Probabilities of Voting Paradoxes with Three Candidates PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Probabilities of Voting Paradoxes with Three Candidates PDF full book. Access full book title Probabilities of Voting Paradoxes with Three Candidates by Leslie M. McDonald. Download full books in PDF and EPUB format.
Author: Leslie M. McDonald
Publisher:
ISBN:
Category : Central limit theorem
Languages : en
Pages : 68
Get Book Here
Book Description
Pardoxes in voting has been an interest of voting theorists since the 1800's when Condorcet demonstrated the key example of a voting paradox: voters with individually transitive rankings produce an election outcome which is not transitive. With Arrow's Impossibility Theorem, the hope of finding a fair voting method which accurately reflected society's preferences seemed unworkable. Recent results, however, have shown that paradoxes are unlikely under certain assumptions. In this paper, we corroborate results found by Gehrelin for the probabilities of paradoxes, but also give results which indicate paradoxes are extremely likely under the right conditions. We use simulations to show there can be many situations where paradoxes can arise, dependent upon the variability of voters' preferences, which echo Saari's statements on the topic.
Author: Leslie M. McDonald
Publisher:
ISBN:
Category : Central limit theorem
Languages : en
Pages : 68
Get Book Here
Book Description
Pardoxes in voting has been an interest of voting theorists since the 1800's when Condorcet demonstrated the key example of a voting paradox: voters with individually transitive rankings produce an election outcome which is not transitive. With Arrow's Impossibility Theorem, the hope of finding a fair voting method which accurately reflected society's preferences seemed unworkable. Recent results, however, have shown that paradoxes are unlikely under certain assumptions. In this paper, we corroborate results found by Gehrelin for the probabilities of paradoxes, but also give results which indicate paradoxes are extremely likely under the right conditions. We use simulations to show there can be many situations where paradoxes can arise, dependent upon the variability of voters' preferences, which echo Saari's statements on the topic.
Author: William V. Gehrlein
Publisher: Springer Science & Business Media
ISBN: 3642031072
Category : Business & Economics
Languages : en
Pages : 392
Get Book Here
Book Description
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: Mostapha Diss
Publisher: Springer Nature
ISBN: 3030485986
Category : Business & Economics
Languages : en
Pages : 412
Get Book Here
Book Description
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.
Author: William V. Gehrlein
Publisher: Springer
ISBN: 3319646591
Category : Business & Economics
Languages : en
Pages : 193
Get Book Here
Book Description
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
Publisher: Springer Science & Business Media
ISBN: 3642204414
Category : Business & Economics
Languages : en
Pages : 353
Get Book Here
Book Description
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
Publisher: Springer Science & Business Media
ISBN: 3540337997
Category : Business & Economics
Languages : en
Pages : 298
Get Book Here
Book Description
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: Hannu Nurmi
Publisher: Springer Science & Business Media
ISBN: 3662037823
Category : Political Science
Languages : en
Pages : 160
Get Book Here
Book Description
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: Adrian Van Deemen
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
Get Book Here
Book Description
In this paper the probability of the voting paradox for weak orderings is calculated analytically for the three-voter-three-alternative case. It appears that the probability obtained this way is considerably smaller than in the corresponding case for linear orderings. The probability of intransitive majority relations for weak orderings in the 3 x 3 case is calculated as well, both with unconcerned and with concerned voters. Basic in the calculations are three theorems which are formulated in the field of domain conditions and restricted preferences.
Author: Donald Saari
Publisher: American Mathematical Soc.
ISBN: 9780821886168
Category : Political Science
Languages : en
Pages : 178
Get Book Here
Book Description
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.
Author: Bernard Grofman
Publisher: University of Michigan Press
ISBN: 9780472083435
Category : Business & Economics
Languages : en
Pages : 298
Get Book Here
Book Description
A review of the consequences for political science of Anthony Downs's seminal work.
