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Reaching Consensus via Non-Bayesian Asynchronous Learning in Social Networks

Authors Michal Feldman, Nicole Immorlica, Brendan Lucier, S. Matthew Weinberg

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Michal Feldman
Nicole Immorlica
Brendan Lucier
S. Matthew Weinberg

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Michal Feldman, Nicole Immorlica, Brendan Lucier, and S. Matthew Weinberg. Reaching Consensus via Non-Bayesian Asynchronous Learning in Social Networks. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2014). Leibniz International Proceedings in Informatics (LIPIcs), Volume 28, pp. 192-208, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)
https://doi.org/10.4230/LIPIcs.APPROX-RANDOM.2014.192

Abstract

We study the outcomes of information aggregation in online social networks. Our main result is that networks with certain realistic structural properties avoid information cascades and enable a population to effectively aggregate information. In our model, each individual in a network holds a private, independent opinion about a product or idea, biased toward a ground truth. Individuals declare their opinions asynchronously, can observe the stated opinions of their neighbors, and are free to update their declarations over time. Supposing that individuals conform with the majority report of their neighbors, we ask whether the population will eventually arrive at consensus on the ground truth. We show that the answer depends on the network structure: there exist networks for which consensus is unlikely, or for which declarations converge on the incorrect opinion with positive probability. On the other hand, we prove that for networks that are sparse and expansive, the population will converge to the correct opinion with high probability.
Keywords
  • Information Cascades
  • Social Networks
  • non-Bayesian Asynchronous Learning
  • Expander Graphs
  • Stochastic Processes

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