Minority Becomes Majority in Social Networks

  • Vincenzo Auletta
  • Ioannis Caragiannis
  • Diodato Ferraioli
  • Clemente Galdi
  • Giuseppe Persiano
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9470)

Abstract

It is often observed that agents tend to imitate the behavior of their neighbors in a social network. This imitating behavior might lead to the strategic decision of adopting a public behavior that differs from what the agent believes is the right one and this can subvert the behavior of the population as a whole.

In this paper, we consider the case in which agents express preferences over two alternatives and model social pressure with the majority dynamics: at each step an agent is selected and its preference is replaced by the majority of the preferences of her neighbors. In case of a tie, the agent does not change her current preference. A profile of the agents’ preferences is stable if the each agent’s preference coincides with the preference of at least half of the neighbors (thus, the system is in equilibrium).

We ask whether there are network topologies that are robust to social pressure. That is, we ask whether there are graphs in which the majority of preferences in an initial profile \({\mathbf {s}}\) always coincides with the majority of the preference in all stable profiles reachable from \({\mathbf {s}}\). We completely characterize the graphs with this robustness property by showing that this is possible only if the graph has no edge or is a clique or very close to a clique. In other words, except for this handful of graphs, every graph admits at least one initial profile of preferences in which the majority dynamics can subvert the initial majority. We also show that deciding whether a graph admits a minority that becomes majority is NP-hard when the minority size is at most 1 / 4-th of the social network size.

References

  1. 1.
    Auletta, V., Caragiannis, I., Ferraioli, D., Galdi, C., Persiano, G.: Minority becomes majority in social networks. CoRR, abs/1402.4050 (2014)Google Scholar
  2. 2.
    Berger, E.: Dynamic monopolies of constant size. J. Comb. Theory Ser. B 83(2), 191–200 (2001)MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Bindel, D., Kleinberg, J.M., Oren, S.: How bad is forming your own opinion? In: Proceedings of the 52nd Annual IEEE Symposium on Foundations of Computer Science (FOCS), pp. 55–66 (2011)Google Scholar
  4. 4.
    Brânzei, S., Caragiannis, I., Morgenstern, J., Procaccia, A.D.: How bad is selfish voting? In: Proceedings of the 27th AAAI Conference on Artificial Intelligence (AAAI), pp. 138–144 (2013)Google Scholar
  5. 5.
    Chierichetti, F., Kleinberg, J.M., Oren, S.: On discrete preferences and coordination. In: Proceedings of the 14th ACM Conference on Electronic Commerce (EC), pp. 233–250 (2013)Google Scholar
  6. 6.
    Coleman, J.S., Katz, E., Menzel, H.: Medical Innovation: A Diffusion Study. Advanced Study in Sociology. Bobbs-Merrill Co., Indianapolis (1966)Google Scholar
  7. 7.
    DeGroot, M.H.: Reaching a consensus. J. Am. Stat. Assoc. 69(345), 118–121 (1974)CrossRefMATHGoogle Scholar
  8. 8.
    Easley, D., Kleinberg, J.: Networks, Crowds, and Markets: Reasoning about A Highly Connected World. Cambridge University Press, New York (2010)CrossRefMATHGoogle Scholar
  9. 9.
    Feldman, M., Immorlica, N., Lucier, B., Weinberg, S.M.: Reaching consensus via non-Bayesian asynchronous learning in social networks. In: Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2014), vol. 28, pp. 192–208 (2014)Google Scholar
  10. 10.
    Ferraioli, D., Goldberg, P.W., Ventre, C.: Decentralized dynamics for finite opinion games. In: Serna, M. (ed.) SAGT 2012. LNCS, vol. 7615, pp. 144–155. Springer, Heidelberg (2012) CrossRefGoogle Scholar
  11. 11.
    Friedkin, N.E., Johnsen, E.C.: Social influence and opinions. J. Math. Sociol. 15(3–4), 193–205 (1990)CrossRefMATHGoogle Scholar
  12. 12.
    Meir, R., Polukarov, M., Rosenschein, J.S., Jennings, N.R.: Convergence to equilibria in plurality voting. In: Proceedings of the 24th AAAI Conference on Artificial Intelligence (AAAI), pp. 823–828 (2010)Google Scholar
  13. 13.
    Mossel, E., Neeman, J., Tamuz, O.: Majority dynamics and aggregation of information in social networks. Auton. Agent. Multi-Agent Syst. 28(3), 408–429 (2014)CrossRefGoogle Scholar
  14. 14.
    Mossel, E., Sly, A., Tamuz, O.: Asymptotic learning on Bayesian social networks. Probab. Theory Relat. Fields 158(1–2), 127–157 (2014)MathSciNetCrossRefMATHGoogle Scholar
  15. 15.
    Peleg, D.: Local majorities, coalitions and monopolies in graphs: a review. Theoret. Comput. Sci. 282, 231–257 (2002)MathSciNetCrossRefMATHGoogle Scholar
  16. 16.
    Ryan, B., Gross, N.G.: Acceptance and diffusion of hybrid corn seed in two Iowa communities, vol. 372. Agricultural Experiment Station, Iowa State College of Agriculture and Mechanic Arts (1950)Google Scholar
  17. 17.
    Tamuz, O., Tessler, R.J.: Majority dynamics and the retention of information. Isr. J. Math. 206(1), 483–507 (2013)MathSciNetCrossRefMATHGoogle Scholar
  18. 18.
    Yoshinaka, R.: Higher-order matching in the linear lambda calculus in the absence of constants is NP-complete. In: Giesl, J. (ed.) RTA 2005. LNCS, vol. 3467, pp. 235–249. Springer, Heidelberg (2005) CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Open Access This chapter is distributed under the terms of the Creative Commons Attribution Noncommercial License, which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.

Authors and Affiliations

  • Vincenzo Auletta
    • 1
  • Ioannis Caragiannis
    • 2
  • Diodato Ferraioli
    • 1
  • Clemente Galdi
    • 3
  • Giuseppe Persiano
    • 1
  1. 1.Università degli Studi di SalernoFiscianoItaly
  2. 2.CTI “Diophantus” and University of PatrasPatrasGreece
  3. 3.Università di Napoli “Federico II”NapoliItaly

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