Download or read book Mathematical Theory of Democracy written by Andranik Tangian and published by Springer Science & Business Media. This book was released on 2013-07-31 with total page 629 pages. Available in PDF, EPUB and Kindle. Book excerpt: The mathematical theory of democracy deals with selection of representatives who make decisions on behalf of the whole society. In this book, the notion of representativeness is operationalized with the index of popularity (the average percentage of the population whose opinion is represented on a number of issues) and the index of universality (the frequency of cases when the opinion of a majority is represented). These indices are applied to evaluate and study the properties of single representatives (e.g. president) and representative bodies (e.g. parliament, magistrate, cabinet, jury, coalition). To bridge representative and direct democracy, an election method is proposed that is based not on voting but on indexing candidates with respect to the electorate’s political profile. In addition, societal and non-societal applications are considered.
Download or read book Mathematical Theory of Democracy written by Andranik Tangian and published by Springer. This book was released on 2013-09-14 with total page 615 pages. Available in PDF, EPUB and Kindle. Book excerpt: The mathematical theory of democracy deals with selection of representatives who make decisions on behalf of the whole society. In this book, the notion of representativeness is operationalized with the index of popularity (the average percentage of the population whose opinion is represented on a number of issues) and the index of universality (the frequency of cases when the opinion of a majority is represented). These indices are applied to evaluate and study the properties of single representatives (e.g. president) and representative bodies (e.g. parliament, magistrate, cabinet, jury, coalition). To bridge representative and direct democracy, an election method is proposed that is based not on voting but on indexing candidates with respect to the electorate’s political profile. In addition, societal and non-societal applications are considered.
Download or read book Numbers Rule written by George Szpiro and published by Princeton University Press. This book was released on 2020-11-03 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Mathematics and Democracy written by Steven J. Brams and published by Princeton University Press. This book was released on 2009-12-02 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Mathematics to the Rescue of Democracy written by Paolo Serafini and published by Springer Nature. This book was released on 2020-03-02 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Aggregation and Representation of Preferences written by Andranick S. Tanguiane and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 335 pages. Available in PDF, EPUB and Kindle. Book excerpt: Aggregation is the conjunction of information, aimed at its compact represen tation. Any time when the totality of data is described in terms of general ized indicators, conventional counts, typical representatives and characteristic dependences, one directly or indirectly deals with aggregation. It includes revealing the most significant characteristics and distinctive features, quanti tative and qualitative analysis. As a result, the information becomes adaptable for further processing and convenient for human perception. Aggregation is widely used in economics, statistics, management, planning, system analysis, and many other fields. That is why aggregation is so important in data pro cessing. Aggregation of preferences is a particular case of the general problem of ag gregation. It arises in multicriteria decision-making and collective choice, when a set of alternatives has to be ordered with respect to contradicting criteria, or various individual opinions. However, in spite of apparent similarity the problems of multicriteria decision-making and collective choice are somewhat different. Indeed, an improvement in some specifications at the cost of worsen ing others is not the same as the satisfaction of interests of some individuals to the prejudice of the rest. In the former case the reciprocal compensations are considered within a certain entirety; in the latter we infringe upon the rights of independent individuals. Moreover, in multicriteria decision-making one usu ally takes into account objective factors, whereas in collective choice one has to compare subjective opinions which cannot be measured properly.
Download or read book Democracy and Mathematics Education written by Kurt Stemhagen and published by Routledge. This book was released on 2021-05-06 with total page 239 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book An Epistemic Theory of Democracy written by Robert E. Goodin and published by Oxford University Press. This book was released on 2018 with total page 469 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book examines the Condorcet Jury Theorem and how its assumptions can be applicable to the real world. It will use the theorem to assess various familiar political practices and alternative institutional arrangements, revealing how best to take advantage of the truth-tracking potential of majoritarian democracy.
Download or read book Political Geometry written by Moon Duchin and published by Birkhäuser. This book was released on 2022-04-02 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: “Why does my congressional district look like a salamander?” Politically engaged citizens have been asking this question for far too long. This volume collects perspectives from a wide cross-section of disciplines to explain what drives gerrymandering, why it can be hard to stamp out, and how we might go about fixing it. With topics ranging from the Voting Rights Act to Markov chains to the geography of communities, this book serves as a 21st century toolkit for how we can better approach this corrosive phenomenon. The volume editors gather experts from a variety of fields to provide as many different perspectives on gerrymandering as possible. Thanks to the breadth of expertise found across these chapters, ranging from lawyers to mathematicians to civil rights activists, readers will discover new ways of thinking about redistricting in the United States. Illustrations and helpful walkthroughs appear throughout to clearly explain otherwise complex ideas from these areas. Political Geometry is a must-have for anybody interested in political representation in the United States elections, and for anyone who’s ever thought, “There must be a better way to do this.”
