Asynchronous Majority Dynamics in Preferential Attachment Trees
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We study information aggregation in networks where agents make binary decisions (labeled incorrect or correct). Agents initially form independent private beliefs about the better decision, which is correct with probability 1/2+δ. The dynamics we consider are asynchronous (each round, a single agent updates their announced decision) and non-Bayesian (agents simply copy the majority announcements among their neighbors, tie-breaking in favor of their private signal). Our main result proves that when the network is a tree formed according to the preferential attachment model <cit.>, with high probability, the process stabilizes in a correct majority. We extend our results to other tree structures, including balanced M-ary trees for any M.
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