Condorcet Domains

This book offers a comprehensive account of Condorcet domains—structured sets of preference orders in which the pairwise majority relation remains transitive for any odd-numbered group of voters. These domains form the foundation for normatively robust voting procedures and enable strong possibility results in incentive-compatible mechanism design. Well-known examples include single-peaked, single-crossing, and group-separable domains. The study of Condorcet domains bridges multiple disciplines, including economics, political science, mathematics, and computer science, and has seen significant theoretical advances in recent years. This monograph systematically presents these developments, covering both foundational concepts and cutting-edge results. It will be of interest to economists, mathematicians, and scholars in related fields seeking a deep understanding of preference aggregation and its structural underpinnings. “This interdisciplinary book by Clemens Puppe and Arkadii Slinko offers a canonical reference on the mathematical foundations of Condorcet domains. It shows how discrete convexity, median graphs, and permutation lattices play a central role in understanding coherent collective decision-making, and applies the insights to voting systems and incentive compatibility.” — Prof. Hervé Moulin, Adam Smith Business School, University of Glasgow, United Kingdom