Author : William V. Gehrlein
Publisher : Springer Science & Business Media
Page : 298 pages
File Size : 44,90 MB
Release : 2006-08-29
Category : Business & Economics
ISBN : 3540337997
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 : William V. Gehrlein
Publisher : Springer Science & Business Media
Page : 392 pages
File Size : 37,7 MB
Release : 2010-11-11
Category : Business & Economics
ISBN : 3642031072
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 : Hannu Nurmi
Publisher : Springer Science & Business Media
Page : 160 pages
File Size : 15,65 MB
Release : 2013-04-17
Category : Political Science
ISBN : 3662037823
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 : William V. Gehrlein
Publisher : Springer
Page : 193 pages
File Size : 17,94 MB
Release : 2017-10-14
Category : Business & Economics
ISBN : 3319646591
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 : Michel Balinski
Publisher : MIT Press
Page : 431 pages
File Size : 31,51 MB
Release : 2022-06-07
Category : Political Science
ISBN : 0262545713
An account of a new theory and method of voting, judging and ranking, majority judgment, shown to be superior to all other known methods. In Majority Judgment, Michel Balinski and Rida Laraki argue that the traditional theory of social choice offers no acceptable solution to the problems of how to elect, to judge, or to rank. They find that the traditional model—transforming the "preference lists" of individuals into a "preference list" of society—is fundamentally flawed in both theory and practice. Balinski and Laraki propose a more realistic model. It leads to an entirely new theory and method—majority judgment—proven superior to all known methods. It is at once meaningful, resists strategic manipulation, elicits honesty, and is not subject to the classical paradoxes encountered in practice, notably Condorcet's and Arrow's. They offer theoretical, practical, and experimental evidence—from national elections to figure skating competitions—to support their arguments. Drawing on insights from wine, sports, music, and other competitions, Balinski and Laraki argue that the question should not be how to transform many individual rankings into a single collective ranking, but rather, after defining a common language of grades to measure merit, how to transform the many individual evaluations of each competitor into a single collective evaluation of all competitors. The crux of the matter is a new model in which the traditional paradigm—to compare—is replaced by a new paradigm—to evaluate.
Author : Thomas Schwartz
Publisher : Cambridge University Press
Page : 176 pages
File Size : 42,54 MB
Release : 2018-03-22
Category : Political Science
ISBN : 1316853233
The centuries-old paradox of voting is that majorities sometimes prefer x to y, y to z, and z to x - a cycle. The discovery of the sources and consequences of such cycles, under majority rule and countless other regimes, constitutes much of the mathematical theory of voting and social choice. This book explores the big questions posed by the paradox of voting: positive questions about how to predict outcomes and explain observed stability, and normative questions about how to hold elections, how to take account of preference intensities, the relevance of social welfare to social choice, and challenges to formal 'rationality', individual and social. The overall lesson is that cycles are facts, ubiquitous, and consequential in non-obvious ways, not puzzles to be solved, much less maladies or misfortunes to be avoided or regretted.
Author : Dan S. Felsenthal
Publisher : Springer Science & Business Media
Page : 353 pages
File Size : 37,7 MB
Release : 2012-01-03
Category : Business & Economics
ISBN : 3642204414
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 : V Raghunathan
Publisher : Penguin UK
Page : 266 pages
File Size : 13,24 MB
Release : 2010-05-04
Category : Literary Collections
ISBN : 8184752075
How can you be ‘a well-known secret agent’? Why is ‘the only voting method that isn’t flawed a dictatorship’? How is it that ‘Corruption is universally disapproved of, and yet universally practised’? The world of dilemmas and paradoxes touch our lives on a regular basis. In The Corruption Conundrum and Other Paradoxes and Dilemmas, V. Raghunathan, the author of the best-seller Games Indians Play, shares the charms of some of the more interesting examples allowing us to delight in the excitement, mystery, confusion, exasperation and that occasional flash of clarity and enlightenment often experienced when the world of paradoxes and dilemmas hits our own. The book takes the reader through some of the fascinating illustrations, classical and well known as well as the less common examples, in the field of management, finance and work life. Can two positives make a negative? Sample a charming little paradox discussed in the book—the blackmail paradox. ‘It is perfectly legal if you gossip, reveal or threaten to reveal somebody’s secret (unless of course you are bound by a non-disclosure agreement). It is also perfectly legal to ask that somebody for some money. But if you undertake a combination of the two acts, each perfectly legal by itself, with respect to somebody, well you are a criminal, a blackmailer!’ Following the same easy, readable style of his previous best-seller, Games Indians Play, this new book should make absorbing reading and will certainly make you more curious about the world that surrounds us.
Author : Steven Brams
Publisher : Springer Science & Business Media
Page : 412 pages
File Size : 11,30 MB
Release : 2009-02-11
Category : Mathematics
ISBN : 3540791280
Peter Fishburn has had a splendidly productive career that led to path-breaking c- tributions in a remarkable variety of areas of research. His contributions have been published in a vast literature, ranging through journals of social choice and welfare, decision theory, operations research, economic theory, political science, mathema- cal psychology, and discrete mathematics. This work was done both on an individual basis and with a very long list of coauthors. The contributions that Fishburn made can roughly be divided into three major topical areas, and contributions to each of these areas are identi?ed by sections of this monograph. Section 1 deals with topics that are included in the general areas of utility, preference, individual choice, subjective probability, and measurement t- ory. Section 2 covers social choice theory, voting models, and social welfare. S- tion 3 deals with more purely mathematical topics that are related to combinatorics, graph theory, and ordered sets. The common theme of Fishburn’s contributions to all of these areas is his ability to bring rigorous mathematical analysis to bear on a wide range of dif?cult problems.
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Publisher : PediaPress
Page : 683 pages
File Size : 10,58 MB
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