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.