Mathematics And Democracy

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.

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.

In Democracy and Mathematics Education, Kurt Stemhagen and Catherine Henney develop a way of thinking about the nature and purposes of math that is inclusive, participatory, and thoroughly human. They use these ideas to create a school mathematics experience that can enhance students’ math abilities and democratic potential. They locate mathematics’ origins in human activity and highlight the rich but often overlooked links between mathematical activity and democratic, social practices. Democratic mathematics education foregrounds student inquiry and brings to light the moral dimensions of a discipline that has both remarkable utility and inevitable limitations. For math educators, the book’s humanities approach helps to see the subject anew. For philosophers, it provides an important real world context for wrestling with perennial and timely questions, engaging democratic and evolutionary theory to transform school math. This alternative approach to mathematics and mathematics education provides a guide for how to use math to make democracy a larger part of school and wider social life. 2021 Winner of the AESA Critics’ Choice Book Award.

This book explains, in a straightforward way, the foundations upon which electoral techniques are based in order to shed new light on what we actually do when we vote. The intention is to highlight the fact that no matter how an electoral system has been designed, and regardless of the intentions of those who devised the system, there will be goals that are impossible to achieve but also opportunities for improving the situation in an informed way. While detailed descriptions of electoral systems are not provided, many references are made to current or past situations, both as examples and to underline particular problems and shortcomings. In addition, a new voting method that avoids the many paradoxes of voting theory is described in detail. While some knowledge of mathematics is required in order to gain the most from the book, every effort has been made to ensure that the subject matter is easily accessible for non-mathematicians, too. In short, this is a book for anyone who wants to understand the meaning of voting.

Mathematics and democracy: the case for quantitative literacy.

In this book, different quantitative approaches to the study of electoral systems have been developed: game-theoretic, decision-theoretic, statistical, probabilistic, combinatorial, geometric, and optimization ones. All the authors are prominent scholars from these disciplines. Quantitative approaches offer a powerful tool to detect inconsistencies or poor performance in actual systems. Applications to concrete settings such as EU, American Congress, regional, and committee voting are discussed.

"A former Wall Street quantitative analyst sounds an alarm on mathematical modeling, a pervasive new force in society that threatens to undermine democracy and widen inequality,"--NoveList.

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

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.

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