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Author: Hannu Nurmi
Publisher: Springer Science & Business Media
ISBN: 3662037823
Category : Political Science
Languages : en
Pages : 160
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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: Hannu Nurmi
Publisher: Springer Science & Business Media
ISBN: 9783540662365
Category : Business & Economics
Languages : en
Pages : 172
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Book Description
Voting paradoxes are unpleasant surprises encountered in elections. They pertain to such phenomena as additional support being detrimental for candidates and not voting leading to better outcomes than voting for some voters. No voting system is immune to all paradoxes and, therefore voting paradoxes are being dealt with by all voting systems currently in use. How they are and how they should be handled is the main subject of this book. The book outlines, explains and classifies a number of paradoxes: Borda`s and Condorcet`s classic ones, several monotonicity and compound majority paradoxes as well as some paradoxes of representation. Both theoretical and practical ways of avoiding them are discussed.
Author: William V. Gehrlein
Publisher: Springer
ISBN: 3319646591
Category : Business & Economics
Languages : en
Pages : 193
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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
ISBN: 3319740334
Category : Business & Economics
Languages : en
Pages : 147
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Book Description
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: Dan S. Felsenthal
Publisher: Springer Science & Business Media
ISBN: 3642204414
Category : Business & Economics
Languages : en
Pages : 353
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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: 3642031072
Category : Business & Economics
Languages : en
Pages : 392
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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: Dan S. Felsenthal
Publisher: Springer
ISBN: 3030126277
Category : Business & Economics
Languages : en
Pages : 92
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Book Description
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: Hannu Nurmi
Publisher: Springer Science & Business Media
ISBN: 3662037823
Category : Political Science
Languages : en
Pages : 160
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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: Donald Saari
Publisher: Cambridge University Press
ISBN: 9780521004046
Category : Business & Economics
Languages : en
Pages : 258
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Book Description
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:
ISBN: 9783642031083
Category :
Languages : en
Pages : 400
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Book Description
Author: Leslie M. McDonald
Publisher:
ISBN:
Category : Central limit theorem
Languages : en
Pages : 68
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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.
