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Mathematics Of Social Choice

Author: Christoph Borgers
Publisher: SIAM
ISBN: 0898716950
Size: 30.93 MB
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An accessible exposition of social choices such as selecting a winning competitor, or dividing up resources.

A Short Introduction To Preferences

Author: Francesca Rossi
Publisher: Morgan & Claypool Publishers
ISBN: 1608455874
Size: 69.73 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: 17.45 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
Publisher: American Mathematical Soc.
ISBN: 1470423219
Size: 27.97 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.

The Math Behind The Music

Author: Leon Harkleroad
Publisher: Cambridge University Press
ISBN: 0521810957
Size: 55.47 MB
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Looks at the mathematical aspects of music, covering such topics as compositional techniques, scales, tuning systems, and music criticism.

Political Institutions

Author: Josep M. Colomer
Publisher: OUP Oxford
ISBN: 0191529257
Size: 11.90 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.

Exact Thinking In Demented Times

Author: Karl Sigmund
Publisher: Basic Books
ISBN: 0465096964
Size: 63.76 MB
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A dazzling group biography of the early twentieth-century thinkers who transformed the way the world thought about math and science Inspired by Albert Einstein's theory of relativity and Bertrand Russell and David Hilbert's pursuit of the fundamental rules of mathematics, some of the most brilliant minds of the generation came together in post-World War I Vienna to present the latest theories in mathematics, science, and philosophy and to build a strong foundation for scientific investigation. Composed of such luminaries as Kurt Gödel and Rudolf Carnap, and stimulated by the works of Ludwig Wittgenstein and Karl Popper, the Vienna Circle left an indelible mark on science. Exact Thinking in Demented Times tells the often outrageous, sometimes tragic, and never boring stories of the men who transformed scientific thought. A revealing work of history, this landmark book pays tribute to those who dared to reinvent knowledge from the ground up.