Download or read book Mathematics of Social Choice written by Christoph Borgers and published by SIAM. This book was released on 2010-01-01 with total page 233 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics of Social Choice is a fun and accessible book that looks at the choices made by groups of people with different preferences, needs, and interests. Divided into three parts, the text first examines voting methods for selecting or ranking candidates. A brief second part addresses compensation problems wherein an indivisible item must be assigned to one of several people who are equally entitled to ownership of the item, with monetary compensation paid to the others. The third part discusses the problem of sharing a divisible resource among several people. Mathematics of Social Choice can be used by undergraduates studying mathematics and students whose only mathematical background is elementary algebra. More advanced material can be skipped without any loss of continuity. The book can also serve as an easy introduction to topics such as the Gibbard-Satterthwaite theorem, Arrow's theorem, and fair division for readers with more mathematical background.
Download or read book Social Choice and the Mathematics of Manipulation written by Alan D. Taylor and published by Cambridge University Press. This book was released on 2005-05-09 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Social Choice and Individual Values written by Kenneth Joseph Arrow and published by Yale University Press. This book was released on 1963-01-01 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: The literature on the theory of social choice has grown considerably beyond the few items in existence at the time the first edition of this book appeared in 1951. Some of the new literature has dealt with the technical, mathematical aspects, more with the interpretive. My own thinking has also evolved somewhat, although I remain far from satisfied with present formulations. The exhaustion of the first edition provides a convenient time for a selective and personal stocktaking in the form of an appended commentary entitled, 'Notes on the Theory of Social Choice, 1963, ' containing reflections on the text and its omissions and on some of the more recent literature. This form has seemed more appropriate than a revision of the original text, which has to some extent acquired a life of its own.
Download or read book The Theory of Social Choice written by Peter C. Fishburn and published by Princeton University Press. This book was released on 2015-03-08 with total page 277 pages. Available in PDF, EPUB and Kindle. Book excerpt: One fundamental premise of democratic theory is that social policy, group choice, or collective action should be based on the preferences of the individuals in the society, group, or collective. Using the tools of formal mathematical analysis, Peter C. Fishburn explores and defines the conditions for social choice and methods for synthesizing individuals' preferences. This study is unique in its emphasis on social choice functions, the general position that individual indifference may not be transitive, and the use of certain mathematics such as linear algebra. The text is divided into three main parts: social choice between two alternatives, which examines a variety of majority-like functions; simple majority social choice, which focuses on social choice among many alternatives when two-element feasible subset choices are based on simple majority; and a general study of aspects and types of social choice functions for many alternatives. Originally published in 1973. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
Download or read book Classics of Social Choice written by Iain McLean and published by University of Michigan Press. This book was released on 1995 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the centuries an intriguing collection of thinkers have realized that voting and social choice are not straightforward. Yet despite the work of many distinguished contributors in this area, the subject has only become established in the last few decades. Indeed, many earlier writings were lost and their content forgotten, only to be rediscovered later and then forgotten again. This puzzling saga of intellectual history unfolds in Classics of Social Choice through these original writings. The editors have included recently discovered pieces and other major contributions - newly translated where necessary. The introduction explains who each writer was, locates him in a historical context, and analyzes his argument. It was only in the 1940s and 1950s that the theory of social choice was established by Duncan Black and Kenneth Arrow - whose Nobel Prize in Economics was awarded in part for this work. It is now a large and thriving branch of economics and politics. Classics of Social Choice will interest anyone working in social choice theory as well as students of medieval thought, the Enlightenment, and constitutions.
Download or read book Welfare Economics and Social Choice Theory written by Allan M. Feldman and published by Springer Science & Business Media. This book was released on 2006-06-14 with total page 401 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers the main topics of welfare economics — general equilibrium models of exchange and production, Pareto optimality, un certainty, externalities and public goods — and some of the major topics of social choice theory — compensation criteria, fairness, voting. Arrow's Theorem, and the theory of implementation. The underlying question is this: "Is a particular economic or voting mechanism good or bad for society?" Welfare economics is mainly about whether the market mechanism is good or bad; social choice is largely about whether voting mechanisms, or other more abstract mechanisms, can improve upon the results of the market. This second edition updates the material of the first, written by Allan Feldman. It incorporates new sections to existing first-edition chapters, and it includes several new ones. Chapters 4, 6, 11, 15 and 16 are new, added in this edition. The first edition of the book grew out of an undergraduate welfare economics course at Brown University. The book is intended for the undergraduate student who has some prior familiarity with microeconomics. However, the book is also useful for graduate students and professionals, economists and non-economists, who want an overview of welfare and social choice results unburdened by detail and mathematical complexity. Welfare economics and social choice both probably suffer from ex cessively technical treatments in professional journals and monographs.
Download or read book Handbook of Computational Social Choice written by Felix Brandt and published by Cambridge University Press. This book was released on 2016-04-25 with total page 553 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive survey of computational aspects of collective decisions for graduate students, researchers, and professionals in computer science and economics.
