Abstract
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 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 , then the SMP with only two communication rounds attains consensus on the majority opinion of the network, and if this difference grows faster than , 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 . We also provide some converse results, showing that these requirements are not only sufficient, but also necessary.
Highlights
Using probabilistic analysis for a large scale, fully-connected network of 2n agents, we prove that the Simple Majority Protocol (SMP) converges rapidly to a consensus on the majority opinion of the network with probability approaching 1 as n → ∞, given that √
We investigate whether leveraging such an assumption helps to solve binary majority consensus, in which the nontriviality clause stipulates that if a majority of agents initially hold the same opinion, all agents must decide on this opinion
We show that if δn grows at a rate of n, the SMP with r = 2 reaches majority consensus with
Summary
The world wide web has facilitated the existence of many useful multiagent systems from messaging apps to cryptocurrency [1] and distributed data storage (or cloud services) [2,3]. The second is that there exists an upper bound on the transmission delay of messages from one agent to another (usually the maximum propagation time of links) [12]. We assume no such underlying structure exists and 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. If the difference between the numbers of agents that hold different opinions is relatively close to zero, the SMP still converges extremely fast to a consensus, but not necessarily on the initial majority opinion of the network
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