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Author: E. Arthur Robinson Jr.
Publisher: CRC Press
ISBN: 1439891176
Category : Business & Economics
Languages : en
Pages : 472
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Book Description
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 pres
Author: E. Arthur Robinson, Jr.
Publisher: CRC Press
ISBN: 9781439819838
Category : Business & Economics
Languages : en
Pages : 0
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Book Description
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 Jr.
Publisher: CRC Press
ISBN: 1439891176
Category : Business & Economics
Languages : en
Pages : 472
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Book Description
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 pres
Author: E. Arthur Robinson
Publisher: CRC Press
ISBN: 1498798888
Category : Mathematics
Languages : en
Pages : 478
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Book Description
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: Alan D. Taylor
Publisher: Springer Science & Business Media
ISBN: 0387776435
Category : Social Science
Languages : en
Pages : 378
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Book Description
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: Sherif El-Helaly
Publisher: Springer
ISBN: 3030147681
Category : Mathematics
Languages : en
Pages : 264
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Book Description
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: Jordan Ellenberg
Publisher: Penguin
ISBN: 0143127535
Category : Mathematics
Languages : en
Pages : 482
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Book Description
“Witty, compelling, and just plain fun to read . . ." —Evelyn Lamb, Scientific American The Freakonomics of math—a math-world superstar unveils the hidden beauty and logic of the world and puts its power in our hands The math we learn in school can seem like a dull set of rules, laid down by the ancients and not to be questioned. In How Not to Be Wrong, Jordan Ellenberg shows us how terribly limiting this view is: Math isn’t confined to abstract incidents that never occur in real life, but rather touches everything we do—the whole world is shot through with it. Math allows us to see the hidden structures underneath the messy and chaotic surface of our world. It’s a science of not being wrong, hammered out by centuries of hard work and argument. Armed with the tools of mathematics, we can see through to the true meaning of information we take for granted: How early should you get to the airport? What does “public opinion” really represent? Why do tall parents have shorter children? Who really won Florida in 2000? And how likely are you, really, to develop cancer? How Not to Be Wrong presents the surprising revelations behind all of these questions and many more, using the mathematician’s method of analyzing life and exposing the hard-won insights of the academic community to the layman—minus the jargon. Ellenberg chases mathematical threads through a vast range of time and space, from the everyday to the cosmic, encountering, among other things, baseball, Reaganomics, daring lottery schemes, Voltaire, the replicability crisis in psychology, Italian Renaissance painting, artificial languages, the development of non-Euclidean geometry, the coming obesity apocalypse, Antonin Scalia’s views on crime and punishment, the psychology of slime molds, what Facebook can and can’t figure out about you, and the existence of God. Ellenberg pulls from history as well as from the latest theoretical developments to provide those not trained in math with the knowledge they need. Math, as Ellenberg says, is “an atomic-powered prosthesis that you attach to your common sense, vastly multiplying its reach and strength.” With the tools of mathematics in hand, you can understand the world in a deeper, more meaningful way. How Not to Be Wrong will show you how.
Author: Alan D. Taylor
Publisher: Cambridge University Press
ISBN: 0521810523
Category : Business & Economics
Languages : en
Pages : 191
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Book Description
Honesty in voting, it turns out, is not always the best policy. Indeed, in the early 1970s, Allan Gibbard and Mark Satterthwaite, building on the seminal work of Nobel laureate Kenneth Arrow, proved that with three or more alternatives there is no reasonable voting system that is non-manipulable; voters will always have an opportunity to benefit by submitting a disingenuous ballot. The ensuing decades produced a number of theorems of striking mathematical naturality that dealt with the manipulability of voting systems. This 2005 book presents many of these results from the last quarter of the twentieth century, especially the contributions of economists and philosophers, from a mathematical point of view, with many new proofs. The presentation is almost completely self-contained, and requires no prerequisites except a willingness to follow rigorous mathematical arguments. Mathematics students, as well as mathematicians, political scientists, economists and philosophers will learn why it is impossible to devise a completely unmanipulable voting system.
Author: Christopher James Phillips
Publisher: University of Chicago Press
ISBN: 022618496X
Category : Education
Languages : en
Pages : 242
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Book Description
An era of sweeping cultural change in America, the postwar years saw the rise of beatniks and hippies, the birth of feminism, and the release of the first video game. This book examines the rise and fall of the new math as a marker of the period's political and social ferment.
Author: George Szpiro
Publisher: Princeton University Press
ISBN: 0691209081
Category : History
Languages : en
Pages : 240
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Book Description
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: P. E. Johnson
Publisher: Elsevier
ISBN: 1483297748
Category : Business & Economics
Languages : en
Pages : 225
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Book Description
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.
