Geometry Of Voting

Author : Donald G. Saari
Publisher : Springer Science & Business Media
Page : 388 pages
File Size : 48,6 Mb
Release : 2012-12-06
Category : Business & Economics
ISBN : 9783642486449

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Geometry of Voting by Donald G. Saari Pdf

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.

Author : Donald G. Saari
Publisher : Springer Science & Business Media
Page : 308 pages
File Size : 46,6 Mb
Release : 2012-12-06
Category : Business & Economics
ISBN : 9783642577482

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Basic Geometry of Voting by Donald G. Saari Pdf

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directed mainly toward students and others wishing to learn about voting, experts will discover here many previously unpublished results.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.

Author : Donald G. Saari
Publisher : Unknown
Page : 398 pages
File Size : 46,9 Mb
Release : 2014-01-15
Category : Electronic
ISBN : 3642486452

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Geometry of Voting by Donald G. Saari Pdf

Author : Ernest W. Adams,James Adams
Publisher : Stanford Univ Center for the Study
Page : 350 pages
File Size : 45,8 Mb
Release : 2014-03-01
Category : Political Science
ISBN : 157586486X

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The Geometry of Elections by Ernest W. Adams,James Adams Pdf

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.

Author : Hannu Nurmi
Publisher : Springer Science & Business Media
Page : 160 pages
File Size : 44,5 Mb
Release : 2013-04-17
Category : Political Science
ISBN : 9783662037829

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Voting Paradoxes and How to Deal with Them by Hannu Nurmi Pdf

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.

Author : Keith T. Poole
Publisher : Cambridge University Press
Page : 252 pages
File Size : 43,7 Mb
Release : 2005-04-11
Category : Political Science
ISBN : 1139446754

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Spatial Models of Parliamentary Voting by Keith T. Poole Pdf

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.

Author : Moon Duchin,Olivia Walch
Publisher : Birkhäuser
Page : 436 pages
File Size : 40,9 Mb
Release : 2022-04-02
Category : Mathematics
ISBN : 3319691600

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Political Geometry by Moon Duchin,Olivia Walch Pdf

“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.”

Author : Justin Fisher,Edward Fieldhouse,Mark N. Franklin,Rachel Gibson,Marta Cantijoch,Christopher Wlezien
Publisher : Routledge
Page : 786 pages
File Size : 46,5 Mb
Release : 2017-09-22
Category : Political Science
ISBN : 9781317494805

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The Routledge Handbook of Elections, Voting Behavior and Public Opinion by Justin Fisher,Edward Fieldhouse,Mark N. Franklin,Rachel Gibson,Marta Cantijoch,Christopher Wlezien Pdf

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.

Author : Moon Duchin,Olivia Walch
Publisher : Unknown
Page : 0 pages
File Size : 41,7 Mb
Release : 2022
Category : Electronic
ISBN : 3319691627

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Political Geometry by Moon Duchin,Olivia Walch Pdf

"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.".

Author : Donald Saari
Publisher : Unknown
Page : 264 pages
File Size : 45,7 Mb
Release : 2008-08-25
Category : Business & Economics
ISBN : UOM:39015077658055

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Disposing Dictators, Demystifying Voting Paradoxes by Donald Saari Pdf

This book is a positive analysis of voting 'paradoxes' and argues that negative 'impossibility' results are not justified.

Author : Saul Stahl,Paul E. Johnson
Publisher : Jones & Bartlett Learning
Page : 284 pages
File Size : 45,9 Mb
Release : 2007
Category : Mathematics
ISBN : 0763734012

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Understanding Modern Mathematics by Saul Stahl,Paul E. Johnson Pdf

Understanding Modern Mathematics is an exceptional collection of topics meant to better acquaint students with mathematics through an exposure to its applications and an analysis of its culture. The text provides an in-depth focus on such key topics as probability, statistics, voting systems, game theory, and linear programming. Two additional chapters on geometry and symmetry can be found on the text's web site, providing students the opportunity to see the 3-dimensional geometric figures in full color. The text provides students with an understanding of how these important mathematical topics are relevant in their everyday lives while emphasizing the history of mathematics . Understanding Modern Mathematics is the perfect complement to any Liberal Arts Mathematics course. Click Here to View Chapter 6 Click Here to View Chapter 7

Author : Heather A. Harrington,Mohamed Omar,Matthew Wright
Publisher : American Mathematical Soc.
Page : 277 pages
File Size : 54,9 Mb
Release : 2017-03-16
Category : Commutative algebra -- Computational aspects and applications -- Applications of commutative algebra (e.g., to statistics, control theory, optimization, etc.)
ISBN : 9781470423216

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Algebraic and Geometric Methods in Discrete Mathematics by Heather A. Harrington,Mohamed Omar,Matthew Wright Pdf

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.

Author : D. Marc Kilgour,Colin Eden
Publisher : Springer Science & Business Media
Page : 473 pages
File Size : 52,9 Mb
Release : 2010-08-02
Category : Mathematics
ISBN : 9789048190973

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Handbook of Group Decision and Negotiation by D. Marc Kilgour,Colin Eden Pdf

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.

Author : Kenneth J. Arrow,A. Sen,Kotaro Suzumura
Publisher : Elsevier
Page : 985 pages
File Size : 49,5 Mb
Release : 2010-10-13
Category : Business & Economics
ISBN : 9780080929828

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Handbook of Social Choice and Welfare by Kenneth J. Arrow,A. Sen,Kotaro Suzumura Pdf

This second part of a two-volume set continues to describe economists' efforts to quantify the social decisions people necessarily make and the philosophies that those choices define. Contributors draw on lessons from philosophy, history, and other disciplines, but they ultimately use editor Kenneth Arrow's seminal work on social choice as a jumping-off point for discussing ways to incentivize, punish, and distribute goods. Develops many subjects from Volume 1 (2002) while introducing new themes in welfare economics and social choice theory Features four sections: Foundations, Developments of the Basic Arrovian Schemes, Fairness and Rights, and Voting and Manipulation Appeals to readers who seek introductions to writings on human well-being and collective decision-making Presents a spectrum of material, from initial insights and basic functions to important variations on basic schemes

Author : Philippos Mordohai,Gérard Medioni
Publisher : Springer Nature
Page : 126 pages
File Size : 47,9 Mb
Release : 2022-06-01
Category : Technology & Engineering
ISBN : 9783031022425

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Tensor Voting by Philippos Mordohai,Gérard Medioni Pdf

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.