The chapter by Lawrence Hubert and Phipps Arabie addresses the problem of comparing two partitions of a finite set of objects, a common issue in clustering literature. They review the Rand index, a widely used measure of partition correspondence, and discuss its normalization to correct for chance. The authors critique a recent normalization strategy by Morey and Agresti, which is based on an incorrect assumption. Instead, they propose a broader framework for comparing partitions using proximity matrices and various scoring rules. This framework includes traditional statistics and extensions tailored to weight certain object pairs differently. Finally, they introduce a new measure based on the comparison of object triples, which has a probabilistic interpretation, is corrected for chance, and is bounded between ±1. The chapter provides a comprehensive review of the Rand index and its extensions, along with a novel approach to partition correspondence.The chapter by Lawrence Hubert and Phipps Arabie addresses the problem of comparing two partitions of a finite set of objects, a common issue in clustering literature. They review the Rand index, a widely used measure of partition correspondence, and discuss its normalization to correct for chance. The authors critique a recent normalization strategy by Morey and Agresti, which is based on an incorrect assumption. Instead, they propose a broader framework for comparing partitions using proximity matrices and various scoring rules. This framework includes traditional statistics and extensions tailored to weight certain object pairs differently. Finally, they introduce a new measure based on the comparison of object triples, which has a probabilistic interpretation, is corrected for chance, and is bounded between ±1. The chapter provides a comprehensive review of the Rand index and its extensions, along with a novel approach to partition correspondence.