Geometry Of Voting

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Basic Geometry of Voting

Author : Donald G. Saari
Publisher : Springer Science & Business Media
ISBN 13 : 3642577482
Total Pages : 308 pages
Book Rating : 4.6/5 (425 download)

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Book Synopsis Basic Geometry of Voting by : Donald G. Saari

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directed mainly toward students and others wishing to learn about voting, experts will discover here many previously unpublished results.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

Geometry of Voting

Author : Donald G. Saari
Publisher : Springer Science & Business Media
ISBN 13 : 3642486444
Total Pages : 388 pages
Book Rating : 4.6/5 (424 download)

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Book Synopsis Geometry of Voting by : Donald G. Saari

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.

Voting Paradoxes and How to Deal with Them

Author : Hannu Nurmi
Publisher : Springer Science & Business Media
ISBN 13 : 3662037823
Total Pages : 160 pages
Book Rating : 4.6/5 (62 download)

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Book Synopsis Voting Paradoxes and How to Deal with Them by : Hannu Nurmi

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.

Spatial Models of Parliamentary Voting

Author : Keith T. Poole
Publisher : Cambridge University Press
ISBN 13 : 9781139446754
Total Pages : 252 pages
Book Rating : 4.4/5 (467 download)

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Book Synopsis Spatial Models of Parliamentary Voting by : Keith T. Poole

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.

The Mathematics of Elections and Voting

Author : W.D. Wallis
Publisher : Springer
ISBN 13 : 3319098101
Total Pages : 103 pages
Book Rating : 4.3/5 (19 download)

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Book Synopsis The Mathematics of Elections and Voting by : W.D. Wallis

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.

The Mathematics of Voting and Apportionment

Author : Sherif El-Helaly
Publisher : Springer
ISBN 13 : 3030147681
Total Pages : 275 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis The Mathematics of Voting and Apportionment by : Sherif El-Helaly

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 275 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.”

The Routledge Handbook of Elections, Voting Behavior and Public Opinion

Author : Justin Fisher
Publisher : Routledge
ISBN 13 : 1317494806
Total Pages : 786 pages
Book Rating : 4.3/5 (174 download)

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Book Synopsis The Routledge Handbook of Elections, Voting Behavior and Public Opinion by : Justin Fisher

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.

Tensor Voting

Author : Philippos Mordohai
Publisher : Springer Nature
ISBN 13 : 3031022424
Total Pages : 126 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Tensor Voting by : Philippos Mordohai

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.

Handbook of Group Decision and Negotiation

Author : D. Marc Kilgour
Publisher : Springer Science & Business Media
ISBN 13 : 9048190975
Total Pages : 473 pages
Book Rating : 4.0/5 (481 download)

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Book Synopsis Handbook of Group Decision and Negotiation by : D. Marc Kilgour

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.

Geometry in everyday life

Author : Karen Morrison
Publisher : Heinemann
ISBN 13 : 9780435898922
Total Pages : 40 pages
Book Rating : 4.8/5 (989 download)

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Book Synopsis Geometry in everyday life by : Karen Morrison

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.

Understanding Modern Mathematics

Author : Saul Stahl
Publisher : Jones & Bartlett Learning
ISBN 13 : 9780763734015
Total Pages : 284 pages
Book Rating : 4.7/5 (34 download)

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Book Synopsis Understanding Modern Mathematics by : Saul Stahl

Download or read book Understanding Modern Mathematics written by Saul Stahl and published by Jones & Bartlett Learning. This book was released on 2007 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Vote!

Author : Eileen Christelow
Publisher : Clarion Books
ISBN 13 : 1328499227
Total Pages : 53 pages
Book Rating : 4.3/5 (284 download)

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Book Synopsis Vote! by : Eileen Christelow

Download or read book Vote! written by Eileen Christelow and published by Clarion Books. This book was released on 2018-09 with total page 53 pages. Available in PDF, EPUB and Kindle. Book excerpt: "It's hard to imagine a more accessible introduction to voting" than Eileen Christelow's hilariously illustrated Vote , now updated for the 2018 midterm elections. (Booklist, starred review) * "It's hard to imagine a more accessible introduction to voting." --Booklist, starred review "Explains the whys and wherefores of the voting process . . . and why it all matters." --Washington Post An ALA Notable Children's Book An IRA-CBC Children's Choice Eileen Christelow's Vote has everything you need to know about voting and how our democracy works--parties, voter registration, campaigns, rallies, debates, Election Day, even recounts Topics are presented in a clear, kid-friendly graphic format as the story of a local election unfolds, with hilarious commentary by the candidates' pets. Includes updated back matter for the 2018 midterm election.