Download or read book Mathematics for Social Justice Resources for the College Classroom written by Gizem Karaali and published by American Mathematical Soc.. This book was released on 2019-07-09 with total page 277 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics for Social Justice offers a collection of resources for mathematics faculty interested in incorporating questions of social justice into their classrooms. The book begins with a series of essays from instructors experienced in integrating social justice themes into their pedagogy; these essays contain political and pedagogical motivations as well as nuts-and-bolts teaching advice. The heart of the book is a collection of fourteen classroom-tested modules featuring ready-to-use activities and investigations for the college mathematics classroom. The mathematical tools and techniques used are relevant to a wide variety of courses including college algebra, math for the liberal arts, calculus, differential equations, discrete mathematics, geometry, financial mathematics, and combinatorics. The social justice themes include human trafficking, income inequality, environmental justice, gerrymandering, voting methods, and access to education. The volume editors are leaders of the national movement to include social justice material into mathematics teaching. Gizem Karaali is Associate Professor of Mathematics at Pomona College. She is one of the founding editors of The Journal of Humanistic Mathematics, and an associate editor for The Mathematical Intelligencer and Numeracy ; she also serves on the editorial board of the MAA's Carus Mathematical Monographs. Lily Khadjavi is Associate Professor of Mathematics at Loyola Marymount University and is a past co-chair of the Infinite Possibilities Conference. She has served on the boards of Building Diversity in Science, the Barbara Jordan-Bayard Rustin Coalition, and the Harvard Gender and Sexuality Caucus.
Download or read book Mathematical Methods in Economics and Social Choice written by norman schofield and published by Springer Science & Business Media. This book was released on 2004-03-15 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years, the usual optimisation techniques have been extended to incorporate more powerful topological and differential methods, and these methods have led to new results on the qualitative behaviour of general economic and political systems. The progression of ideas presented in this book will familiarize the student with the geometric concepts underlying these topological methods, and, as a result, make mathematical economics, general equilibrium theory, and social choice theory more accessible.
Download or read book Maths for Social Sciences written by Lorenzo Peccati and published by Springer. This book was released on 2018-12-28 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is aimed at students in social sciences programs that include some course in quantitative methods. Stats for social sciences is frequently the subject of textbooks, while maths for social sciences is often neglected: monographs on specific themes (like, for instance, social choice systems or game theory applications) are available, but they do not adequately cover the topic in general. This textbook stems from the Bocconi University’s new "Bachelor in Government", which was launched in 2015, and is intended for undergraduate students who do not exclude maths from their toolbox. It discusses various concrete applications in political economics, political science, sociology, and demography and explores topics like Grexit, Macron’s success, immigration effects and the Arab Spring.
Download or read book A Primer in Social Choice Theory written by Wulf Gaertner and published by Oxford University Press, USA. This book was released on 2006 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introductory text explores the theory of social choice. Written as a primer suitable for advanced undergraduates and graduates, this text will act as an important starting point for students grappling with the complexities of social choice theory. Rigorous yet accessible, this primer avoids the use of technical language and provides an up-to-date discussion of this rapidly developing field. This is the first in a series of texts published in association with the LSE.
Download or read book Behavioral Social Choice written by Michel Regenwetter and published by Cambridge University Press. This book was released on 2006-05-15 with total page 21 pages. Available in PDF, EPUB and Kindle. Book excerpt: Behavioral Social Choice looks at the probabilistic foundations of collective decision-making rules. The authors challenge much of the existing theoretical wisdom about social choice processes, and seek to restore faith in the possibility of democratic decision-making. In particular, they argue that worries about the supposed prevalence of majority rule cycles that would preclude groups from reaching a final decision about what alternative they prefer have been greatly overstated. In practice, majority rule can be expected to work well in most real-world settings. They provide new insights into how alternative model specifications can change our estimates of social orderings.
Download or read book Population Issues in Social Choice Theory Welfare Economics and Ethics written by Charles Blackorby and published by Cambridge University Press. This book was released on 2005-08-22 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores how different ideas of the common good may be compared, contrasted and ranked.
Download or read book Game Theory Social Choice and Ethics written by H. Brock and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 195 pages. Available in PDF, EPUB and Kindle. Book excerpt: There are problems to whose solution I would attach an infinitely greater import ancf! than to those of mathematics, for example touching ethics, or our relation to God, or conceming our destiny and our future; but their solution lies wholly beyond us and completely outside the province 0 f science. J. F. C. Gauss For a1l his prescience in matters physical and mathematieal, the great Gauss apparently did not foresee one development peculiar to OUT own time. The development I have in mind is the use of mathematical reasoning - in partieu lar the axiomatic method - to explicate alternative concepts of rationality and morality. The present bipartite collection of essays (Vol. 11, Nos. 2 and 3 of this journal) is entitled 'Game Theory, Social Choiee, and Ethics'. The eight papers represent state-of-the-art research in formal moral theory. Their intended aim is to demonstrate how the methods of game theory, decision theory, and axiomatic social choice theory can help to illuminate ethical questions central not only to moral theory, but also to normative public policy analysis. Before discussion of the contents of the papers, it should prove helpful to recall a number of pioneering papers that appeared during the decade of the 1950s. These papers contained aseries of mathematical and conceptual break through which laid the basis for much of today's research in formal moral theory. The papers deal with two somewhat distinct topics: the concept of individual and collective rationality, and the concept of social justiee.
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 Application of Fuzzy Logic to Social Choice Theory written by John N. Mordeson and published by CRC Press. This book was released on 2015-03-03 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fuzzy social choice theory is useful for modeling the uncertainty and imprecision prevalent in social life yet it has been scarcely applied and studied in the social sciences. Filling this gap, Application of Fuzzy Logic to Social Choice Theory provides a comprehensive study of fuzzy social choice theory.The book explains the concept of a fuzzy max
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.
