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Paradoxes --- Game theory --- Voting --- Economics --- Economics, Mathematical --- Mathematics --- Operations research --- Political science --- Mathematical models --- Voting - Mathematical models

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Honesty in voting, it turns out, is not always the best policy. Indeed, in the early 1970s, Allan Gibbard and Mark Satterthwaite, building on the seminal work of Nobel laureate Kenneth Arrow, proved that with three or more alternatives there is no reasonable voting system that is non-manipulable; voters will always have an opportunity to benefit by submitting a disingenuous ballot. The ensuing decades produced a number of theorems of striking mathematical naturality that dealt with the manipulability of voting systems. This 2005 book presents many of these results from the last quarter of the twentieth century, especially the contributions of economists and philosophers, from a mathematical point of view, with many new proofs. The presentation is almost completely self-contained, and requires no prerequisites except a willingness to follow rigorous mathematical arguments. Mathematics students, as well as mathematicians, political scientists, economists and philosophers will learn why it is impossible to devise a completely unmanipulable voting system.

Microeconomics --- Voting --- Social choice --- Political science --- Game theory. --- Mathematical models. --- Games, Theory of --- Theory of games --- Mathematical models --- Mathematics --- Polls --- Elections --- Politics, Practical --- Suffrage --- Balloting --- Voting - Mathematical models. --- Social choice - Mathematical models. --- Political science - Mathematical models.

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This book is a theoretical and completely rigorous analysis of voting in committees that provides mathematical proof of the existence of democratic voting systems, which are immune to the manipulation of preferences of coalitions of voters. The author begins by determining the power distribution among voters that is induced by a voting rule, giving particular consideration to choice by plurality voting and Borda's rule. He then constructs, for all possible committees, well-behaved representative voting procedures which are not distorted by strategic voting, giving complete solutions for certain important classes of committees. The solution to the problem of mass elections is fully characterised.

Social choice --- Voting --- Committees --- Game theory --- Choix collectif --- Vote --- Comités --- Théorie des jeux --- Mathematical models --- Modèles mathématiques --- Comités --- Théorie des jeux --- Modèles mathématiques --- Mathematical models. --- Business, Economy and Management --- Economics --- Social choice - Mathematical models --- Voting - Mathematical models --- Committees - Mathematical models --- Game theory. --- Games, Theory of --- Theory of games --- Mathematics --- Associations, institutions, etc. --- Meetings --- Balloting --- Polls --- Elections --- Politics, Practical --- Suffrage

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Kenneth J. Arrow's pathbreaking "impossibility theorem" was a watershed innovation in the history of welfare economics, voting theory, and collective choice, demonstrating that there is no voting rule that satisfies the four desirable axioms of decisiveness, consensus, non-dictatorship, and independence. In this book Eric Maskin and Amartya Sen explore the implications of Arrow's theorem. Sen considers its ongoing utility, exploring the theorem's value and limitations in relation to recent research on social reasoning, and Maskin discusses how to design a voting rule that gets us closer to the ideal-given the impossibility of achieving the ideal. The volume also contains a contextual introduction by social choice scholar Prasanta K. Pattanaik and commentaries from Joseph E. Stiglitz and Kenneth J. Arrow himself, as well as essays by Maskin, Dasgupta, and Sen outlining the mathematical proof and framework behind their assertions.

Voting --- Social choice --- Probabilities --- Voting - Mathematical models --- Social choice - Mathematical models --- Probabilities - Mathematical models --- Arrow, Kenneth Joseph, - 1921-2017 --- Voting. --- Social choice. --- Probabilities. --- Mathematical models. --- Balloting --- Polls --- Elections --- Politics, Practical --- Suffrage --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk --- Choice, Social --- Collective choice --- Public choice --- Choice (Psychology) --- Social psychology --- Welfare economics

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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.

Voting --- Mathematical models. --- Condorcet, Jean-Antoine-Nicolas de Caritat, --- Political science. --- Political economy. --- Game theory. --- Economic theory. --- Public finance. --- Economics. --- Economic Theory/Quantitative Economics/Mathematical Methods. --- Political Economy. --- Public Economics. --- Political Science. --- Game Theory, Economics, Social and Behav. Sciences. --- Polls --- Elections --- Politics, Practical --- Social choice --- Suffrage --- Caritat, Jean-Antoine-Nicolas de, --- Condorcet, Antoine-Nicolas Caritat de, --- Condorcet, C.-F., --- Condorcet, Marie Jean Antoine Nicolas, --- Condorcet, --- De Caritat, Jean-Antoine-Nicolas, --- Kondorsė, Zhan Antuan, --- Mathematics. --- International Political Economy. --- Math --- Science --- Administration --- Civil government --- Commonwealth, The --- Government --- Political theory --- Political thought --- Politics --- Science, Political --- Social sciences --- State, The --- Cameralistics --- Public finance --- Currency question --- Economic theory --- Political economy --- Economic man --- Public finances --- Games, Theory of --- Theory of games --- Mathematical models --- Mathematics --- de Caritat, Jean-Antoine-Nicolas, --- Condorcet --- Condorcet, Jean-Antoine-Nicolas de Caritat --- de Condorcet, Marie Jean Antoine Nicolas de Caritat --- de Condorcet, Nicolas --- Schwartz, Joachim, --- Game theory --- Voting - Mathematical models --- Paradoxes --- Condorcet, Jean-Antoine-Nicolas de Caritat, - marquis de, - 1743-1794