Simple Majority Consensus in Networks with Unreliable Communication †

In this work, we analyze the performance of a simple majority-rule protocol solving a fundamental coordination problem in distributed systems—binary majority consensus—in the presence of probabilistic message loss. Using probabilistic analysis for a large-scale, fully-connected, network of [Formula: see text] agents, we prove that the Simple Majority Protocol (SMP) reaches consensus in only three communication rounds, with probability approaching 1 as n grows to infinity. Moreover, if the difference between the numbers of agents that hold different opinions grows at a rate of [Formula: see text] , then the SMP with only two communication rounds attains consensus on the majority opinion of the network, and if this difference grows faster than [Formula: see text] , then the SMP reaches consensus on the majority opinion of the network in a single round, with probability converging to 1 as exponentially fast as [Formula: see text]. We also provide some converse results, showing that these requirements are not only sufficient, but also necessary.