A cluster of computers typically establishes a quorum, i.e., a software method for establishing agreement, to coordinate access to shared resources, such as a shared data store, in applications that must recover from the failure of one or more computers or their associated components. Prior art which associates a single quorum with an entire cluster, has inherent overheads that limit the size of the cluster to a small number of computers. The present invention comprises a scalable, software-based architecture for implementing a quorum mechanism to coordinate the actions of a cluster of computers. In contrast to prior art, the present invention advantageously encapsulates the quorum in a software construct, called a quorum object, which is disassociated from the cluster as a whole and spans a designated subset of the cluster's membership. By employing multiple quorum objects that are distributed across the cluster's membership, the cluster can uniformly scale to a large number of computers that handle a scalable processing workload, such as a partitioned database management system. The software methods that implement one embodiment of the present invention are described in detail.