Voting Paradoxes And How To Deal With Them

Author : Hannu Nurmi
Publisher : Springer Science & Business Media
Page : 160 pages
File Size : 49,5 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 : Dan S. Felsenthal,Hannu Nurmi
Publisher : Springer
Page : 134 pages
File Size : 40,9 Mb
Release : 2018-01-19
Category : Business & Economics
ISBN : 9783319740331

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Voting Procedures for Electing a Single Candidate by Dan S. Felsenthal,Hannu Nurmi Pdf

This book deals with 18 voting procedures used or proposed for use in elections resulting in the choice of a single winner. These procedures are evaluated in terms of their ability to avoid paradoxical outcomes. Together with a companion volume by the same authors, Monotonicity Failures Afflicting Procedures for Electing a Single Candidate, published by Springer in 2017, this book aims at giving a comprehensive overview of the most important advantages and disadvantages of procedures thereby assisting decision makers in the choice of a voting procedure that would best suit their purposes.

Author : William V. Gehrlein,Dominique Lepelley
Publisher : Springer
Page : 183 pages
File Size : 40,6 Mb
Release : 2017-10-14
Category : Business & Economics
ISBN : 9783319646596

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Elections, Voting Rules and Paradoxical Outcomes by William V. Gehrlein,Dominique Lepelley Pdf

This monograph studies voting procedures based on the probability that paradoxical outcomes like the famous Condorcet Paradox might exist. It is well known that hypothetical examples of many different paradoxical election outcomes can be developed, but this analysis examines factors that are related to the process by which voters form their preferences on candidates that will significantly reduce the likelihood that such voting paradoxes will ever actually be observed. It is found that extreme forms of voting paradoxes should be uncommon events with a small number of candidates. Another consideration is the propensity of common voting rules to elect the Condorcet Winner, which is widely accepted as the best choice as the winner, when it exists. All common voting rules are found to have identifiable scenarios for which they perform well on the basis of this criterion. But, Borda Rule is found to consistently work well at electing the Condorcet Winner, while the other voting rules have scenarios where they work poorly or have a very small likelihood of electing a different candidate than Borda Rule. The conclusions of previous theoretical work are presented in an expository format and they are validated with empirically-based evidence. Practical implications of earlier studies are also developed.

Author : Dan S. Felsenthal,Moshé Machover
Publisher : Springer Science & Business Media
Page : 352 pages
File Size : 50,6 Mb
Release : 2012-01-03
Category : Business & Economics
ISBN : 9783642204418

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Electoral Systems by Dan S. Felsenthal,Moshé Machover Pdf

Both theoretical and empirical aspects of single- and multi-winner voting procedures are presented in this collection of papers. Starting from a discussion of the underlying principles of democratic representation, the volume includes a description of a great variety of voting procedures. It lists and illustrates their susceptibility to the main voting paradoxes, assesses (under various models of voters' preferences) the probability of paradoxical outcomes, and discusses the relevance of the theoretical results to the choice of voting system.

Author : William V. Gehrlein,Dominique Lepelley
Publisher : Unknown
Page : 400 pages
File Size : 52,5 Mb
Release : 2011-03-30
Category : Electronic
ISBN : 3642031080

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Voting Paradoxes and Group Coherence by William V. Gehrlein,Dominique Lepelley Pdf

Author : Dan S. Felsenthal,Hannu Nurmi
Publisher : Springer
Page : 92 pages
File Size : 50,6 Mb
Release : 2019-04-02
Category : Business & Economics
ISBN : 9783030126278

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Voting Procedures Under a Restricted Domain by Dan S. Felsenthal,Hannu Nurmi Pdf

This book deals with 20 voting procedures used or proposed for use in elections resulting in the choice of a single winner. These procedures are evaluated in terms of their ability to avoid five important paradoxes in a restricted domain, viz., when a Condorcet winner exists and is elected in the initial profile. Together with the two companion volumes by the same authors, published by Springer in 2017 and 2018, this book aims at giving a comprehensive overview of the most important advantages and disadvantages of voting procedures thereby assisting decision makers in the choice of a voting procedure that would best suit their purposes.

