Download or read book Basic Geometry of Voting written by Donald G. Saari and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: Amazingly, the complexities of voting theory can be explained and resolved with comfortable geometry. A geometry which unifies such seemingly disparate topics as manipulation, monotonicity, and even the apportionment issues of the US Supreme Court. Although directed mainly toward students and others wishing to learn about voting, experts will discover here many previously unpublished results. As an example, a new profile decomposition quickly resolves the age-old controversies of Condorcet and Borda, demonstrates that the rankings of pairwise and other methods differ because they rely on different information, casts serious doubt on the reliability of a Condorcet winner as a standard for the field, makes the famous Arrow's Theorem predictable, and simplifies the construction of examples.
Download or read book Geometry of Voting written by Donald G. Saari and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over two centuries of theory and practical experience have taught us that election and decision procedures do not behave as expected. Instead, we now know that when different tallying methods are applied to the same ballots, radically different outcomes can emerge, that most procedures can select the candidate, the voters view as being inferior, and that some commonly used methods have the disturbing anomaly that a winning candidate can lose after receiving added support. A geometric theory is developed to remove much of the mystery of three-candidate voting procedures. In this manner, the spectrum of election outcomes from all positional methods can be compared, new flaws with widely accepted concepts (such as the "Condorcet winner") are identified, and extensions to standard results (e.g. Black's single-peakedness) are obtained. Many of these results are based on the "profile coordinates" introduced here, which makes it possible to "see" the set of all possible voters' preferences leading to specified election outcomes. Thus, it now is possible to visually compare the likelihood of various conclusions. Also, geometry is applied to apportionment methods to uncover new explanations why such methods can create troubling problems.
Download or read book Geometry of Voting written by Donald G. Saari and published by . This book was released on 2014-01-15 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Geometry of Elections written by Ernest W. Adams and published by Stanford Univ Center for the Study. This book was released on 2014-03-01 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: How can we ensure that the "right" person is elected to office? Voter turnout, balloting methods, candidates, and, in the case of the 2000 U.S. presidential election, the courts all conspire to produce electoral results that are horrific to some, wonderful to others, and tolerable to most. The Geometry of Elections utilizes mathematical theories to analyze how people vote and explores possible voting systems that could minimize the likelihood of the "wrong" candidate being elected. The Geometry of Elections examines real world elections held in the United States, Britain, and France and asks: What criteria do voters use to determine the "right" candidate or party, and if there is a "right" candidate, how can we design a more accurate voting system? Applying spatial modeling and insights from geometry to real-world political elections, the authors present an intriguing examination of how voters conceptualize and eventually vote for politicians and policy positions.
Download or read book Political Geometry written by Moon Duchin and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Why does my congressional district look like a salamander?" Politically engaged citizens have been asking this question for far too long. This volume collects perspectives from a wide cross-section of disciplines to explain what drives gerrymandering, why it can be hard to stamp out, and how we might go about fixing it. With topics ranging from the Voting Rights Act to Markov chains to the geography of communities, this book serves as a 21st century toolkit for how we can better approach this corrosive phenomenon. The volume editors gather experts from a variety of fields to provide as many different perspectives on gerrymandering as possible. Thanks to the breadth of expertise found across these chapters, ranging from lawyers to mathematicians to civil rights activists, readers will discover new ways of thinking about redistricting in the United States. Illustrations and helpful walkthroughs appear throughout to clearly explain otherwise complex ideas from these areas. Political Geometry is a must-have for anybody interested in political representation in the United States elections, and for anyone who's ever thought, "There must be a better way to do this.".
Download or read book Voting Paradoxes and How to Deal with Them written by Hannu Nurmi and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: Voting paradoxes are unpleasant surprises encountered in voting. Typically they suggest that something is wrong with the way in dividual opinions are being expressed or processed in voting. The outcomes are bizarre, unfair or otherwise implausible, given the expressed opinions of voters. Voting paradoxes have an important role in the history of social choice theory. The founding fathers of the theory, Marquis de Condorcet and Jean-Charles de Borda, were keenly aware of some of them. Indeed, much of the work of these and other forerunners of the modern social choice theory dealt with ways of avoiding paradoxes related to voting. One of the early paradoxes, viz. that bearing the name of Condorcet, has subsequently gained such a prominent place in the literature that it is sometimes called the paradox of voting. One of the aims of the present work is to show that Condorcet's is but one of many paradoxes of voting. Some of these are pretty closely interrelated making it meaningful to classify them. This is the second main aim of this book. The third objective is to suggest ways of dealing with paradoxes. Since voting is and has always been an essential instrument of democratic rule, it is of some in terest to find out how voting paradoxes are being dealt with by past and present methods of voting. Of even greater interest is to find ways of minimizing the probability of occurrence of various paradoxes. By their very nature some paradoxes are unavoidable.
