Basic Geometry Of Voting
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Basic Geometry Of Voting
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Author : Donald G. Saari
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Basic Geometry Of Voting written by Donald G. Saari and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Business & Economics categories.
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directed mainly toward students and others wishing to learn about voting, experts will discover here many previously unpublished results.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
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Author : Donald G. Saari
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Geometry Of Voting written by Donald G. Saari and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Business & Economics categories.
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.
Geometry Of Voting
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Author : Donald G. Saari
language : en
Publisher:
Release Date : 2014-01-15
Geometry Of Voting written by Donald G. Saari and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.
The Geometry Of Elections
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Author : Ernest W. Adams
language : en
Publisher: Stanford Univ Center for the Study
Release Date : 2014-10-15
The Geometry Of Elections written by Ernest W. Adams and has been published by Stanford Univ Center for the Study this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-10-15 with Language Arts & Disciplines categories.
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.
Algebraic And Geometric Methods In Discrete Mathematics
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Author : Heather A. Harrington
language : en
Publisher: American Mathematical Soc.
Release Date : 2017-03-16
Algebraic And Geometric Methods In Discrete Mathematics written by Heather A. Harrington and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-03-16 with Commutative algebra -- Computational aspects and applications -- Applications of commutative algebra (e.g., to statistics, control theory, optimization, etc.) categories.
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
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Author : Manfred J Holler
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-19
Power Voting And Voting Power 30 Years After written by Manfred J Holler and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-19 with Business & Economics categories.
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
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Author : Donald Saari
language : en
Publisher: American Mathematical Soc.
Release Date : 2001-04-03
Chaotic Elections written by Donald Saari and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-04-03 with Political Science categories.
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.
Disposing Dictators Demystifying Voting Paradoxes
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Author : Donald Saari
language : en
Publisher:
Release Date : 2008-08-25
Disposing Dictators Demystifying Voting Paradoxes written by Donald Saari and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-08-25 with Business & Economics categories.
This book is a positive analysis of voting 'paradoxes' and argues that negative 'impossibility' results are not justified.
Advances In Neural Networks Isnn 2009
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Author : Wen Yu
language : en
Publisher: Springer
Release Date : 2009-05-20
Advances In Neural Networks Isnn 2009 written by Wen Yu and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-05-20 with Computers categories.
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
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Author : Donald Saari
language : en
Publisher: Cambridge University Press
Release Date : 2001-10-22
Decisions And Elections written by Donald Saari and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-10-22 with Business & Economics categories.
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.