Download or read book The Mathematics of Voting and Elections A Hands On Approach written by Jonathan K. Hodge and published by American Mathematical Soc.. This book was released on 2018-10-01 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Weapons of Math Destruction written by Cathy O'Neil and published by Crown Publishing Group (NY). This book was released on 2016 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: "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.
Download or read book Analytical Theory of Democracy written by Andranik Tangian and published by Springer Nature. This book was released on 2020-03-30 with total page 1048 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book operationalizes the idea of political representation, which is fundamental to modern democracies. Both individual representatives and representative bodies are evaluated using the indices of popularity (the average percentage of the population whose opinion is represented on topical policy issues) and universality (the percentage of issues for which the prevailing public opinion is represented). Viewed as objective functions, these indices can aid in the search for optimal representatives and representative bodies. By replacing the consistency analysis of the social choice axioms with the calculation of the best compromises, the paradoxes of social choice, such as those of Condorcet and Arrow, can be overcome. These indices also form the core of an alternative election method that is aimed at enhancing policy representation — a recent concept of political representation, which is not supported by the conventional voting systems shaped during the American and French Revolutions. This method is tested in a series of election experiments that focus on implementation details. In addition, non-societal applications such as MCDM, finance or traffic control are considered, where the objects that reflect the properties or behavior of other objects are regarded as their “representatives.” Given its scope, the book will appeal to political scientists, economists and operations researchers, as well as to politicians interested in improving democratic performance and electoral system design.
Download or read book Mathematics and Democracy written by Bruno Simeone and published by Springer Science & Business Media. This book was released on 2007-01-09 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Mathematics and Democracy written by Steven J. Brams and published by . This book was released on 2008 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Social Choice and Democracy written by Norman Schofield and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: The mathematical theory of voting has intellectual roots extending back two centuries to the writings of Borda and Condorcet. Yet it has only been in the last forty years that general theorems have begun to emerge. With the publication of this volume, Norman Schofield brings the results together in a ,common framework. SOCIAL CHOICE AND DEMOCRACY, however, is not merely a synthetic exercise, for Schofield's own work over the last decade has constituted a major initiative in deepening and' broadening our general understanding of voting arrangements. At last the results of his research, bits and pieces of which have been reported in a number of journals of international standing and in various collections, are coherently and systematically presented as an entirety. For students of democracy -- chiefly philosophers and political scientists, but increasingly economists as well -- the insights of this volume are profound. From it I infer the following.
Download or read book Democracy and Mathematics Education written by Kurt Stemhagen and published by Taylor & Francis. This book was released on 2021-05-06 with total page 213 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book A Democratic Theory of Judgment written by Linda M.G. Zerilli and published by University of Chicago Press. This book was released on 2016-12-12 with total page 401 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this sweeping look at political and philosophical history, Linda M. G. Zerilli unpacks the tightly woven core of Hannah Arendt’s unfinished work on a tenacious modern problem: how to judge critically in the wake of the collapse of inherited criteria of judgment. Engaging a remarkable breadth of thinkers, including Ludwig Wittgenstein, Leo Strauss, Immanuel Kant, Frederick Douglass, John Rawls, Jürgen Habermas, Martha Nussbaum, and many others, Zerilli clears a hopeful path between an untenable universalism and a cultural relativism that forever defers the possibility of judging at all. Zerilli deftly outlines the limitations of existing debates, both those that concern themselves with the impossibility of judging across cultures and those that try to find transcendental, rational values to anchor judgment. Looking at Kant through the lens of Arendt, Zerilli develops the notion of a public conception of truth, and from there she explores relativism, historicism, and universalism as they shape feminist approaches to judgment. Following Arendt even further, Zerilli arrives at a hopeful new pathway—seeing the collapse of philosophical criteria for judgment not as a problem but a way to practice judgment anew as a world-building activity of democratic citizens. The result is an astonishing theoretical argument that travels through—and goes beyond—some of the most important political thought of the modern period.
