Paradox of Voting Under an Urn Model

Book Review: Paradox of Voting Under an Urn Model

As I delved into the pages of Sven Berg’s “Paradox of Voting Under an Urn Model,” I found myself captivated by the intricate details of the mathematical model and its application to voting systems. Despite its relatively short page count, this book packs a punch in terms of depth and complexity.

Berg presents a unique perspective on voting theory, introducing the concept of an urn model to help explain the mysterious discrepancies that can occur in election results. His thorough analysis and careful consideration of various

Paradox of Voting Under an Urn Model

publishedDate : 1982

authors : Sven Berg

publishers :

pageCount : 30

Paradox of Voting under an Urn Model: The Effect of Homogeneity – JSTOR

Paradox of voting under an urn model : The effect of homogeneity* SVEN BERG Department of Statistics, University of Lund, Box 7008, S-220 07 Lund, Sweden Abstract We propose a simple P61ya-variety urn model for calculating paradox-of-voting probabilities. The model contains a homogeneity parameter, and for specific values of this parameter the …

Voting Systems and the Condorcet Paradox | Infinite Series

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Paradox Of Voting Under An Urn Model


Paradox Of Voting Under An Urn Model

Author by :
Languange Used : en
Release Date : 1982
Publisher by :

ISBN :

Description : ...






Voting Paradoxes And Group Coherence


Voting Paradoxes And Group Coherence

Author by : William V. Gehrlein
Languange Used : en
Release Date : 2010-11-11
Publisher by : Springer Science & Business Media

ISBN :

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....






Elections Voting Rules And Paradoxical Outcomes


Elections Voting Rules And Paradoxical Outcomes

Author by : William V. Gehrlein
Languange Used : en
Release Date : 2017-10-14
Publisher by : Springer

ISBN :

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....






Voting Procedures For Electing A Single Candidate


Voting Procedures For Electing A Single Candidate

Author by : Dan S. Felsenthal
Languange Used : en
Release Date : 2018-01-19
Publisher by : Springer

ISBN :

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....






Electoral Systems


Electoral Systems

Author by : Dan S. Felsenthal
Languange Used : en
Release Date : 2012-01-03
Publisher by : Springer Science & Business Media

ISBN :

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....






Evaluating Voting Systems With Probability Models


Evaluating Voting Systems With Probability Models

Author by : Mostapha Diss
Languange Used : en
Release Date : 2020-12-18
Publisher by : Springer Nature

ISBN :

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....






Voting Paradoxes And How To Deal With Them


Voting Paradoxes And How To Deal With Them

Author by : Hannu Nurmi
Languange Used : en
Release Date : 2013-04-17
Publisher by : Springer Science & Business Media

ISBN :

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....






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