Abstract
This paper focuses on influence maximization or opinion control in the voting dynamics on social networks. We show two simple heuristics that are effective strategies to enhance vote shares: (i) avoiding the nodes controlled by your opponent when having a lower budget while focusing on them when having a larger budget (shadowing) and (ii) ring-fencing her influence by targeting control on adjacent nodes (shielding). The paper presents an empirical numerical evaluation of these strategies for various classes of complex networks which is backed up by analytical results obtained via a mean-field approach, in good agreement with numerical results. Importantly, we also show that optimal influence allocations tend to not be localized, but can include targeting nodes significant distances away from opposing influence.
This work was supported by the University of Southampton and by the Turing-sponsored pilot project Strategic Influence in Dynamic Opinion Formation.
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References
Alshamsi, A., Pinheiro, F.L., Hidalgo, C.A.: Optimal diversification strategies in the networks of related products and of related research areas. Nat. Commun. 9(1), 1328 (2018). https://doi.org/10.1038/s41467-018-03740-9
Arendt, D.L., Blaha, L.M.: Opinions, influence, and zealotry: a computational study on stubbornness. Comput. Math. Organ. Theory 21, 184 (2015)
Barabási, A.L., Albert, R.: Emergence of scaling in random networks. Science 286(5439), 509–512 (1999). https://doi.org/10.1126/science.286.5439.509
Beckett, L.: Trump digital director says facebook helped win the white house (2017). https://www.theguardian.com/technology/2017/oct/08/trump-digital-director-brad-parscale-facebook-advertising
Braha, D., de Aguiar, M.A.M.: Voting contagion: modeling and analysis of a century of U.S. presidential elections. PLoS ONE 12(5), e0177970 (2017)
Brede, M.: How does active participation effect consensus: adaptive network model of opinion dynamics and influence maximizing rewiring. Complexity 2019, 1486909 (2019)
Brede, M., Restocchi, V., Stein, S.: Resisting influence: how the strength of predispositions to resist control can change strategies for optimal opinion control in the voter model. Front. Robot. AI 5, 34 (2018)
Brede, M., Restocchi, V., Stein, S.: Effects of time horizons on influence maximization in the voter dynamics. J. Complex Networks 7(3), 445–468 (2019). https://academic.oup.com/comnet/article/7/3/445/5149693
Brede, M., Restocchi, V., Stein, S.: Transmission errors and influence maximization in the voter model. J. Stat. Mech. Theory Exp. 2019(3), 033401 (2019)
Castellano, C., Fortunato, S., Loreto, V.: Statistical physics of social dynamics. Rev. Mod. Phys. 81(2), 591–646 (2009)
Clifford, P., Sudbury, A.: A model for spatial conflict. Biometrika 60(3), 581–588 (1973)
Deffuant, G., Neau, D., Amblard, F., Weisbuch, G.: Mixing beliefs among interacting agents. Adv. Complex Syst. 3, 87–89 (2000)
DeGroot, M.: Reaching a consensus. J. Am. Stat. Assoc. 69, 118–121 (1974)
Galam, S.: Minority opinion spreading in random geometry. Eur. Phys. J. B 25, 403 (2002)
Galam, S., Gefen, Y., Shapir, Y.: Sociophysics: a new approach of sociological collective behaviour. i. mean-behaviour description of a strike. J. Math. Sociol. 9, 1–13 (1982)
Galam, S., Javarone, M.A.: Modelling radicalization phenomena in heterogeneous populations. PLoS ONE 11, e0155407 (2016)
Galam, S.: Stubbornness as an unfortunate key to win a public debate: an illustration from sociophysics. Mind Soc. 15(1), 117–130 (2016)
Goldenberg, J., Libai, B., Muller, E.: Talk of the network: a complex systems look at the underlying process of word-of-mouth. Mark. Lett. 12(3), 211–223 (2001)
Hegselmann, R., König, S., Kurz, S., Niemann, C., Rambau, J.: Optimal opinion control: the campaign problem. J. Artif. Soc. Soc. Simul. 18 (2015)
Holley, R.A., Liggett, T.M.: Ergodic theorems for weakly interacting infinite systems and the voter model. Ann. Probab. 3(4), 643–663 (1975)
