social choice and the mathematics of manipulation outlooks

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Social Choice And The Mathematics Of Manipulation

Author : Alan D. Taylor
ISBN : 0521008832
Genre : Mathematics
File Size : 73. 26 MB
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A mathematical look at why it is impossible to devise a completely unmanipulable voting system, first published in 2005.

Models Of Conflict And Cooperation

Author : Rick Gillman
ISBN : 9780821848722
Genre : Business & Economics
File Size : 49. 18 MB
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Models of Conflict and Cooperation is a comprehensive, introductory, game theory text for general undergraduate students. As a textbook, it provides a new and distinctive experience for students working to become quantitatively literate. Each chapter begins with a ``dialogue'' that models quantitative discourse while previewing the topics presented in the rest of the chapter. Subsequent sections develop the key ideas starting with basic models and ending with deep concepts and results. Throughout all of the sections, attention is given to promoting student engagement with the material through relevant models, recommended activities, and exercises. The general game models that are discussed include deterministic, strategic, sequential, bargaining, coalition, and fair division games. A separate, essential chapter discusses player preferences. All of the chapters are designed to strengthen the fundamental mathematical skills of quantitative literacy: logical reasoning, basic algebra and probability skills, geometric reasoning, and problem solving. A distinctive feature of this book is its emphasis on the process of mathematical modeling.

Algebraic And Geometric Methods In Discrete Mathematics

Author : Heather A. Harrington
ISBN : 9781470423216
Genre : Commutative algebra -- Computational aspects and applications -- Applications of commutative algebra (e.g., to statistics, control theory, optimization, etc.)
File Size : 85. 63 MB
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This volume contains the proceedings of the AMS Special Session on Algebraic and Geometric Methods in Applied Discrete Mathematics, held on January 11, 2015, in San Antonio, Texas. The papers present connections between techniques from “pure” mathematics and various applications amenable to the analysis of discrete models, encompassing applications of combinatorics, topology, algebra, geometry, optimization, and representation theory. Papers not only present novel results, but also survey the current state of knowledge of important topics in applied discrete mathematics. Particular highlights include: a new computational framework, based on geometric combinatorics, for structure prediction from RNA sequences; a new method for approximating the optimal solution of a sum of squares problem; a survey of recent Helly-type geometric theorems; applications of representation theory to voting theory and game theory; a study of fixed points of tensors; and exponential random graph models from the perspective of algebraic statistics with applications to networks. This volume was written for those trained in areas such as algebra, topology, geometry, and combinatorics who are interested in tackling problems in fields such as biology, the social sciences, data analysis, and optimization. It may be useful not only for experts, but also for students who wish to gain an applied or interdisciplinary perspective.

Outlooks And Insights On Group Decision And Negotiation

Author : Bogumił Kamiński
ISBN : 9783319195155
Genre : Computers
File Size : 53. 20 MB
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This book constitutes the proceedings of the 15th International Conference on Group Decision and Negotiation, GDN 2015, held in Warsaw, Poland, in June 2015. The GDN meetings aim to bring together researchers and practitioners from a wide spectrum of fields, including economics, management, computer science, engineering, and decision science. From a total of 119 submissions, 32 papers were accepted for publication in this volume. The papers are organized into topical sections on group problem structuring and negotiation, negotiation and group processes, preference analysis and decision support, formal models, voting and collective decision making, conflict resolution in energy and environmental management, negotiation support systems and studies, online collaboration and competition, and market mechanisms and their users.

Mathematics Of Social Choice

Author : Christoph Bo”rgers
ISBN : 9780898717624
Genre : Elections
File Size : 68. 79 MB
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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.

Mathematics And Politics

Author : Alan D. Taylor
ISBN : 9780387776439
Genre : Social Science
File Size : 32. 7 MB
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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

The Theory Of Committees And Elections By Duncan Black And Committee Decisions With Complementary Valuation By Duncan Black And R A Newing

Author : Iain S. McLean
ISBN : 9789401148603
Genre : Political Science
File Size : 22. 33 MB
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R. H. Coase Duncan Black was a close and dear friend. A man of great simplicity, un worldly, modest, diffident, with no pretensions, he was devoted to scholarship. In his single-minded search for the truth, he is an example to us all. Black's first degree at the University of Glasgow was in mathematics and physics. Mathematics as taught at Glasgow seems to have been designed for engineers and did not excite him and he switched to economics, which he found more congenial. But it was not in a lecture in economics but in one on politics that he found his star. One lecturer, A. K. White, discussed the possibility of constructing a pure science of politics. This question caught his imagination, perhaps because of his earlier training in physics, and it came to absorb his thoughts for the rest of his life. But almost certainly nothing would have come of it were it not for his appointment to the newly formed Dundee School of Economics where the rest of the. teaching staff came from the London School of Economics. At Glasgow, economics, as in the time of Adam Smith, was linked with moral philosophy. At Dundee, Black was introduced to the analytical x The Theory o/Committees and Elections approach dominant at the London School of Economics. This gave him the approach he used in his attempt to construct a pure science of politics.

The Math Behind The Music

Author : Leon Harkleroad
ISBN : 9780521810951
Genre : Mathematics
File Size : 28. 91 MB
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Looks at the mathematical aspects of music, covering such topics as compositional techniques, scales, tuning systems, and music criticism.

Majority Judgment

Author : Michel Balinski
ISBN : 9780262294454
Genre : Political Science
File Size : 22. 12 MB
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In Majority Judgment, Michel Balinski and Rida Laraki argue that the traditional theory of social choice offers no acceptable solution to the problems of how to elect, to judge, or to rank. They find that the traditional model -- transforming the "preference lists" of individuals into a "preference list" of society -- is fundamentally flawed in both theory and practice. Balinski and Laraki propose a more realistic model. It leads to an entirely new theory and method--majority judgment -- proven superior to all known methods. It is at once meaningful, resists strategic manipulation, elicits honesty, and is not subject to the classical paradoxes encountered in practice, notably Condorcet's and Arrow's. They offer theoretical, practical, and experimental evidence -- from national elections to figure skating competitions -- to support their arguments. Drawing on insights from wine, sports, music, and other competitions, Balinski and Laraki argue that the question should not be how to transform many individual rankings into a single collective ranking, but rather, after defining a common language of grades to measure merit, how to transform the many individual evaluations of each competitor into a single collective evaluation of all competitors. The crux of the matter is a new model in which the traditional paradigm -- to compare -- is replaced by a new paradigm -- to evaluate.

Equity

Author : H. Peyton Young
ISBN : 0691044643
Genre : Business & Economics
File Size : 65. 7 MB
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Governments and institutions, perhaps even more than markets, determine who gets what in our society. They make the crucial choices about who pays the taxes, who gets into college, which patients get medical care, who gets drafted, where the hazardous waste dump is sited, and how much we pay for public services. Debate about these issues inevitably centers on the question of whether the solution is "fair." In Equity: In Theory and Practice, H. Peyton Young offers a systematic explanation of what we mean by fairness in distributing public resources and burdens, and applies the theory to actual cases. Young begins by reviewing some of the major theories of social justice, showing that none of them explains how societies resolve distributive problems in practice. He then suggests an alternative approach to analyzing fairness in concrete situations: equity, he argues, does not boil down to a single formula, but represents a balance between competing principles of need, desert, and social utility. The case studies Young uses to illustrate his approach include the design of income tax schedules, priority schemes for allocating scarce medical resources, formulas for distributing political representation, and criteria for setting fees for public services. Each represents a unique blend of historical perspective, rigorous analysis, and an emphasis on practical solutions.

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