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directed mainly toward students and others wishing to learn about voting, experts will discover here many previously unpublished results.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

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.

Algebraic and Geometric Methods in Discrete Mathematics

Author : Heather A. Harrington
Publisher : American Mathematical Soc.
ISBN 13 : 1470423219
Total Pages : 290 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Algebraic and Geometric Methods in Discrete Mathematics by : Heather A. Harrington

Download or read book Algebraic and Geometric Methods in Discrete Mathematics written by Heather A. Harrington and published by American Mathematical Soc.. This book was released on 2017-03-16 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Power, Voting, and Voting Power: 30 Years After

Author : Manfred J Holler
Publisher : Springer Science & Business Media
ISBN 13 : 3642359299
Total Pages : 752 pages
Book Rating : 4.6/5 (423 download)

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Book Synopsis Power, Voting, and Voting Power: 30 Years After by : Manfred J Holler

Download or read book Power, Voting, and Voting Power: 30 Years After written by Manfred J Holler and published by Springer Science & Business Media. This book was released on 2013-03-19 with total page 752 pages. Available in PDF, EPUB and Kindle. Book excerpt: The developments over a thirty-year time span in the study of power, especially voting power, are traced in this book, which provides an up-to-date overview of applications of n-person game theory to the study of power in multimember bodies. Other theories that shed light on power distribution (e.g. aggregation theory) are treated as well. The book revisits the themes discussed in the well-known 1982 publication "Power, Voting and Voting Power" (edited by Manfred J. Holler). Thirty years later this essential topic has been taken up again and many of the authors from its predecessor participate here again in discussing the state-of-the-art, demonstrating the achievements of three decades of intensive research, and pointing the way to key issues for future work.

Chaotic Elections!

Author : Donald Saari
Publisher : American Mathematical Soc.
ISBN 13 : 9780821886168
Total Pages : 178 pages
Book Rating : 4.8/5 (861 download)

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Book Synopsis Chaotic Elections! by : Donald Saari

Download or read book Chaotic Elections! written by Donald Saari and published by American Mathematical Soc.. This book was released on 2001-04-03 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: What does the 2000 U.S. presidential election have in common with selecting a textbook for a calculus course in your department? Was Ralph Nader's influence on the election of George W. Bush greater than the now-famous chads? In Chaotic Elections!, Don Saari analyzes these questions, placing them in the larger context of voting systems in general. His analysis shows that the fundamental problems with the 2000 presidential election are not with the courts, recounts, or defective ballots, but are caused by the very way Americans vote for president. This expository book shows how mathematics can help to identify and characterize a disturbingly large number of paradoxical situations that result from the choice of a voting procedure. Moreover, rather than being able to dismiss them as anomalies, the likelihood of a dubious election result is surprisingly large. These consequences indicate that election outcomes--whether for president, the site of the next Olympics, the chair of a university department, or a prize winner--can differ from what the voters really wanted. They show that by using an inadequate voting procedure, we can, inadvertently, choose badly. To add to the difficulties, it turns out that the mathematical structures of voting admit several strategic opportunities, which are described. Finally, mathematics also helps identify positive results: By using mathematical symmetries, we can identify what the phrase ``what the voters really want'' might mean and obtain a unique voting method that satisfies these conditions. Saari's book should be required reading for anyone who wants to understand not only what happened in the presidential election of 2000, but also how we can avoid similar problems from appearing anytime any group is making a choice using a voting procedure. Reading this book requires little more than high school mathematics and an interest in how the apparently simple situation of voting can lead to surprising paradoxes.

Advances in Neural Networks - ISNN 2009

Author : Wen Yu
Publisher : Springer
ISBN 13 : 3642015077
Total Pages : 1270 pages
Book Rating : 4.6/5 (42 download)

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Book Synopsis Advances in Neural Networks - ISNN 2009 by : Wen Yu

