This book is a survey on the problem of choosing from a tournament. It brings together under a unified and self-contained presentation results and concepts from Graph Theory, Choice Theory, Decision Science and Social Choice which were discovered in the last ten years. Classical scoring and ranking methods are introduced, including the Slater orderings, as well as new statistical methods for describing a tournament, graph-theoretical methods based on the covering relation and game-theoretical methods. As an illustration, results are applied to the classical problem of Majority Voting: How to deal with the Condorcet Paradox.

This book is a survey on the problem of choosing from a tournament. It brings together under a unified and self-contained presentation results and concepts from Graph Theory, Choice Theory, Decision Science and Social Choice which were discovered in the last ten years. Classical scoring and ranking methods are introduced, including the Slater orderings, as well as new statistical methods for describing a tournament, graph-theoretical methods based on the covering relation and game-theoretical methods. As an illustration, results are applied to the classical problem of Majority Voting: How to deal with the Condorcet Paradox.

This Handbook provides an overview of interdisciplinary research related to social choice and voting that is intended for a broad audience. Expert contributors from various fields present critical summaries of the existing literature, including intuitive explanations of technical terminology and well-known theorems, suggesting new directions for research.

This textbook contains a rigorous exposition of the mathematical foundations of two of the most important topics in politics and economics: voting and apportionment, at the level of upper undergraduate and beginning graduate students. It stands out among comparable books by providing, in one volume, an extensive and mathematically rigorous treatment of these two topics. The text’s three chapters cover social choice, yes-no voting, and apportionment, respectively, and can be covered in any order, allowing teachers ample flexibility. Each chapter begins with an elementary introduction and several examples to motivate the concepts and to gradually lead to more advanced material. Landmark theorems are presented with detailed and streamlined proofs; those requiring more complex proofs, such as Arrow’s theorems on dictatorship, Gibbard’s theorem on oligarchy, and Gärdenfors’ theorem on manipulation, are broken down into propositions and lemmas in order to make them easier to grasp. Simple and intuitive notations are emphasized over non-standard, overly complicated symbols. Additionally, each chapter ends with exercises that vary from computational to “prove or disprove” types. The Mathematics of Voting and Apportionment will be particularly well-suited for a course in the mathematics of voting and apportionment for upper-level undergraduate and beginning graduate students in economics, political science, or philosophy, or for an elective course for math majors. In addition, this book will be a suitable read for to any curious mathematician looking for an exposition to these unpublicized mathematical applications. No political science prerequisites are needed. Mathematical prerequisites (included in the book) are minimal: elementary concepts in combinatorics, graph theory, order relations, and the harmonic and geometric means. What is needed most is the level of maturity that enables the student to think logically, derive results from axioms and hypotheses, and intuitively grasp logical notions such as “contrapositive” and “counterexample.”

This book contains a selection of refereed papers presented at the "International Conference on Operations Research (OR 2014)", which took place at RWTH Aachen University, Germany, September 2-5, 2014. More than 800 scientists and students from 47 countries attended OR 2014 and presented more than 500 papers in parallel topical streams, as well as special award sessions. The theme of the conference and its proceedings is "Business Analytics and Optimization".

This volume presents the state of the art of new developments, and some interesting and relevant applications of the OWA (ordered weighted averaging) operators. The OWA operators were introduced in the early 1980s by Ronald R. Yager as a conceptually and numerically simple, easily implementable, yet extremely powerful general aggregation operator. That simplicity, generality and implementability of the OWA operators, combined with their intuitive appeal, have triggered much research both in the foundations and extensions of the OWA operators, and in their applications to a wide variety of problems in various fields of science and technology. Part I: Methods includes papers on theoretical foundations of OWA operators and their extensions. The papers in Part II: Applications show some more relevant applications of the OWA operators, mostly means, as powerful yet general aggregation operators. The application areas are exemplified by environmental modeling, social networks, image analysis, financial decision making and water resource management.

Both theoretical and empirical aspects of single- and multi-winner voting procedures are presented in this collection of papers. Starting from a discussion of the underlying principles of democratic representation, the volume includes a description of a great variety of voting procedures. It lists and illustrates their susceptibility to the main voting paradoxes, assesses (under various models of voters' preferences) the probability of paradoxical outcomes, and discusses the relevance of the theoretical results to the choice of voting system.

“A major piece of work . . . a classic. There is no other book like it.” —Norman Schofield, Washington University “The authors succeed brilliantly in tackling a large number of important questions concerning the interaction among voters and elected representatives in the political arena, using a common, rigorous language.” —Antonio Merlo, University of Pennsylvania Positive Political Theory II: Strategy and Structure is the second volume in Jeffrey Banks and David Austen-Smith’s monumental study of the links between individual preferences and collective choice. The book focuses on representative systems, including both elections and legislative decision-making processes, clearly connecting individual preferences to collective outcomes. This book is not a survey. Rather, it is the coherent, cumulative result of the authors’ brilliant efforts to indirectly connect preferences to collective choice through strategic behaviors such as agenda-selection and voting. The book will be an invaluable reference and teaching tool for economists and political scientists, and an essential companion to any scholar interested in the latest theoretical advances in positive political theory.

This book provides an overview of the main methods and results in the formal study of the human decision-making process, as defined in a relatively wide sense. A key aim of the approach contained here is to try to break down barriers between various disciplines encompassed by this field, including psychology, economics and computer science. All these approaches have contributed to progress in this very important and much-studied topic in the past, but none have proved sufficient so far to define a complete understanding of the highly complex processes and outcomes. This book provides the reader with state-of-the-art coverage of the field, essentially forming a roadmap to the field of decision analysis. The first part of the book is devoted to basic concepts and techniques for representing and solving decision problems, ranging from operational research to artificial intelligence. Later chapters provide an extensive overview of the decision-making process under conditions of risk and uncertainty. Finally, there are chapters covering various approaches to multi-criteria decision-making. Each chapter is written by experts in the topic concerned, and contains an extensive bibliography for further reading and reference.

The rapidly growing field of computational social choice, at the intersection of computer science and economics, deals with the computational aspects of collective decision making. This handbook, written by thirty-six prominent members of the computational social choice community, covers the field comprehensively. Chapters devoted to each of the field's major themes offer detailed introductions. Topics include voting theory (such as the computational complexity of winner determination and manipulation in elections), fair allocation (such as algorithms for dividing divisible and indivisible goods), coalition formation (such as matching and hedonic games), and many more. Graduate students, researchers, and professionals in computer science, economics, mathematics, political science, and philosophy will benefit from this accessible and self-contained book.