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.

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

"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.

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

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.

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.

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.

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.

Zusammenfassung: This book presents the mathematical tools that politicians use to make rational decisions about health, education, culture, economy, finance, transportation, and national defense for their citizens. The selection of topics addressed is based on the experiences of four veteran politicians who have doctorates or master's degrees in mathematics. The exposition also considers the mathematical tools used by politicians to capture votes or optimize their impact on the design of electoral districts, i.e., gerrymandering, without forgetting the mathematics applied to parliamentary activity and political science. Aimed at a general educated readership, a basic knowledge of mathematics is the only requisite to understanding most of the book. Certain sections, denoted in the book with a star, contain more advanced material and require some knowledge of undergraduate math. A later chapter is dedicated to applications and techniques of machine learning and the final chapter discusses a variety of cases where political decisions have affected mathematical development. Readers gravitating towards this book are those who are curious about the history of mathematics, including optimizers and mathematicians who would like to learn more about the historical roots of their discipline. There will also be strong appeal to mathematically-oriented economists, political scientists, and people generally interested in mathematics. Mathematics is - or it should be! - an important part of our culture. The impact of mathematics is sometimes silent, but a powerful one. The authors of this book did an incredible work in digging out areas of mathematical reasoning that pervades social and political life. Reading this book, we will all enrich our vision of mathematics' value for society. (Nuno Crato, Professor of Applied Mathematics, University of Lisbon, former minister of Education and Science of Portugal 2011-2015) This monograph shows in an impressive way that mathematics can be very helpful in making and evaluating political decisions and that it is indispensable in the progressive penetration of all areas of society with scientific methods. This also includes politics. Not everything in politics can be justified or related to mathematics, but politics should not be made in contradiction to mathematical truths. For me, this is a central message of this publication. (Johanna Wanka, Professor of Applied Mathematics, Merseburg University of Applied Sciences, former Minister of Education and Research, Germany 2013-2018)

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. This is a good text for a graduate seminar in formal modeling. It is also suitable as an introductory text in fuzzy mathematics.