Elections, Voting Rules and Paradoxical Outcomes


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.




Electoral Systems


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.




Voting Paradoxes and Group Coherence


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.




Voting Procedures for Electing a Single Candidate


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.




Voting Paradoxes and How to Deal with Them


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.




Electoral Systems


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.




Representation, Power and Electoral Rules


Book Description

Is the human being, single man or group, able to understand the influence she has inside a decisional committee? Is she able to treat aIl members fairly in the designing process of a parliamentary assembly, or she will give life to bizarre creatures with pure political motivations? Are current voting rules able to avoid paradoxical outcomes after an election has been run? This thesis answers to these questions using tools from cooperative and non-cooperative game theory, combining a computational and an experimental approach. The first part of the work analyze two-tiers voting systems and electoral laws. The second part focuses on human learning in games associated to the ability of people to choose the situation attributing them the largest power.




Cardinal Voting


Book Description

Unlock the power of voting systems with "Cardinal Voting," part of the "Political Science" series. This book delves into cardinal voting—a revolutionary method where voters rate candidates, offering a new perspective on electoral fairness and decision-making. 1-Cardinal Voting-Learn the basics of cardinal voting, where voters use a numerical scale to express preferences, providing a richer view than traditional methods. 2-Approval Voting-Understand approval voting, where voters simply approve or disapprove of candidates, and its connection to cardinal voting for better accuracy. 3-Score Voting-Explore score voting, where candidates are rated, and its impact on elections compared to other systems. 4-Condorcet Paradox-Discover the Condorcet paradox and its effects on cardinal voting by highlighting voting system complexities. 5-Arrow's Impossibility Theorem-Analyze Arrow's theorem and its implications for designing effective cardinal voting systems. 6-Independence of Irrelevant Alternatives-Examine this key criterion affecting fairness in voting systems and its relevance to cardinal voting. 7-Gibbard–Satterthwaite Theorem-Understand this theorem’s insights into strategic voting and its limitations within cardinal voting. 8-Bucklin Voting-Learn about Bucklin voting, blending ranked and cardinal voting elements, and its decision-making impact. 9-Majority Criterion-Review the majority criterion’s role in ensuring cardinal voting reflects true majority preferences. 10-Positional Voting-Compare positional and cardinal voting systems, and see how each affects electoral outcomes. 11-Strategic Voting-Investigate strategic voting and its impact on the integrity of cardinal voting systems. 12-Allan Gibbard-Explore Allan Gibbard’s contributions to voting theory and their influence on cardinal voting. 13-Social Choice and Individual Values-Examine the link between social choice theory and individual preferences in cardinal voting. 14-Later-no-harm Criterion-Understand how this criterion preserves voter preferences in cardinal voting systems. 15-Majority Judgment-Consider majority judgment as an alternative to cardinal voting and its potential benefits. 16-Ranked Voting-Compare ranked voting with cardinal voting to evaluate the strengths and weaknesses of each. 17-Comparison of Electoral Systems-Get a detailed comparison of electoral systems and the unique benefits of cardinal voting. 18-Gibbard's Theorem-Revisit Gibbard’s theorem and its effect on strategic behavior in cardinal voting. 19-Combined Approval Voting-Explore combined approval voting and its integration with cardinal voting principles. 20-Highest Median Voting Rules-Understand highest median voting rules and their role in cardinal voting. 21-Usual Judgment-Learn about usual judgment and its impact on electoral outcomes alongside cardinal voting. "Cardinal Voting" offers deep insights into electoral systems, bridging theory with practical application. Elevate your understanding of voting systems today.




Chaotic Elections!


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.




Making Multicandidate Elections More Democratic


Book Description

This book addresses a significant area of applied social-choice theory--the evaluation of voting procedures designed to select a single winner from a field of three or more candidates. Such procedures can differ strikingly in the election outcomes they produce, the opportunities for manipulation that they create, and the nature of the candidates--centrist or extremist--whom they advantage. The author uses computer simulations based on models of voting behavior and reconstructions of historical elections to assess the likelihood that each multicandidate voting system meets political objectives. Alternative procedures abound: the single-vote plurality method, ubiquitous in the United States, Canada, and Britain; runoff, used in certain primaries; the Borda count, based on rank scores submitted by each voter; approval voting, which permits each voter to support several candidates equally; and the Hare system of successive eliminations, to name a few. This work concludes that single-vote plurality is most often at odds with the majoritarian principle of Condorcet. Those methods most likely to choose the Condorcet candidate under sincere voting are generally the most vulnerable to manipulation. Approval voting and the Hare and runoff methods emerge from the analyses as the most reliable. Originally published in 1988. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.