Large-scale HPC systems experience failures arising from faults in hardware, software, and/or networking. Failure rates continue to grow as systems scale up and out. Crash fault tolerance has up to now been the focus when considering means to augment the Message Passing Interface (MPI) for fault-tolerant operations. This narrow model of faults (usually restricted only to process or node failures) is insufficient. Without a more general model for consensus, gaps in the ability to detect, isolate, mitigate, and recover HPC applications efficiently will arise. Focusing on crash failures is insufficient because a chain of underlying components may lead to system failures in MPI. What is more, clusters and leadership-class machines alike often have Reliability, Availability, and Serviceability Systems to convey predictive and real-time fault and error information, which does not map strictly to process and node crashes. A broader study of failures beyond crash failures in MPI will thus be useful in conjunction with consensus mechanism for developers as they continue to design, develop, and implement fault-tolerant HPC systems that reflect observable faults in actual systems. We describe key factors that must be considered during consensus-mechanism design. We illustrate some of the current MPI fault tolerance models based on use cases. We offer a novel classification of common consensus mechanisms based on these factors such as the network model, failure types, and based on use cases (e.g., fault detection, synchronization) of the consensus in the computation process, including crash fault tolerance as one category.