Voting Paradoxes and How to Deal with Them
Voting Paradoxes and How to Deal with Them

Author: Hannu Nurmi

Publisher: Springer Science & Business Media

Published: 2013-04-17

Total Pages: 160

ISBN-13: 3662037823

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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.

Voting Paradoxes and Group Coherence
Voting Paradoxes and Group Coherence

Author: William V. Gehrlein

Publisher: Springer Science & Business Media

Published: 2010-11-11

Total Pages: 392

ISBN-13: 3642031072

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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.

Chaotic Elections!
Chaotic Elections!

Author: Donald Saari

Publisher: American Mathematical Soc.

Published: 2001-04-03

Total Pages: 178

ISBN-13: 9780821886168

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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.

Mathematics to the Rescue of Democracy
Mathematics to the Rescue of Democracy

Author: Paolo Serafini

Publisher: Springer Nature

Published: 2020-03-02

Total Pages: 138

ISBN-13: 3030383687

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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.

Paradox and Perception
Paradox and Perception

Author: Carol L. Graham

Publisher: Rowman & Littlefield

Published: 2010-09-01

Total Pages: 274

ISBN-13: 0815703953

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The "quality of life" concept of quality of life is a broad one. It incorporates basic needs but also extends beyond them to include capabilities, the "livability" of the environment, and life appreciation and happiness. Latin America's diversity in culture and levels of development provide a laboratory for studying how quality of life varies with a number of objective and subjective measures. These measures range from income levels to job insecurity and satisfaction, to schooling attainment and satisfaction, to measured and self-assessed health, among others. Paradox and Perception greatly improves our understanding of the determinants of well-being in Latin America based on a broad "quality of life" concept that challenges some standard assumptions in economics, including those about the relationship between happiness and income. The authors' analysis builds upon a number of new approaches in economics, particularly those related to the study of happiness and finds a number of paradoxes as the region's respondents evaluate their well-being. These include the paradox of unhappy growth at the macroeconomic level, happy peasants and frustrated achievers at the microlevel, and surprisingly high levels of satisfaction with public services among the region's poorest. They also have important substantive links with several of the region's realities, such as high levels of income inequality, volatile macroeconomic performance, and low expectations of public institutions and faith in the capacity of the state to deliver. Identifying these perceptions, paradoxes, and their causes will contribute to the crafting of better public policies, as well as to our understanding of why "populist" politics still pervade in much of the region.

Condorcet's Paradox
Condorcet's Paradox

Author: William V. Gehrlein

Publisher: Springer Science & Business Media

Published: 2006-08-29

Total Pages: 298

ISBN-13: 3540337997

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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.

Numbers Rule
Numbers Rule

Author: George Szpiro

Publisher: Princeton University Press

Published: 2020-11-03

Total Pages: 240

ISBN-13: 0691209081

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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.

Gaming the Vote
Gaming the Vote

Author: William Poundstone

Publisher: Macmillan

Published: 2009-02-17

Total Pages: 360

ISBN-13: 9780809048922

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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.

Handbook of Computational Social Choice
Handbook of Computational Social Choice

Author: Felix Brandt

Publisher: Cambridge University Press

Published: 2016-04-25

Total Pages: 553

ISBN-13: 1316489752

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The rapidly growing field of computational social choice, at the intersection of computer science and economics, deals with the computational aspects of collective decision making. This handbook, written by thirty-six prominent members of the computational social choice community, covers the field comprehensively. Chapters devoted to each of the field's major themes offer detailed introductions. Topics include voting theory (such as the computational complexity of winner determination and manipulation in elections), fair allocation (such as algorithms for dividing divisible and indivisible goods), coalition formation (such as matching and hedonic games), and many more. Graduate students, researchers, and professionals in computer science, economics, mathematics, political science, and philosophy will benefit from this accessible and self-contained book.

Decisions and Elections
Decisions and Elections

Author: Donald Saari

Publisher: Cambridge University Press

Published: 2001-10-22

Total Pages: 258

ISBN-13: 9780521004046

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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.