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Mathematics Of Social Choice

Author: Christoph Borgers
Publisher: SIAM
ISBN: 0898716950
Size: 71.11 MB
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An accessible exposition of social choices such as selecting a winning competitor, or dividing up resources.

Mathematics And Politics

Author: Alan D. Taylor
Publisher: Springer Science & Business Media
ISBN: 0387776435
Size: 59.51 MB
Format: PDF, ePub
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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

A Short Introduction To Preferences

Author: Francesca Rossi
Publisher: Morgan & Claypool Publishers
ISBN: 1608455874
Size: 23.63 MB
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Computational social choice is an expanding field that merges classical topics like economics and voting theory with more modern topics like artificial intelligence, multiagent systems, and computational complexity. This book provides a concise introduction to the main research lines in this field, covering aspects such as preference modelling, uncertainty reasoning, social choice, stable matching, and computational aspects of preference aggregation and manipulation. The book is centered around the notion of preference reasoning, both in the single-agent and the multi-agent setting. It presents the main approaches to modeling and reasoning with preferences, with particular attention to two popular and powerful formalisms, soft constraints and CP-nets. The authors consider preference elicitation and various forms of uncertainty in soft constraints. They review the most relevant results in voting, with special attention to computational social choice. Finally, the book considers preferences in matching problems. The book is intended for students and researchers who may be interested in an introduction to preference reasoning and multi-agent preference aggregation, and who want to know the basic notions and results in computational social choice. Table of Contents: Introduction / Preference Modeling and Reasoning / Uncertainty in Preference Reasoning / Aggregating Preferences / Stable Marriage Problems

Models Of Conflict And Cooperation

Author: Rick Gillman
Publisher: American Mathematical Soc.
ISBN: 0821848720
Size: 66.59 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.

The Math Behind The Music

Author: Leon Harkleroad
Publisher: Cambridge University Press
ISBN: 0521810957
Size: 72.46 MB
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Looks at the mathematical aspects of music, covering such topics as compositional techniques, scales, tuning systems, and music criticism.

Algebraic And Geometric Methods In Discrete Mathematics

Author: Heather A. Harrington
Publisher: American Mathematical Soc.
ISBN: 1470423219
Size: 54.67 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.

Political Institutions

Author: Josep M. Colomer
Publisher: OUP Oxford
ISBN: 0191529257
Size: 30.13 MB
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The role of institutions is to establish the domains of public activity and the rules to select leaders. Democratic regimes organize in simple institutional frameworks to foster the concentration of power and alternative successive absolute winners and losers. They favour political satisfaction of relatively small groups, as well as policy instability. In contrast, pluralistic institutions produce multiple winners, including multiparty co-operation and agreements. They favour stable, moderate, and consensual policies that can satisfy large groups' interests on a great number of issues. The more complex the political institutions, the more stable and socially efficient the outcome will be. This book develops an extensive analysis of this relationship. It explores concepts, questions and insights based on social choice theory, while empirical focus is cast on more than 40 democratic countries and a few international organizations from late medieval times to the present. The book argues that pluralistic democratic institutions are judged to be better than simple formula of their higher capacity of producing socially satisfactory results.

This Is Your Brain On Parasites

Author: Kathleen McAuliffe
Publisher: Houghton Mifflin Harcourt
ISBN: 0544193229
Size: 29.92 MB
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“Engrossing … [An] expedition through the hidden and sometimes horrifying microbial domain.” —Wall Street Journal “Fascinating—and full of the kind of factoids you can't wait to share.” —Scientific American Parasites can live only inside another animal and, as Kathleen McAuliffe reveals, these tiny organisms have many evolutionary motives for manipulating the behavior of their hosts. With astonishing precision, parasites can coax rats to approach cats, spiders to transform the patterns of their webs, and fish to draw the attention of birds that then swoop down to feast on them. We humans are hardly immune to their influence. Organisms we pick up from our own pets are strongly suspected of changing our personality traits and contributing to recklessness and impulsivity—even suicide. Germs that cause colds and the flu may alter our behavior even before symptoms become apparent. Parasites influence our species on the cultural level, too. Drawing on a huge body of research, McAuliffe argues that our dread of contamination is an evolved defense against parasites. The horror and revulsion we are programmed to feel when we come in contact with people who appear diseased or dirty helped pave the way for civilization, but may also be the basis for major divisions in societies that persist to this day. This Is Your Brain on Parasites is both a journey into cutting-edge science and a revelatory examination of what it means to be human. “If you’ve ever doubted the power of microbes to shape society and offer us a grander view of life, read on and find yourself duly impressed.” —Heather Havrilesky, Bookforum