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Opinions, influence, and zealotry: a computational study on stubbornness

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Abstract

We present a simple, efficient, and predictive model for opinion dynamics with zealots. Our model captures curvature-driven dynamics (e.g., clear, smooth boundaries separating domains whose curvature decreases over time) through a simple, individual rule, providing a method for rapidly testing basic hypotheses about innovation diffusion, opinion dynamics, and related phenomena. Our model belongs to a class of models called dimer automata, which are asynchronous, graph-based (i.e., non-uniform lattice) variants of cellular automata. Individuals in the model update their states via a dyadic update rule; population opinion dynamics emerge from these pairwise interactions. Zealots are stubborn individuals whose opinion is not susceptible to influence by others. We observe experimentally that a system without zealots usually converges to the majority opinion, but a relatively small number of zealots can sway the opinion of the whole population. The influence of zealots can be further increased by placing zealots at more effective locations within the network. These locations can be determined by rankings from standard social network analysis metrics, or by using a greedy algorithm for influence maximization. We apply the influence maximization technique to a politically polarized social network to explore opinion dynamics in a real-world network and to gain insight about influence and political entrenchment through the zealot model’s ability to sway the entire network to one side or the other.

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Notes

  1. In our experience, a rule of thumb for designing individual models is to avoid, as much as possible, rules that move the system towards the desired global outcome. Doing so can produce interesting and sometimes counter intuitive relationships between the local interactions and the global phenomenon.

  2. Thus, the term “dimer” in dimer automaton refers to the manner in which the rule is applied to pairs of adjacent cells.

  3. How long should the simulation be run? We find that performing \(O(|V|^{1.5})\) updates is a reasonable number of steps for the experiments in this paper.

  4. A time epoch consists of \(O(|V|)\) edge updates.

  5. For this experiment the zealot density is relative to the number of unconverted nodes in the initial configuration. When there are l left-leaning vertices and \(r\) right-leaning vertices, if we are trying to convert left-leaning to right-leaning, and we use \(z_r\) right-leaning zealots, then the zealot density is \(z_r/l\) instead of \(z_r/(r+l)\).

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Acknowledgments

Distribution A: Approved for public release; distribution unlimited. 88ABW cleared 11/08/2013; 88 ABW-2013-4691. This work was supported by AFOSR LRIR 12RH12COR to L.M.B. This research was performed while D.L.A. held a National Research Council Research Associateship Award at the Air Force Research Laboratory.

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Authors and Affiliations

  1. Pacific Northwest National Laboratory, 902 Battelle Boulevard, Richland, WA, USA

    Dustin L. Arendt

  2. Air Force Research Laboratory, 2255 H St., Wright-Patterson AFB, OH, USA

    Leslie M. Blaha

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Correspondence to Dustin L. Arendt.

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Arendt, D.L., Blaha, L.M. Opinions, influence, and zealotry: a computational study on stubbornness. Comput Math Organ Theory 21, 184–209 (2015). https://doi.org/10.1007/s10588-015-9181-1

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