Download or read book The Mathematics of Elections and Voting written by W.D. Wallis and published by Springer. This book was released on 2014-10-08 with total page 103 pages. Available in PDF, EPUB and Kindle. Book excerpt: This title takes an in-depth look at the mathematics in the context of voting and electoral systems, with focus on simple ballots, complex elections, fairness, approval voting, ties, fair and unfair voting, and manipulation techniques. The exposition opens with a sketch of the mathematics behind the various methods used in conducting elections. The reader is lead to a comprehensive picture of the theoretical background of mathematics and elections through an analysis of Condorcet’s Principle and Arrow’s Theorem of conditions in electoral fairness. Further detailed discussion of various related topics include: methods of manipulating the outcome of an election, amendments, and voting on small committees. In recent years, electoral theory has been introduced into lower-level mathematics courses, as a way to illustrate the role of mathematics in our everyday life. Few books have studied voting and elections from a more formal mathematical viewpoint. This text will be useful to those who teach lower level courses or special topics courses and aims to inspire students to understand the more advanced mathematics of the topic. The exercises in this text are ideal for upper undergraduate and early graduate students, as well as those with a keen interest in the mathematics behind voting and elections.
Download or read book Political Geometry written by Moon Duchin and published by Birkhäuser. This book was released on 2022-04-02 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: “Why does my congressional district look like a salamander?” Politically engaged citizens have been asking this question for far too long. This volume collects perspectives from a wide cross-section of disciplines to explain what drives gerrymandering, why it can be hard to stamp out, and how we might go about fixing it. With topics ranging from the Voting Rights Act to Markov chains to the geography of communities, this book serves as a 21st century toolkit for how we can better approach this corrosive phenomenon. The volume editors gather experts from a variety of fields to provide as many different perspectives on gerrymandering as possible. Thanks to the breadth of expertise found across these chapters, ranging from lawyers to mathematicians to civil rights activists, readers will discover new ways of thinking about redistricting in the United States. Illustrations and helpful walkthroughs appear throughout to clearly explain otherwise complex ideas from these areas. Political Geometry is a must-have for anybody interested in political representation in the United States elections, and for anyone who’s ever thought, “There must be a better way to do this.”
Download or read book The Mathematics of Voting and Apportionment written by Sherif El-Helaly and published by Springer. This book was released on 2019-05-21 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.”
Download or read book Spatial Models of Parliamentary Voting written by Keith T. Poole and published by Cambridge University Press. This book was released on 2005-04-11 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a simple geometric model of voting as a tool to analyze parliamentary roll call data. Each legislator is represented by one point and each roll call is represented by two points that correspond to the policy consequences of voting Yea or Nay. On every roll call each legislator votes for the closer outcome point, at least probabilistically. These points form a spatial map that summarizes the roll calls. In this sense a spatial map is much like a road map because it visually depicts the political world of a legislature. The closeness of two legislators on the map shows how similar their voting records are, and the distribution of legislators shows what the dimensions are. These maps can be used to study a wide variety of topics including how political parties evolve over time, the existence of sophisticated voting and how an executive influences legislative outcomes.
Download or read book The Routledge Handbook of Elections Voting Behavior and Public Opinion written by Justin Fisher and published by Routledge. This book was released on 2017-09-22 with total page 786 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of elections, voting behavior and public opinion are arguably among the most prominent and intensively researched sub-fields within Political Science. It is an evolving sub-field, both in terms of theoretical focus and in particular, technical developments and has made a considerable impact on popular understanding of the core components of liberal democracies in terms of electoral systems and outcomes, changes in public opinion and the aggregation of interests. This handbook details the key developments and state of the art research across elections, voting behavior and the public opinion by providing both an advanced overview of each core area and engaging in debate about the relative merits of differing approaches in a comprehensive and accessible way. Bringing geographical scope and depth, with comparative chapters that draw on material from across the globe, it will be a key reference point both for advanced level students and researchers developing knowledge and producing new material in these sub-fields and beyond. The Routledge Handbook of Elections, Voting Behavior and Public Opinion is an authoritative and key reference text for students, academics and researchers engaged in the study of electoral research, public opinion and voting behavior.
