Consensus time in 3-Majority is ilde{\Theta}(\min\{1/\|\alpha^{(0)}\|_\infty, \sqrt{n}\}) and in 2-Choices is \tilde{\Theta}(1/\|\alpha^{(0)}\|_\infty) w.h.p., governed by maximum initial opinion density for every starting configuration.
A simple population protocol for fast robust approximate majority.Distributed Comput., 21(2):87–102, 2008
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Consensus Time in 3-Majority and 2-Choices Is Determined by the Maximum Initial Opinion Density
Consensus time in 3-Majority is ilde{\Theta}(\min\{1/\|\alpha^{(0)}\|_\infty, \sqrt{n}\}) and in 2-Choices is \tilde{\Theta}(1/\|\alpha^{(0)}\|_\infty) w.h.p., governed by maximum initial opinion density for every starting configuration.