Reaching Consensus via Non-Bayesian Asynchronous Learning in Social Networks

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

Thumbnail PDF


  • Filesize: 482 kB
  • 17 pages

Document Identifiers

Author Details

Michal Feldman
Nicole Immorlica
Brendan Lucier
S. Matthew Weinberg

Cite AsGet BibTex

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)


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.
  • Information Cascades
  • Social Networks
  • non-Bayesian Asynchronous Learning
  • Expander Graphs
  • Stochastic Processes


  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    PDF Downloads


  1. Daron Acemoglu, Munther A. Dahleh, Ilan Lobel, and Asuman Ozdaglar. Bayesian learning in social networks. Review of Economic Studies, 78(4):1201-1236, 2011. Google Scholar
  2. Abhijit Banerjee and Drew Fudenberg. Word-of-mouth learning. Games and Economic Behavior, 46(1):1-22, January 2004. Google Scholar
  3. Abhijit V. Banerjee. A simple model of herd behavior. The Quarterly Journal of Economics, 107(3):797-817, 1992. Google Scholar
  4. Eli Berger. Dynamic monopolies of constant size. J. Comb. Theory, Ser. B, 83(2):191-200, 2001. Google Scholar
  5. Sushil Bikhchandani, David Hirshleifer, and Ivo Welch. A theory of fads, fashion, custom, and cultural change in informational cascades. Journal of Political Economy, 100(5):992-1026, October 1992. Google Scholar
  6. F. Chung and R. Graham. Quasi-random graphs with given degree sequences. Random Structures & Algorithms, 32(1):1-19, 2008. Google Scholar
  7. Morris H. DeGroot. Reaching a consensus. Review of Economic Studies, 69(345):118-121, 1974. Google Scholar
  8. Benjamin Golub and Matthew O. Jackson. Naïve learning in social networks and the wisdom of crowds. American Economic Journal: Microeconomics, 2(1):112-149, 2010. Google Scholar
  9. David Kempe, Alin Dobra, and Johannes Gehrke. Gossip-based computation of aggregate information. In FOCS, pages 482-491, 2003. Google Scholar
  10. Jure Leskovec, Kevin J. Lang, Anirban Dasgupta, and Michael W. Mahoney. Statistical properties of community structure in large social and information networks. In WWW, pages 695-704, 2008. Google Scholar
  11. Fragkiskos D. Malliaros and Vasileios Megalooikonomou. Expansion properties of large social graphs. In DASFAA Workshops, pages 311-322, 2011. Google Scholar
  12. Elchanan Mossel, Joe Neeman, and Omer Tamuz. Majority dynamics and aggregation of information in social networks. In Autonomous Agents and Multi-Agent Systems (AAMAS), 2013. Google Scholar
  13. Lones Smith and Peter Sorensen. Pathological outcomes of observational learning. Econometrica, 68(2):371-398, March 2000. Google Scholar
  14. Omer Tamuz and Ran Tessler. Majority dynamics and the retention of information. In Working paper, 2013. Google Scholar
Questions / Remarks / Feedback

Feedback for Dagstuhl Publishing

Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail