The centuries-old paradox of voting is that majorities sometimes prefer x to y, y to z, and z to x - a cycle. The discovery of the sources and consequences of such cycles, under majority rule and countless other regimes, constitutes much of the mathematical theory of voting and social choice. This book explores the big questions posed by the paradox of voting: positive questions about how to predict outcomes and explain observed stability, and normative questions about how to hold elections, how to take account of preference intensities, the relevance of social welfare to social choice, and challenges to formal 'rationality', individual and social. The overall lesson is that cycles are facts, ubiquitous, and consequential in non-obvious ways, not puzzles to be solved, much less maladies or misfortunes to be avoided or regretted.

‘Thomas Schwartz reveals the mysteries of voting cycles, including their connections to famous results in social choice theory and game theory. Instead of bewailing cycles as incoherent, he casts them in a penetrating, positive light. Additionally, Cycles and Social Choice illuminates the philosophical implications of cycles for democratic rule, and their empirical ramifications for such political institutions as legislatures and political parties.'

Steven J. Brams - New York University

‘Thomas Schwartz has been one of the handful of most important political science scholars in the formal study of properties of voting and social choice. He has made seminal contributions on topics such as logrolling, agenda manipulation, dimensionality of voting, and cycle sets. This book provides an integrated treatment of Schwartz's contributions over many decades. The ideas in it are relevant to anyone seriously interested in the study of democracy, regardless of whether their interests are primarily theoretical or primarily empirical.'

Bernard Grofman - Jack W. Peltason Endowed Chair of Democracy Studies, University of California, Irvine