Download or read book Advances in Neural Networks - ISNN 2009 written by Wen Yu and published by Springer. This book was released on 2009-05-20 with total page 1270 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book and its companion volumes, LNCS vols. 5551, 5552 and 5553, constitute the proceedings of the 6th International Symposium on Neural Networks (ISNN 2009), held during May 26–29, 2009 in Wuhan, China. Over the past few years, ISNN has matured into a well-established premier international symposium on neural n- works and related fields, with a successful sequence of ISNN symposia held in Dalian (2004), Chongqing (2005), Chengdu (2006), Nanjing (2007), and Beijing (2008). Following the tradition of the ISNN series, ISNN 2009 provided a high-level inter- tional forum for scientists, engineers, and educators to present state-of-the-art research in neural networks and related fields, and also to discuss with international colleagues on the major opportunities and challenges for future neural network research. Over the past decades, the neural network community has witnessed tremendous - forts and developments in all aspects of neural network research, including theoretical foundations, architectures and network organizations, modeling and simulation, - pirical study, as well as a wide range of applications across different domains. The recent developments of science and technology, including neuroscience, computer science, cognitive science, nano-technologies and engineering design, among others, have provided significant new understandings and technological solutions to move the neural network research toward the development of complex, large-scale, and n- worked brain-like intelligent systems. This long-term goal can only be achieved with the continuous efforts of the community to seriously investigate different issues of the neural networks and related fields.

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.

Voting Procedures under Uncertainty

Author : Hannu Nurmi
Publisher : Springer Science & Business Media
ISBN 13 : 3540248307
Total Pages : 176 pages
Book Rating : 4.5/5 (42 download)

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Book Synopsis Voting Procedures under Uncertainty by : Hannu Nurmi

Download or read book Voting Procedures under Uncertainty written by Hannu Nurmi and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt: We live in an uncertain world, is a truism most of us hear more often than we would like. What one usually means to say by this is that we do not know what will happen in the future. Since changes, even major ones, have occurred in the past, it is possible that they will occur again in the future. In politics institutions are ways of coping with continuity and change. In democratic systems the electoral institutions provide ways of peaceful adjustment to changes in popular opinions. This book is about uncertainty as it pertains to electoral institutions. We shall deal with the ways in which analytic models are capable of taking into account voter uncertainty, ignorance and incompetence. We shall also discuss how uncertainty pertains to electoral outcomes. Given voter opinions, there is often a wide variation in the possible electoral outcomes. This could be called procedure-dependence of outcomes. Its existence shows that uncertainty is not something that can characterize only future events. It can pertain to past ones as well. This work is part of the Democracy and Constitution Project of Center for Business and Policy Studies (SNS). The idea of writing a book on the performance of voting procedures under uncertain cir cumstances came up in my correspondence with Dr. Per Molander of SNS a few years ago.

The Theory of Committees and Elections by Duncan Black and Committee Decisions with Complementary Valuation by Duncan Black and R.A. Newing

Download The Theory of Committees and Elections by Duncan Black and Committee Decisions with Complementary Valuation by Duncan Black and R.A. Newing PDF Online Free

Author : Iain S. McLean
Publisher : Springer Science & Business Media
ISBN 13 : 9401148600
Total Pages : 492 pages
Book Rating : 4.4/5 (11 download)

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Book Synopsis The Theory of Committees and Elections by Duncan Black and Committee Decisions with Complementary Valuation by Duncan Black and R.A. Newing by : Iain S. McLean

Download or read book The Theory of Committees and Elections by Duncan Black and Committee Decisions with Complementary Valuation by Duncan Black and R.A. Newing written by Iain S. McLean and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 492 pages. Available in PDF, EPUB and Kindle. Book excerpt: R. H. Coase Duncan Black was a close and dear friend. A man of great simplicity, un worldly, modest, diffident, with no pretensions, he was devoted to scholarship. In his single-minded search for the truth, he is an example to us all. Black's first degree at the University of Glasgow was in mathematics and physics. Mathematics as taught at Glasgow seems to have been designed for engineers and did not excite him and he switched to economics, which he found more congenial. But it was not in a lecture in economics but in one on politics that he found his star. One lecturer, A. K. White, discussed the possibility of constructing a pure science of politics. This question caught his imagination, perhaps because of his earlier training in physics, and it came to absorb his thoughts for the rest of his life. But almost certainly nothing would have come of it were it not for his appointment to the newly formed Dundee School of Economics where the rest of the. teaching staff came from the London School of Economics. At Glasgow, economics, as in the time of Adam Smith, was linked with moral philosophy. At Dundee, Black was introduced to the analytical x The Theory o/Committees and Elections approach dominant at the London School of Economics. This gave him the approach he used in his attempt to construct a pure science of politics.

