Simple Majority Consensus in Networks with Unreliable Communication
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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 2n 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 √(n), then the SMP with only two communication rounds attains consensus on the majority opinion of the network, and if this difference grows faster than √(n), then the SMP reaches consensus on the majority opinion of the network in a single round, with probability converging to 1 exponentially fast as n →∞. We also provide some converse results, showing that these requirements are not only sufficient, but also necessary.
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