A binary vote based comparison of simple majority and hierarchical decision for survivable networks

Nodes are replicated in fault-tolerant networks not only to increase the aggregate decision reliability but also to survive the failure of a subset of those nodes. A simple majority rule is the most common aggregate decision rule. One may believe that a simple majority rule may not be optimal when node replication is performed in organization following a hierarchical structure like a corporation or a military command. This research shows that if the node's observations are better than random, then a simple majority rule is better than a hierarchical decision. Moreover, even though there are a few compromised nodes that falsify their vote, a simple majority rule will still be superior. However, a hierarchical decision process is more scalable and the vote can be aggregated faster. This paper also proposed a technique based on the law of diminishing marginal utility to calculate the optimum number of nodes in a decision process.