Voting Paradoxes and How to Deal with Them

Author : Hannu Nurmi
Publisher : Springer Science & Business Media
ISBN 13 : 9783540662365
Total Pages : 172 pages
Book Rating : 4.6/5 (623 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 1999-09-17 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: Voting paradoxes are unpleasant surprises encountered in elections. They pertain to such phenomena as additional support being detrimental for candidates and not voting leading to better outcomes than voting for some voters. No voting system is immune to all paradoxes and, therefore voting paradoxes are being dealt with by all voting systems currently in use. How they are and how they should be handled is the main subject of this book. The book outlines, explains and classifies a number of paradoxes: Borda`s and Condorcet`s classic ones, several monotonicity and compound majority paradoxes as well as some paradoxes of representation. Both theoretical and practical ways of avoiding them are discussed.

Mathematical Analyses of Decisions, Voting and Games

Author : Michael A. Jones
Publisher : American Mathematical Society
ISBN 13 : 1470469782
Total Pages : 210 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Mathematical Analyses of Decisions, Voting and Games by : Michael A. Jones

Download or read book Mathematical Analyses of Decisions, Voting and Games written by Michael A. Jones and published by American Mathematical Society. This book was released on 2024-03-25 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the virtual AMS Special Session on Mathematics of Decisions, Elections and Games, held on April 8, 2022. Decision theory, voting theory, and game theory are three related areas of mathematics that involve making optimal decisions in different contexts. While these three areas are distinct, much of the recent research in these fields borrows techniques from other branches of mathematics such as algebra, combinatorics, convex geometry, logic, representation theory, etc. The papers in this volume demonstrate how the mathematics of decisions, elections, and games can be used to analyze problems from the social sciences.

Meeting Procedures

Author : James Lochrie
Publisher : Scarecrow Press
ISBN 13 : 0810844230
Total Pages : 230 pages
Book Rating : 4.8/5 (18 download)

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Book Synopsis Meeting Procedures by : James Lochrie

Download or read book Meeting Procedures written by James Lochrie and published by Scarecrow Press. This book was released on 2003-03-12 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt: From voting and debating to rules on quorum, this is a complete, modern guide to meeting procedures. Packed with simplified information that avoids jargon, it meets the needs of most non-profit organizations and professional associations. The author emphasizes the principles of meetings and introduces the use of modern technology in meetings.

Handbook of Social Choice and Voting

Author : Jac C. Heckelman
Publisher : Edward Elgar Publishing
ISBN 13 : 1783470739
Total Pages : 421 pages
Book Rating : 4.7/5 (834 download)

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Book Synopsis Handbook of Social Choice and Voting by : Jac C. Heckelman

Download or read book Handbook of Social Choice and Voting written by Jac C. Heckelman and published by Edward Elgar Publishing. This book was released on 2015-12-18 with total page 421 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Condorcet's Paradox

Author : William V. Gehrlein
Publisher : Springer Science & Business Media
ISBN 13 : 3540337997
Total Pages : 298 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Condorcet's Paradox by : William V. Gehrlein

Download or read book Condorcet's Paradox written by William V. Gehrlein and published by Springer Science & Business Media. This book was released on 2006-08-29 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book compiles research on Condorcet's Paradox over some two centuries. It begins with a historical overview of the discovery of Condorcet's Paradox in the 18th Century, reviews numerous studies conducted to find actual occurrences of the paradox, and compiles research that has been done to develop mathematical representations for the probability that the paradox will be observed. Combines all approaches that have been used to study this very interesting phenomenon.

The Handbook of Electoral System Choice

Author : J. Colomer
Publisher : Springer
ISBN 13 : 0230522742
Total Pages : 571 pages
Book Rating : 4.2/5 (35 download)

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Book Synopsis The Handbook of Electoral System Choice by : J. Colomer

Download or read book The Handbook of Electoral System Choice written by J. Colomer and published by Springer. This book was released on 2016-01-05 with total page 571 pages. Available in PDF, EPUB and Kindle. Book excerpt: The topic of electoral reform is an extremely timely one. The accelerated expansion of the number of new democracies in the world generates increasing demand for advice on the choice of electoral rules; at the same time, a new reformism in well established democracies seeks new formulae favouring both more representative institutions and more accountable rulers. The Handbook of Electoral System Choice addresses the theoretical and comparative issues of electoral reform in relation to democratization, political strategies in established democracies and the relative performance of different electoral systems. Case studies on virtually every major democracy or democratizing country in the world are included.

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.