Abstract
We study how multi-hop information impacts convergence in social influence networks. In influence networks, nodes have a choice between two options A and B, and each node prefers to end up choosing the option that a majority of its neighbors choose. We consider the case of innovation adoption in which nodes can only change from A to B, but not backwards. For this model, we ask the question, when is it safe for a node to switch from A to B? If nodes have multi-hop information about the network, rather than knowing only the state of their immediate neighbors, the answer to this question becomes complex. The reason is that a node needs to recursively reason about what its neighbors know, and whether given their knowledge they will also upgrade to B.
In this paper, we assume that each node has complete knowledge about its k-hop neighborhood, but does not know anything about the network beyond k-hops. We study how different local decision algorithms achieve different properties in terms of safety and conversion ratio (how many nodes ultimately upgrade to B). We characterize the possible algorithms by classifying them into a hierarchy of algorithms. Each class of algorithms in this hierarchy is distinguished by a natural safety property that it guarantees. For each class, we give an optimal algorithm in terms of conversion ratio, and we show that each class is fully contained in the class of lower safety level. Conversely, each lower-safety class can achieve strictly higher conversion ratio than any algorithm in the safer class. Thus, our hierarchy reveals a strict trade-off between safety and conversion ratio. Finally, we show that each class of algorithms satisfies two natural closure properties.
This work was supported in part by the National Basic Research Program of China Grant 2011CBA00300, 2011CBA00301, the National Natural Science Foundation of China Grant 61033001, 61361136003.
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References
Arthur, W.B., Lane, D.A.: Information contagion. Structural Change and Economic Dynamics 4(1), 81–104 (1993)
Chen, W., Wang, C., Wang, Y.: Scalable influence maximization for prevalent viral marketing in large-scale social networks. In: Proceedings of the 16th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 1029–1038. ACM (2010)
Frischknecht, S., Keller, B., Wattenhofer, R.: Convergence in (Social) influence networks. In: Afek, Y. (ed.) DISC 2013. LNCS, vol. 8205, pp. 433–446. Springer, Heidelberg (2013)
Gardner, M.: Mathematical games: The fantastic combinations of john conways new solitaire game life. Scientific American 223(4), 120–123 (1970)
Goles, E., Olivos, J.: Periodic behaviour of generalized threshold functions. Discrete Mathematics 30(2), 187–189 (1980)
Goles, E., Tchuente, M.: Iterative behaviour of generalized majority functions. Mathematical Social Sciences 4(3), 197–204 (1983)
Granovetter, M.: Threshold models of collective behavior. American Journal of Sociology 83(6), 1420 (1978)
Kempe, D., Kleinberg, J., Tardos, É.: Maximizing the spread of influence through a social network. In: Proceedings of the ninth ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 137–146. ACM (2003)
Kempe, D., Kleinberg, J.M., Tardos, É.: Influential nodes in a diffusion model for social networks. In: Caires, L., Italiano, G.F., Monteiro, L., Palamidessi, C., Yung, M. (eds.) ICALP 2005. LNCS, vol. 3580, pp. 1127–1138. Springer, Heidelberg (2005)
Leskovec, J., Krause, A., Guestrin, C., Faloutsos, C., VanBriesen, J., Glance, N.: Cost-effective outbreak detection in networks. In: Proceedings of the 13th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 420–429. ACM (2007)
Macy, M.W.: Chains of cooperation: Threshold effects in collective action. American Sociological Review, pp. 730–747 (1991)
Macy, M.W., Willer, R.: From factors to actors: Computational sociology and agent-based modeling. Annual review of sociology, pp. 143–166 (2002)
Morris, S.: Contagion. The Review of Economic Studies 67(1), 57–78 (2000)
Peleg, D.: Local majorities, coalitions and monopolies in graphs: a review. Theoretical Computer Science 282(2), 231–257 (2002)
Poljak, S., Sra, M.: On periodical behaviour in societies with symmetric influences. Combinatorica 3(1), 119–121 (1983)
Rogers Everett, M.: Diffusion of innovations. New York (1995)
Schelling, T.C.: Hockey helmets, concealed weapons, and daylight saving: A study of binary choices with externalities. Journal of Conflict Resolution, 381–428 (1973)
Schelling, T.C.: Micromotives and macrobehavior. WW Norton & Company (2006)
Valente, T.W.: Network models of the diffusion of innovations. Computational & Mathematical Organization Theory 2(2), 163–164 (1996)
Wasserman, S.: Social network analysis: Methods and applications, vol. 8. Cambridge University Press (1994)
Winkler, P.: Puzzled delightful graph theory. Communications of the ACM 51(8), 104–104 (2008)
Young, H.P.: Individual strategy and social structure: An evolutionary theory of institutions. Princeton University Press (2001)
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Lv, Y., Moscibroda, T. (2015). Local Information in Influence Networks. In: Moses, Y. (eds) Distributed Computing. DISC 2015. Lecture Notes in Computer Science(), vol 9363. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-48653-5_20
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DOI: https://doi.org/10.1007/978-3-662-48653-5_20
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