Javarone, M.A.: Network strategies in election campaigns. J. Stat. Mech. 2014, P08013 (2014)
Kempe, D., Kleinberg, J., Tardos, E.: Maximizing the spread of influence through a social network. In: Proceedings of the Ninth ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, KDD 2003, pp. 137–146. ACM, New York (2003). https://doi.org/10.1145/956750.956769
Kuhlman, C.J., Kumar, V.A., Ravi, S.: Controlling opinion propagation in online networks. Comput. Netw. 57(10), 2121–2132 (2013)
Laciana, C.E., Rovere, S.L.: Ising-like agent-based technology diffusion model: adoption patterns versus seeding strategies. Physica A 390, 1139 (2011)
Lallouache, M., Chakrabarti, A.S., Chakraborti, A., Chakrabarti, B.K.: Opinion formation in kinetic exchange models: spontaneous symmetry-breaking transition. Phys. Rev. E 82, 056112 (2010)
Liu, S., Shakkottai, S.: Influence maximization in social networks: an ising-model-based approach. In: Proceedings of of the 48th Annual Allerton Conference, p. 570 (2010)
Liu, Y.Y., Slotine, J.J., Barabási, A.L.: Controllability of complex networks. Nature 473(7346), 167–173 (2011)
Lynn, C.W., Lee, D.D.: Maximizing influence in an ising network: a mean-field optimal solution. In: Proceedings of the 30th International Conference on Neural Information Processing Systems, NIPS 2016, pp. 2495–2503 (2016)
Masuda, N.: Opinion control in complex networks. New J. Phys. 17, 1–11 (2015)
McFaul, M., Kass, B.: Understanding Putin’s Intentions and Actions in the 2016 U.S. Presidential Election. Technical report, Standford University, June 2019
Mobilia, M.: Does a single zealot affect an infinite group of voters? Phys. Rev. Lett. 91, 028701 (2003)
Mobilia, M., Petersen, A., Redner, S.: On the role of zealotry in the voter model. J. Stat. Mech. Theory Exp. 2007(08), P08029–P08029 (2007)
Morone, F., Makse, H.A.: Influence maximization in complex networks through optimal percolation. Nature 524, 65 (2015)
Porfiri, M., di Bernardo, M.: Criteria for global pinning-controllability of complex networks. Automatica 44(12), 3100–3106 (2008)
Ramos, M., Shao, J., Reis, S.D.S., Anteneodo, C., Andrade, J.S., Havlin, S., Makse, H.A.: How does public opinion become extreme? Sci. Rep. 5, 10032 (2015)
Romero Moreno, G., Tran-Thanh, L., Brede, M.: Continuous influence maximisation for the voter dynamics: Analytical solution for leader-follower networks and gradient ascent algorithm. Manuscript submitted for publication (2019)
Sen, P.: Phase transitions in a two-parameter model of opinion dynamics with random kinetic exchanges. Phys. Rev. E 83, 016108 (2011)
Sîrbu, A., Loreto, V., Servedio, V.D.P., Tria, F.: Opinion Dynamics: Models, Extensions and External Effects, pp. 363–401. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-25658-0_17
Sznajd-Weron, K., Sznajd, J.: Opinion evolution in closed community. Int. J. Mod. Phys. C 11, 1157–1165 (2000)
Watts, D.J., Strogatz, S.H.: Collective dynamics of ‘small-world’ networks. Nature 393(6684), 440–442 (1998). http://www.nature.com/articles/30918
Yadav, A., Wilder, B., Rice, E., Petering, R., Craddock, J., Yoshioka-Maxwell, A., Hemler, M., Onasch-Vera, L., Tambe, M., Woo, D.: Influence maximization in the field: The arduous journey from emerging to deployed application. In: Proceedings of the International Joint Conference on Autonomous Agents and Multiagent Systems, AAMAS (2017)
Yildiz, E., Ozdaglar, A., Acemoglu, D., Saberi, A., Scaglione, A.: Binary opinion dynamics with stubborn agents. ACM Trans. Econ. Comput. 1(4), 1–30 (2013)
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Romero Moreno, G., Tran-Thanh, L., Brede, M. (2020). Shielding and Shadowing: A Tale of Two Strategies for Opinion Control in the Voting Dynamics. In: Cherifi, H., Gaito, S., Mendes, J., Moro, E., Rocha, L. (eds) Complex Networks and Their Applications VIII. COMPLEX NETWORKS 2019. Studies in Computational Intelligence, vol 881. Springer, Cham. https://doi.org/10.1007/978-3-030-36687-2_57
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