Voting is a solution to allowing correct executions in a distributed system in the presence of failures. This solution has been studied by the authors in earlier papers (e.g., [1]), while this paper presents their most recent findings. Their earlier findings included a representation of voting assignments, which they called coteries, and a subclass called nondominated (ND) coteries, which possess many valuable properties. In this paper, these properties are presented in the form of several lemmas and proofs throughout the first three sections of the paper. Theorems are presented that define the cardinality of node vulnerability and the state space for the cardinality of edge vulnerability. The rest of the paper expands the notion of ND-coteries for “real world” situations and presents heuristics for vote assignments in large systems.

The proofs presented in the paper are very clear and easy to follow. The definitions, lemmas, and theorems are logical and present desirable results. Potentially valuable exhaustive work is presented in smaller cases. The only disappointment in this paper is that the heuristics given for the larger cases do not provide the results one would desire. Other than this, the paper is an excellent place to research vote assignments in distributed systems.