb
Release : 1973
Category : Political Science
ISBN : UOM:39015002394743

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Mathematical Approaches to Politics by Karl Wolfgang Deutsch,Antoine H. Stoetzel Pdf

Author : Anatol Rapoport
Publisher : University of Michigan Press
Page : 420 pages
File Size : 45,6 Mb
Release : 1960
Category : Business & Economics
ISBN : 047208741X

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Fights, Games, and Debates by Anatol Rapoport Pdf

A scientifically grounded method by which we can understand human conflict in all its forms

Author : Alan D. Taylor
Publisher : Springer Science & Business Media
Page : 302 pages
File Size : 54,5 Mb
Release : 1995-03-09
Category : Mathematics
ISBN : 9780387943916

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Mathematics and Politics by Alan D. Taylor Pdf

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.

Author : Jeff Gill
Publisher : Cambridge University Press
Page : 449 pages
File Size : 54,6 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 : David C. Vella
Publisher : Cambridge University Press
Page : 543 pages
File Size : 42,7 Mb
Release : 2021-03-11
Category : Business & Economics
ISBN : 9781108476256

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Invitation to Linear Programming and Game Theory by David C. Vella Pdf

Discover interplay between matrices, linear programming, and game theory at an introductory level, requiring only high school algebra and curiosity.

Author : Will H. Moore,David A. Siegel
Publisher : Princeton University Press
Page : 456 pages
File Size : 49,8 Mb
Release : 2013-07-24
Category : Political Science
ISBN : 9781400848614

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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