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.
Download or read book Voting Procedures for Electing a Single Candidate written by Dan S. Felsenthal and published by Springer. This book was released on 2018-01-19 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Elections Voting Rules and Paradoxical Outcomes written by William V. Gehrlein and published by Springer. This book was released on 2017-10-14 with total page 183 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Voting Paradoxes and Group Coherence written by William V. Gehrlein and published by Springer Science & Business Media. This book was released on 2010-11-11 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Electoral Systems written by Dan S. Felsenthal and published by Springer Science & Business Media. This book was released on 2012-01-03 with total page 353 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Voting Procedures Under a Restricted Domain written by Dan S. Felsenthal and published by Springer. This book was released on 2019-04-02 with total page 92 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Voting Paradoxes and Group Coherence written by William V. Gehrlein and published by . This book was released on 2011-03-30 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
Download or read book Mathematics to the Rescue of Democracy written by Paolo Serafini and published by Springer Nature. This book was released on 2020-03-02 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
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.
Download or read book Electoral Systems written by Dan S. Felsenthal and published by Springer. This book was released on 2012-01-05 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
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.
Download or read book The Measurement of Voting Power written by Dan S. Felsenthal and published by Edward Elgar Publishing. This book was released on 1998 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Gaming the Vote written by William Poundstone and published by Macmillan. This book was released on 2009-02-17 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: At least five U.S. presidential elections have been won by the second most popular candidate, because of "spoilers"--Minor candidates who take enough votes away from the most popular candidate to tip the election. The spoiler effect is a consequence of the "impossibility theorem," discovered by Nobel laureate economist Kenneth Arrow, which asserts that voting is fundamentally unfair--and political strategists are exploiting the mathematical faults of the simple majority vote. This book presents a solution to the spoiler problem: a system called range voting, already widely used on the Internet, which is the fairest voting method of all, according to computer studies. Range voting remains controversial, however, and author Poundstone assesses the obstacles confronting any attempt to change the American electoral system.--From publisher description.
Download or read book Disposing Dictators Demystifying Voting Paradoxes written by Donald Saari and published by . This book was released on 2014-05-14 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a positive analysis of voting 'paradoxes' and argues that negative 'impossibility' results are not justified.
Download or read book Numbers Rule written by George Szpiro and published by Princeton University Press. This book was released on 2020-11-03 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: The author takes the general reader on a tour of the mathematical puzzles and paradoxes inherent in voting systems, such as the Alabama Paradox, in which an increase in the number of seats in the Congress could actually lead to a reduced number of representatives for a state, and the Condorcet Paradox, which demonstrates that the winner of elections featuring more than two candidates does not necessarily reflect majority preferences. Szpiro takes a roughly chronological approach to the topic, traveling from ancient Greece to the present and, in addition to offering explanations of the various mathematical conundrums of elections and voting, also offers biographical details on the mathematicians and other thinkers who thought about them, including Plato, Pliny the Younger, Pierre Simon Laplace, Thomas Jefferson, John von Neumann, and Kenneth Arrow.
Download or read book Evaluating Voting Systems with Probability Models written by Mostapha Diss and published by Springer. This book was released on 2021-12-19 with total page 403 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book includes up-to-date contributions in the broadly defined area of probabilistic analysis of voting rules and decision mechanisms. Featuring papers from all fields of social choice and game theory, it presents probability arguments to allow readers to gain a better understanding of the properties of decision rules and of the functioning of modern democracies. In particular, it focuses on the legacy of William Gehrlein and Dominique Lepelley, two prominent scholars who have made important contributions to this field over the last fifty years. It covers a range of topics, including (but not limited to) computational and technical aspects of probability approaches, evaluation of the likelihood of voting paradoxes, power indices, empirical evaluations of voting rules, models of voters’ behavior, and strategic voting. The book gathers articles written in honor of Gehrlein and Lepelley along with original works written by the two scholars themselves.