Author : William V. Gehrlein,Dominique Lepelley
Publisher : Springer Science & Business Media
Page : 392 pages
File Size : 51,9 Mb
Release : 2010-11-11
Category : Business & Economics
ISBN : 9783642031076

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Voting Paradoxes and Group Coherence by William V. Gehrlein,Dominique Lepelley Pdf

The likelihood of observing Condorcet's Paradox is known to be very low for elections with a small number of candidates if voters’ preferences on candidates reflect any significant degree of a number of different measures of mutual coherence. This reinforces the intuitive notion that strange election outcomes should become less likely as voters’ preferences become more mutually coherent. Similar analysis is used here to indicate that this notion is valid for most, but not all, other voting paradoxes. This study also focuses on the Condorcet Criterion, which states that the pairwise majority rule winner should be chosen as the election winner, if one exists. Representations for the Condorcet Efficiency of the most common voting rules are obtained here as a function of various measures of the degree of mutual coherence of voters’ preferences. An analysis of the Condorcet Efficiency representations that are obtained yields strong support for using Borda Rule.

Author : Dan S. Felsenthal,Moshé Machover
Publisher : Springer
Page : 352 pages
File Size : 47,7 Mb
Release : 2012-01-05
Category : Business & Economics
ISBN : 3642204406

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Electoral Systems by Dan S. Felsenthal,Moshé Machover Pdf

Both theoretical and empirical aspects of single- and multi-winner voting procedures are presented in this collection of papers. Starting from a discussion of the underlying principles of democratic representation, the volume includes a description of a great variety of voting procedures. It lists and illustrates their susceptibility to the main voting paradoxes, assesses (under various models of voters' preferences) the probability of paradoxical outcomes, and discusses the relevance of the theoretical results to the choice of voting system.

Author : Paolo Serafini
Publisher : Springer Nature
Page : 138 pages
File Size : 44,6 Mb
Release : 2020-03-02
Category : Mathematics
ISBN : 9783030383688

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Mathematics to the Rescue of Democracy by Paolo Serafini Pdf

This book explains, in a straightforward way, the foundations upon which electoral techniques are based in order to shed new light on what we actually do when we vote. The intention is to highlight the fact that no matter how an electoral system has been designed, and regardless of the intentions of those who devised the system, there will be goals that are impossible to achieve but also opportunities for improving the situation in an informed way. While detailed descriptions of electoral systems are not provided, many references are made to current or past situations, both as examples and to underline particular problems and shortcomings. In addition, a new voting method that avoids the many paradoxes of voting theory is described in detail. While some knowledge of mathematics is required in order to gain the most from the book, every effort has been made to ensure that the subject matter is easily accessible for non-mathematicians, too. In short, this is a book for anyone who wants to understand the meaning of voting.

Author : Donald Saari
Publisher : Unknown
Page : 257 pages
File Size : 43,5 Mb
Release : 2014-05-14
Category : Political Science
ISBN : 0511429797

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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 : Donald Saari
Publisher : Cambridge University Press
Page : 258 pages
File Size : 51,5 Mb
Release : 2001-10-22
Category : Business & Economics
ISBN : 0521004047

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Decisions and Elections by Donald Saari Pdf

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.

Author : William V. Gehrlein
Publisher : Springer Science & Business Media
Page : 298 pages
File Size : 48,7 Mb
Release : 2006-08-29
Category : Business & Economics
ISBN : 9783540337997

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Condorcet's Paradox by William V. Gehrlein Pdf

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.

Author : Len Fisher
Publisher : Basic Books
Page : 288 pages
File Size : 46,9 Mb
Release : 2009-11-17
Category : Science
ISBN : 9780465020850

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The Perfect Swarm by Len Fisher Pdf

The process of "self-organization" reveals itself in the inanimate worlds of crystals and seashells, but, as Len Fisher shows, it is also evident in living organisms, from fish to ants to human beings. Understanding the "swarm intelligence" inherent in groups can help us do everything from throw a better party to start a fad to make our interactions with others more powerful. Humorous and enlightening, The Perfect Swarm demonstrates how complexity arises from nature's simple rules and how we can use their awesome power to untangle the frustrating complexities of life in our ever more chaotic world.

Author : Dan S. Felsenthal,Moshé Machover
Publisher : Edward Elgar Publishing
Page : 360 pages
File Size : 52,7 Mb
Release : 1998
Category : Political Science
ISBN : UOM:39015045621870

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The Measurement of Voting Power by Dan S. Felsenthal,Moshé Machover Pdf

This work measures a priori voting power in social choice theory, presenting a systematic and critical examination of a priori voting, and analyzing the foundations and methodological assumptions underlying the theory. At the same time, it presents case study examples.

Author : Donald Saari
Publisher : American Mathematical Soc.
Page : 178 pages
File Size : 50,7 Mb
Release : 2001-04-03
Category : Political Science
ISBN : 0821886169

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Chaotic Elections! by Donald Saari Pdf

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.