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Asynchronous Majority Dynamics in Preferential Attachment Trees

Authors Maryam Bahrani, Nicole Immorlica, Divyarthi Mohan, S. Matthew Weinberg

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Author Details

Maryam Bahrani
  • Princeton University, NJ, USA
Nicole Immorlica
  • Microsoft Research, Cambridge, MA, USA
Divyarthi Mohan
  • Princeton University, NJ, USA
S. Matthew Weinberg
  • Princeton University, NJ, USA

Funding

  • Weinberg, S. Matthew: Supported by NSF CCF-1717899.

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Maryam Bahrani, Nicole Immorlica, Divyarthi Mohan, and S. Matthew Weinberg. Asynchronous Majority Dynamics in Preferential Attachment Trees. In 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 168, pp. 8:1-8:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020) https://doi.org/10.4230/LIPIcs.ICALP.2020.8

Abstract

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 [Barabási and Albert, 1999], with high probability, the process stabilizes in a correct majority within O(n log n/log log n) rounds. We extend our results to other tree structures, including balanced M-ary trees for any M.

Subject Classification

ACM Subject Classification
  • Theory of computation → Algorithmic game theory and mechanism design
  • Networks → Network dynamics
Keywords
  • Opinion Dynamics
  • Information Cascades
  • Preferential Attachment
  • Majority Dynamics
  • non-Bayesian Asynchronous Learning
  • Stochastic Processes

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