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An analytical formulation for multidimensional continuous opinion models

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  • Pedraza, Lucía
  • Pinasco, Juan Pablo
  • Saintier, Nicolas
  • Balenzuela, Pablo

Abstract

Usually, opinion formation models assume that individuals have an opinion about a given topic which can change due to interactions with others. However, individuals can have different opinions on different topics and therefore n-dimensional models are best suited to deal with these cases. While there have been many efforts to develop analytical models for one dimensional opinion models, less attention has been paid to multidimensional ones. In this work, we develop an analytical approach for multidimensional models of continuous opinions. We show that for any generic reciprocal interactions between agents, the mean value of initial opinion distribution is conserved. Moreover, for positive social influence interaction mechanisms, the variance of opinion distributions decreases with time and the system converges to a delta distributed function. In particular, we calculate the convergence time when agents get closer in a discrete quantity after interacting, showing a clear difference between cases where the approach is through Manhattan or Euclidean distance.

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  • Pedraza, Lucía & Pinasco, Juan Pablo & Saintier, Nicolas & Balenzuela, Pablo, 2021. "An analytical formulation for multidimensional continuous opinion models," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    • Handle: RePEc:eee:chsofr:v:152:y:2021:i:c:s0960077921007220
    DOI: 10.1016/j.chaos.2021.111368
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    References listed on IDEAS

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    Cited by:

    1. Ni, Xuelian & Xiong, Fei & Pan, Shirui & Chen, Hongshu & Wu, Jia & Wang, Liang, 2023. "How heterogeneous social influence acts on human decision-making in online social networks," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    2. Martin-Gutierrez, Samuel & Losada, Juan C. & Benito, Rosa M., 2023. "Multipolar social systems: Measuring polarization beyond dichotomous contexts," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).

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