The Measurement of Voting Power
Theory and Practice, Problems and Paradoxes
This book is the first of its kind: a monograph devoted to a systematic critical examination and exposition of the theory of a priori voting power. This important branch of social-choice theory overlaps with game theory and is concerned with the ability of members in bodies that make yes or no decisions by vote to affect the outcome. The book includes, among other topics, a reasoned distinction between two fundamental types of voting power, the authors' discoveries on the paradoxes of voting power, and a novel analysis of decision rules that admit abstention. Formal mathematical statements are accompanied by reader-friendly informal explanations. The theory is applied and illustrated in extensive case studies. A series of US court cases concerning the application of the principle of 'one person, one vote' are critically examined in the light of the theory. The history of 'qualified majority voting' in the European Community's Council of Ministers is outlined and the distribution of voting power under this rule is analysed for each period of the community's growth.
The measurement of voting power where abstention is a distinct option is illustrated with the examples of the US Congress and the UN Security Council. This important book breaks new ground and will be of interest to students and researchers in social choice, game theory, and in related disciplines such as political economy, business administration and constitutional law.
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What Reviewers Are Saying
'The book under review is of exceptional interest for a wide range of potential readers: 1) for students and postgraduates as a basic textbook and a handbook; 2) for lecturers delivering courses connected with decision making as the source of mathematical models and real examples; 3) for researchers as a handbook as well as an inexhaustible source of unsolved problems.' -- V.G. Skobolev, Zentralblatt fur Mathematik und ihre Grenzgebiete 'Felsenthal and Machover's book is a well-balanced mixture of overview, evaluation and new results. It is both a fine scholarly achievement and a most readable text. No one working in the field of formal political theory, institutional design and/or applied social choice theory can afford to ignore it.' -- Hannu Nurmi, European Journal of Political Economy '... provides a systematic critical examination and exposition of the foundations and methodological presuppositions of the theory of a priori voting power... it will prove to be a very valuable source of reference and a starting point for every scholar doing research in the field of voting power analysis. The book or parts of it could also be used as a standard textbook for a course on voting power at an advanced graduate level ... The Measurement of Voting Power is an excellent book, full of stimulating insights and with some suggestions for future research. It is mathematically rigorous, but at the same time very reader-friendly due to informative informal explanations. It is at the cutting edge of research in the theory and measurement of a priori voting power, but it is also of practical and political relevance, insofar as it provides a sound basis for the analysis of real-life decision-making processes.' -- Matthias Sutter, Public Choice 'This book provides an extensive survey in the field of voting power measurement (and further), well documented and self contained... The book provides a very up-to-date and exhaustive bibliography, but does not neglect to remind and often clear up the historical origin of the various theoretical developments. Covering its subject widely, it presents not only the groundwork of the theory of voting power measurement and its main tools ... but also the related backgrounds, applications and discussions, with wide incursions into the US and European voting systems. Read it: its a must!' -- Gisele De Meur, Universite Libre de Bruxelles, Belgium 'To say that this book is excellent would be an understatement. It is really remarkable. Not only would it help people using power indices to redirect their analysis, but it could also incite game theorists in general to reconsider the bad opinion they have of cooperative game theory (must I say that there are several texts that exist on game theory in which cooperative game theory is hardly mentioned?). In brief, it is very highly recommended to social choice theorists, game theorists (and mathematical economists using game theory), and mathematically-inclined political scientists.' -- Maurice Salles, Social Choice and Welfare 'This is an excellent book. Felsenthal and Machover do a remarkable job of weaving together extended discussions of real-world voting systems, the philosophical and historical aspects of measuring power in such contexts, and the paradoxes of voting power - including the striking examples from their own recent work with Zwicker. Anyone interested in voting and social choice, mathematicians, economists, political scientists, philosophers should own a copy.' -- Alan Taylor, Union College, US 'The history of the power indices goes back more than fifty years and is told accurately and completely, for the first time, in this volume. More important, Felsenthal and Machover elucidate the conceptual foundations of the power indices, discover new paradoxes to which the various indices are vulnerable, and draw important lessons, using empirical cases, about the proper measurement and interpretation of voting power.' -- Steven Brams, New York University, US 'Dan Felsenthal and Moshe Machover have been writing stimulating and important papers on the voting power indices for several years. This book collects them together and adds new material. It is both mathematically rigorous and politically important. It will become a required reference for anyone working on weighted voting games, whether in US legislatures or the European Union.' -- Iain McLean, Nuffield College, Oxford University, UK 'This book pulls no punches in exposing confusions in the orthodox approach to voting power. Its clarity and good sense point the way to a better founded theory.' -- Ken Binmore, University College London, UK