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Learning to predict opinion share and detect anti-majority opinionists in social networks

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Abstract

We address the problem of detecting anti-majority opinionists using the value-weighted mixture voter (VwMV) model. This problem is motivated by the fact that 1) each opinion has its own value and an opinion with a higher value propagates more easily/rapidly and 2) there are always people who have a tendency to disagree with any opinion expressed by the majority. We extend the basic voter model to include these two factors with the value of each opinion and the anti-majoritarian tendency of each node as new parameters, and learn these parameters from a sequence of observed opinion data over a social network. We experimentally show that it is possible to learn the opinion values correctly using a short observed opinion propagation data and to predict the opinion share in the near future correctly even in the presence of anti-majoritarians, and also show that it is possible to learn the anti-majoritarian tendency of each node if longer observation data is available. Indeed, the learned model can predict the future opinion share much more accurately than a simple polynomial extrapolation can do. Ignoring these two factors substantially degrade the performance of share prediction. We also show theoretically that, in a situation where the local opinion share can be approximated by the average opinion share, 1) when there are no anti-majoritarians, the opinion with the highest value eventually takes over, but 2) when there are a certain fraction of anti-majoritarians, it is not necessarily the case that the opinion with the highest value prevails and wins, and further, 3) in both cases, when the opinion values are uniform, the opinion share prediction problem becomes ill-defined and any opinion can win. The simulation results support that this holds for typical real world social networks. These theoretical results help understand the long term behavior of opinion propagation.

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Notes

  1. This may look a rather unnatural assumption because it is unlikely that all the different opinions are initiated at the same time. Since each opinion is initiated by a single person and the goal is to see how it is propagated, it should be allowed that each opinion is assigned to only one node and all the remaining nodes are in neutral states, i.e., unaffected by any opinion yet. We could have changed the timing of each opinion’s initial utterance, but chose the simplest case.

  2. This assumes that the average delay time is 1.

  3. If the goal is to predict which opinion wins eventually, it is sufficient to identify which opinion has the highest value, but if we want to estimate the share of each opinion, we need to estimate the values accurately.

  4. This makes the analysis drastically simpler, but the results remains valid qualitatively.

  5. Their results is that the basic voter model converges after O(n 3logn) steps with probability 1- o(1) where n is the number of nodes.

  6. Opinion propagation is directional. Choosing bidirectional networks means that opinion can propagate in both directions.

  7. It would be the best if we can use the real opinion propagation data. However, as we are not able to find such data, the next best is to use the network structures constructed from the real world social media data (not synthetic networks).

  8. It may sound more reasonable to weight each difference by the share itself, but we decided not to do so. We rather considered the prediction problem as the classification problem.

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Authors and Affiliations

  1. Department of Electronics and Informatics, Ryukoku University, Otsu, 520-2194, Japan

    Masahiro Kimura

  2. School of Administration and Informatics, University of Shizuoka, Shizuoka, 422-8526, Japan

    Kazumi Saito

  3. Department of Integrated Information Technology, Aoyama Gakuin University, Kanagawa, 229-8558, Japan

    Kouzou Ohara

  4. Institute of Scientific and Industrial Research, Osaka University, Osaka, 567-0047, Japan

    Hiroshi Motoda

Authors
  1. Masahiro Kimura
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  2. Kazumi Saito
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  3. Kouzou Ohara
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  4. Hiroshi Motoda
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Corresponding author

Correspondence to Masahiro Kimura.

Additional information

This work was partly supported by Asian Office of Aerospace Research and Development, Air Force Office of Scientific Research under Grant No. AOARD-10-4053, and JSPS Grant-in-Aid for Scientific Research (C) (No. 23500194).

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Kimura, M., Saito, K., Ohara, K. et al. Learning to predict opinion share and detect anti-majority opinionists in social networks. J Intell Inf Syst 41, 5–37 (2013). https://doi.org/10.1007/s10844-012-0222-7

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  • DOI: https://doi.org/10.1007/s10844-012-0222-7

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