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Analysis and control of agreement and disagreement opinion cascades

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Abstract

We introduce and analyze a continuous time and state-space model of opinion cascades on networks of large numbers of agents that form opinions about two or more options. By leveraging our recent results on the emergence of agreement and disagreement states, we introduce novel tools to analyze and control agreement and disagreement opinion cascades. New notions of agreement and disagreement centrality, which depend only on network structure, are shown to be key to characterizing the nonlinear behavior of agreement and disagreement opinion formation and cascades. Our results are relevant for the analysis and control of opinion cascades in real-world networks, including biological, social, and artificial networks, and for the design of opinion-forming behaviors in robotic swarms. We illustrate an application of our model to a multi-robot task-allocation problem and discuss extensions and future directions opened by our modeling framework.

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Notes

  1. The assumption that the minimum eigenvalue of \(\tilde{A}\) has algebraic multiplicity one is usually true for all sufficiently large complex networks. The case in which this multiplicity is larger can also be analyzed, but for simplicity we do not address it here.

  2. The proposed agreement cascade control algorithm naturally generalizes to the case in which inputs bring mixed information about the various options.

  3. The proposed disagreement cascade control algorithm naturally generalizes to the case in which inputs bring mixed information about the various options as long as \({\varvec{b}}_{i}=\pm {\varvec{b}}_0\), \(i=1,\ldots ,{N_\mathrm{a}}\).

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Authors and Affiliations

  1. Math Department, National Autonomous University of Mexico, 04510, Mexico City, Mexico

    Alessio Franci

  2. Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ, 08544, USA

    Anastasia Bizyaeva, Shinkyu Park & Naomi Ehrich Leonard

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  1. Alessio Franci
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Correspondence to Alessio Franci.

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This research has been supported in part by NSF grant CMMI-1635056, ONR grant N00014-19-1-2556, ARO grant W911NF-18-1-0325, DGAPA-UNAM PAPIIT grant IN102420, Conacyt grant A1-S-10610, and by NSF Graduate Research Fellowship DGE-2039656. Any opinion, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the NSF.

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Franci, A., Bizyaeva, A., Park, S. et al. Analysis and control of agreement and disagreement opinion cascades. Swarm Intell 15, 47–82 (2021). https://doi.org/10.1007/s11721-021-00190-w

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