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.

This book presents a probabilistic approach to studying the fundamental role of labor in capitalist economies and develops a non-deterministic theoretical framework for the foundations of political economy. By applying the framework to real-world data, the authors offer new insights into the dynamics of growth, wages, and accumulation in capitalist development around the globe. The book demonstrates that a probabilistic political economy based on labor inputs enables us to describe central organizing principles in modern capitalism. Starting from a few basic assumptions, it shows that the working time of employees is the main regulating variable for determining strict numerical limits on the rate of economic growth, the range of wages, and the pace of accumulation under the present global economic system. This book will appeal to anyone interested in how the capitalist mode of production works and its inherent limitations; in particular, it will be useful to scholars and students of Marxian economics. "Emmanuel Farjoun and Moshe Machover, follow up their pathbreaking work on the application of statistical physics methods to political economy in this book with David Zachariah, in which they develop methods for making educated and structured estimates of stylized facts applicable to capitalist economies. There's a lot for economists and anyone interested in the political economy of capitalism to learn from their reasoning on these issues, including their novel and challenging suggestion of bounds on the rates of increase of use-value productivity of labor, and on the range of variation of the wage share." Duncan K. Foley, Leo Model Professor of Economics, New School for Social Research

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.

These essays, written between 1966 and 2010 by lifelong Israeli activist and theorist Moshe Machover, cover diverse aspects of Israeli society and the Israeli-Palestinian conflict. Elaborating on the ideas of the Socialist Organization in Israel (Matzpen), two interrelated themes appear throughout the collection: the necessity of understanding the Israeli-Palestinian conflict in a regional context and the connection between Palestinian liberation and the struggle for socialism throughout the Middle East.

A defining work of Econophysics, republished for the first time since 1983, Laws of Chaos is an attempt to construct a non-deterministic theoretical framework for the foundations of political economy. It relies on probabilistic and statistical methods of the kind used in the modern foundations of several other sciences, introducing scientific modelling into economics for the first time.

In this introduction to set theory and logic, the author discusses first order logic, and gives a rigorous axiomatic presentation of Zermelo-Fraenkel set theory. He includes many methodological remarks and explanations, and demonstrates how the basic concepts of mathematics can be reduced to set theory. He explains concepts and results of recursion theory in intuitive terms, and reaches the limitative results of Skolem, Tarski, Church and Gödel (the celebrated incompleteness theorems). For students of mathematics and philosophy, this book provides an excellent introduction to logic and set theory.