Download or read book Handbook of Group Decision and Negotiation written by D. Marc Kilgour and published by Springer Science & Business Media. This book was released on 2010-08-02 with total page 473 pages. Available in PDF, EPUB and Kindle. Book excerpt: Publication of the Handbook of Group Decision and Negotiation marks a milestone in the evolution of the group decision and negotiation (GDN) eld. On this occasion, editors Colin Eden and Marc Kilgour asked me to write a brief history of the eld to provide background and context for the volume. They said that I am in a good position to do so: Actively involved in creating the GDN Section and serving as its chair; founding and leading the GDN journal, Group Decision and Negotiation as editor-in-chief, and the book series, “Advances in Group Decision and Negotiation” as editor; and serving as general chair of the GDN annual meetings. I accepted their invitation to write a brief history. In 1989 what is now the Institute for Operations Research and the Management Sciences (INFORMS) established its Section on Group Decision and Negotiation. The journal Group Decision and Negotiation was founded in 1992, published by Springer in cooperation with INFORMS and the GDN Section. In 2003, as an ext- sion of the journal, the Springer book series, “Advances in Group Decision and Negotiation” was inaugurated.
Download or read book Geometry in everyday life written by Karen Morrison and published by Heinemann. This book was released on 2000 with total page 40 pages. Available in PDF, EPUB and Kindle. Book excerpt: Focusing on geometry, this is one of a series exploring issues of interest to children in Africa, and designed to introduce students to reading non-fiction for pleasure and information.
Download or read book Tensor Voting written by Philippos Mordohai and published by Springer Nature. This book was released on 2022-06-01 with total page 126 pages. Available in PDF, EPUB and Kindle. Book excerpt: This lecture presents research on a general framework for perceptual organization that was conducted mainly at the Institute for Robotics and Intelligent Systems of the University of Southern California. It is not written as a historical recount of the work, since the sequence of the presentation is not in chronological order. It aims at presenting an approach to a wide range of problems in computer vision and machine learning that is data-driven, local and requires a minimal number of assumptions. The tensor voting framework combines these properties and provides a unified perceptual organization methodology applicable in situations that may seem heterogeneous initially. We show how several problems can be posed as the organization of the inputs into salient perceptual structures, which are inferred via tensor voting. The work presented here extends the original tensor voting framework with the addition of boundary inference capabilities; a novel re-formulation of the framework applicable to high-dimensional spaces and the development of algorithms for computer vision and machine learning problems. We show complete analysis for some problems, while we briefly outline our approach for other applications and provide pointers to relevant sources.
Download or read book Geometric Ways of Understanding Voting Problems written by Tomas McIntee and published by . This book was released on 2015 with total page 153 pages. Available in PDF, EPUB and Kindle. Book excerpt: General conclusions relating pairwise tallies with positional (e.g., plurality, antiplurality ('vote-for-two')) election outcomes were previously known only for the Borda Count. While it has been known since the eighteenth century that the Borda and Condorcet winners need not agree, it had not been known, for instance, in which settings the Condorcet and plurality winners can disagree, or must agree. Results of this type are developed here for all three-alternative positional rules. These relationships are based on an easily used method that connects pairwise tallies with admissible positional outcomes; e.g., a special case provides the first necessary and sufficient conditions ensuring that the Condorcet winner is the plurality winner; another case identifies when there must be a profile whereby each candidate is the 'winner' with some positional rule. Previous work relating the probability of positional and pairwise tallies have used specific selected distributions (primarily the Impartial Culture and Impartial Anonymous Culture assumptions) and specific voting rules (particularly plurality). Techniques are developed here that can be applied to analyzing the probability of conflict between all different positional methods, and between combinations of pairwise tallies with positional results. Results are given for several broad categories of probability distribution, along with a qualitative analysis of the relationship between probability distributions over voter profiles and the likelihood of voting paradoxes. A method of geometrically comparing multiple-stage and single-stage elections is developed, which shows that multiple stage elections are not necessarily more vulnerable to being manipulated, but less vulnerable when all rank-order outcomes matter, and specifically only similar when an election only identifies a first-place winner. In the case where results are defined in terms of a singular winner, a plurality vote is identified as less manipulable in a single stage than in multiple stages, while an antiplurality vote is identified as more vulnerable in a single stage than in multiple stages.
Download or read book Computational Geometry written by Franco P. Preparata and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 413 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the reviews: "This book offers a coherent treatment, at the graduate textbook level, of the field that has come to be known in the last decade or so as computational geometry. ... ... The book is well organized and lucidly written; a timely contribution by two founders of the field. It clearly demonstrates that computational geometry in the plane is now a fairly well-understood branch of computer science and mathematics. It also points the way to the solution of the more challenging problems in dimensions higher than two." #Mathematical Reviews#1 "... This remarkable book is a comprehensive and systematic study on research results obtained especially in the last ten years. The very clear presentation concentrates on basic ideas, fundamental combinatorial structures, and crucial algorithmic techniques. The plenty of results is clever organized following these guidelines and within the framework of some detailed case studies. A large number of figures and examples also aid the understanding of the material. Therefore, it can be highly recommended as an early graduate text but it should prove also to be essential to researchers and professionals in applied fields of computer-aided design, computer graphics, and robotics." #Biometrical Journal#2
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.