The Joy of X

Author : Steven Henry Strogatz
Publisher : Houghton Mifflin Harcourt
ISBN 13 : 0547517653
Total Pages : 333 pages
Book Rating : 4.5/5 (475 download)

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Book Synopsis The Joy of X by : Steven Henry Strogatz

Download or read book The Joy of X written by Steven Henry Strogatz and published by Houghton Mifflin Harcourt. This book was released on 2012 with total page 333 pages. Available in PDF, EPUB and Kindle. Book excerpt: A delightful tour of the greatest ideas of math, showing how math intersects with philosophy, science, art, business, current events, and everyday life, by an acclaimed science communicator and regular contributor to the "New York Times."

Mathematics of Social Choice

Author : Christoph Borgers
Publisher : SIAM
ISBN 13 : 0898717620
Total Pages : 233 pages
Book Rating : 4.8/5 (987 download)

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Book Synopsis Mathematics of Social Choice by : Christoph Borgers

Download or read book Mathematics of Social Choice written by Christoph Borgers and published by SIAM. This book was released on 2010-01-01 with total page 233 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics of Social Choice is a fun and accessible book that looks at the choices made by groups of people with different preferences, needs, and interests. Divided into three parts, the text first examines voting methods for selecting or ranking candidates. A brief second part addresses compensation problems wherein an indivisible item must be assigned to one of several people who are equally entitled to ownership of the item, with monetary compensation paid to the others. The third part discusses the problem of sharing a divisible resource among several people. Mathematics of Social Choice can be used by undergraduates studying mathematics and students whose only mathematical background is elementary algebra. More advanced material can be skipped without any loss of continuity. The book can also serve as an easy introduction to topics such as the Gibbard-Satterthwaite theorem, Arrow's theorem, and fair division for readers with more mathematical background.

Computational Geometry

Author : Franco P. Preparata
Publisher : Springer Science & Business Media
ISBN 13 : 1461210984
Total Pages : 413 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Computational Geometry by : Franco P. Preparata

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

Rightfully Ours

Author : Kerrie Logan Hollihan
Publisher : Chicago Review Press
ISBN 13 : 1883052920
Total Pages : 146 pages
Book Rating : 4.8/5 (83 download)

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Book Synopsis Rightfully Ours by : Kerrie Logan Hollihan

Download or read book Rightfully Ours written by Kerrie Logan Hollihan and published by Chicago Review Press. This book was released on 2012-08-01 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt: Though the Declaration of Independence stated that &“all men are created equal,&” married women and girls in the early days of the United States had few rights. For better or worse, their lives were controlled by their husbands and fathers. Married women could not own property, and few girls were educated beyond reading and simple math. Women could not work as doctors, lawyers, or in the ministry. Not one woman could vote, but that would change with the tireless efforts of Lucretia Mott, Lucy Stone, Elizabeth Cady Stanton, Sojourner Truth, Susan B. Anthony, Carrie Chapman Catt, Jeannette Rankin, Alice Paul, and thousands of women across the nation. Rightfully Ours tells of the century-long struggle for woman suffrage in the United States, a movement that began alongside the abolitionist cause and continued through the ratification of the 19th amendment. In addition to its lively narrative, this history includes a time line, online resources, and hands-on activities that will give readers a sense of everyday lives of the suffragists. Children will create a banner for suffrage, host a Victorian tea, feel what it was like to wear a corset, and more. And through it all, readers will gain a richer appreciation for women who secured the right to fully participate in American democracy—and why they must never take that right for granted. Kerrie Logan Hollihan is the author of Isaac Newton and Physics for Kids, Theodore Roosevelt for Kids, and Elizabeth I, The People's Queen. She lives in Blue Ash, Ohio.

Decisions and Elections

Author : Donald Saari
Publisher : Cambridge University Press
ISBN 13 : 9780521004046
Total Pages : 258 pages
Book Rating : 4.0/5 (4 download)

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Book Synopsis Decisions and Elections by : Donald Saari

Download or read book Decisions and Elections written by Donald Saari and published by Cambridge University Press. This book was released on 2001-10-22 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is not uncommon to be frustrated by the outcome of an election or a decision in voting, law, economics, engineering, and other fields. Does this 'bad' result reflect poor data or poorly informed voters? Or does the disturbing conclusion reflect the choice of the decision/election procedure? Nobel Laureate Kenneth Arrow's famed theorem has been interpreted to mean 'no decision procedure is without flaws'. Similarly, Nobel Laureate Amartya Sen dashes hope for individual liberties by showing their incompatibility with societal needs. This highly accessible book offers a new, different interpretation and resolution of Arrow's and Sen's theorems. Using simple mathematics, it shows that these negative conclusions arise because, in each case, some of their assumptions negate other crucial assumptions. Once this is understood, not only do the conclusions become expected, but a wide class of other phenomena can also be anticipated.