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directed mainly toward students and others wishing to learn about voting, experts will discover here many previously unpublished results.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.
Geometric Ways Of Understanding Voting Problems
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Author : Tomas McIntee
language : en
Publisher:
Release Date : 2015
Geometric Ways Of Understanding Voting Problems written by Tomas McIntee and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with categories.
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.
The Likelihood Of Dubious Election Outcomes
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Author : Donald G. Saari
language : en
Publisher:
Release Date : 1999
The Likelihood Of Dubious Election Outcomes 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 1999 with categories.
A disturbing phenomenon in voting, which causes most of the problems as well as the interest in the field, is that election outcomes (for fixed preferences) can change with the way the ballots are tallied. This causes difficulties because with each possible choice, some set of voters can be dubious about whether it is the "correct" one. But, how likely are these settings allowing multiple election outcomes? By combining properties of the geometry of voting developed by Saari with a analytic-geometric technique created by Schlafli, we determine the likelihood that a three candidate election can cause these potentially dubious outcomes.
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.
Political Geometry
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Author : Moon Duchin
language : en
Publisher: Birkhäuser
Release Date : 2022-04-02
Political Geometry written by Moon Duchin and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-04-02 with Mathematics categories.
“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.”
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.
Understanding Modern Mathematics
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Author : Saul Stahl
language : en
Publisher: Jones & Bartlett Learning
Release Date : 2007
Understanding Modern Mathematics written by Saul Stahl and has been published by Jones & Bartlett Learning this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.
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