Convergence properties of the heterogeneous Deffuant–Weisbuch model

Chen, Ge; Su, Wei; Mei, Wenjun; Bullo, Francesco

doi:10.1016/j.automatica.2020.108825

Cited by 38 publications

(16 citation statements)

References 21 publications

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“…We remark that our model has asynchronous updating of the opinions since only two opinions are updated simultaneously and independently per time step instead of all opinions at once (which would be synchronous updating). This type of updating has been present in other previous opinion models, e.g., in the Deffuant-Weisbuch model [9]. An example of selecting edges for the opinion updating is to do it uniformly as follows: let m be the number of edges in the graph (e.g., m = n 2 for complete graphs), then we can assign to every pair of agents the same probability of being selected and have p ij = 1/m for any pair {i, j}.…”

Section: The Modelsupporting

confidence: 67%

“…An example of selecting edges for the opinion updating is to do it uniformly as follows: let m be the number of edges in the graph (e.g., m = n 2 for complete graphs), then we can assign to every pair of agents the same probability of being selected and have p ij = 1/m for any pair {i, j}. [4,19]), and the case o min = 0 and o max = 1 characterizes various works in the literature of opinion dynamics over graphs with positive weights (e.g., [3]) or bounded-confidence models (e.g., [9]).…”

Section: The Modelmentioning

confidence: 99%

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Polarization and Fluctuations in Signed Social Networks

Cisneros-Velarde¹,

Chan²,

Bullo³

2019

Preprint

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Much recent research on social networks has focused on the modeling and analysis of how opinions evolve as a function of interpersonal relationships. It is also of great interest to model and understand the implications of friendly and antagonistic relationships. In this paper, we propose a new, simple and intuitive model that incorporates the socio-psychological phenomenon of the boomerang effect in opinion dynamics. We establish that, under certain conditions on the structure of the signed network that corresponds to the so-called structural balance property, the opinions in the network polarize. Compared to other models in the literature, our model displays a richer and perhaps more intuitive behavior of the opinions when the social network does not satisfy structural balance. In particular, we analyze signed networks in which the opinions show persistent fluctuations (including the case of the so-called clustering balance).

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Section: The Modelsupporting

confidence: 67%

Section: The Modelmentioning

confidence: 99%

Polarization and Fluctuations in Signed Social Networks

Cisneros-Velarde¹,

Chan²,

Bullo³

2019

Preprint

Self Cite

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“…In the literature, models with any of these features are still relatively few. In classical bounded confidence models interactions are reciprocal as long as the interaction thresholds are equal for all agents [3], [11], [12], [13], and any lack of reciprocity makes the analysis much more delicate [14], [15], [16]. In our model, not only interactions are non-reciprocal, but they are also non-metric: whether two agents interact is not solely determined by the distance between their two opinions.…”

Section: Introductionmentioning

confidence: 99%

Opinion Dynamics With Topological Gossiping: Asynchronous Updates Under Limited Attention

Rossi

Frasca

2020

IEEE Control Syst. Lett.

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This paper introduces a general model of opinion dynamics with opinion-dependent connectivity. Agents update their opinions asynchronously: for the updating agent, the new opinion is the average of the k closest opinions within a subset of m agents that are sampled from the population of size n. Depending on k and m with respect to n, the dynamics can have a variety of equilibria, which include consensus and clustered configurations. The model covers as special cases a classical gossip update (if m = n) and a deterministic update defined by the k nearest neighbors (if m = k). We prove that the dynamics converges to consensus if n > 2(m − k). Before convergence, however, the dynamics can remain for long time in the vicinity of metastable clustered configurations.

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“…We establish the almost-sure convergence of the SIH dynamics by showing that, for any initial condition, there exists at least one finite update sequence along which the trajectory achieves triad-wise structural balance. This argument is formalized as a lemma and is presented in Appendix E. A similar proof strategy has been adopted in [8]. Note that a manual update sequence is one path to almost sure convergence.…”

Section: Convergence To Triad-wise Structural Balancementioning

confidence: 99%

Structural Balance and Interpersonal Appraisals Dynamics: Beyond All-to-All and Two-Faction Networks

Mei¹,

Chen²,

Friedkin³

et al. 2020

Preprint

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Structural balance theory describes stable configurations of topologies of signed interpersonal appraisal networks. Existing models explaining the convergence of appraisal networks to structural balance either diverge in finite time, or could get stuck in jammed states, or converge to only complete graphs. In this paper we study the open problem how steady non-all-to-all structural balance emerges via local dynamics of interpersonal appraisals. We first compare two well-justified definitions of structural balance for general non-all-to-all graphs, i.e., the triad-wise structural balance and the two-faction structural balance, and thoroughly study their relations. Secondly, based on three widely adopted sociological mechanisms: the symmetry mechanism, the influence mechanism, and the homophily mechanism, we propose two simple models of gossip-like appraisal dynamics, the symmetry-influence-homophily (SIH) dynamics and the symmetry-influence-opinion-homophily (SIOH) dynamics. In these models, the appraisal network starting from any initial condition almost surely achieves non-all-to-all triad-wise and twofaction structural balance in finite time respectively. Moreover, the SIOH dynamics capture the co-evolution of interpersonal appraisals and individuals' opinions. Regarding the theoretical contributions, we show that the equilibrium set of the SIH (SIOH resp.) dynamics corresponds to the set of all the possible triad-wise (two-faction resp.) structural balance configurations of the appraisal networks. Moreover, we prove that, for any initial condition, the appraisal networks in the SIH (SIOH resp.) dynamics almost surely achieve triad-wise (two-faction resp.) structural balance in finite time. Numerical studies of the SIH dynamics are conducted on how the final proportion of negative links depends on the initial proportion of negative links and the network topology. These simulation results imply some insightful take-home messages on whether multilateral relations reduce or exacerbate conflicts.

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Convergence properties of the heterogeneous Deffuant–Weisbuch model

Cited by 38 publications

References 21 publications

Polarization and Fluctuations in Signed Social Networks

Polarization and Fluctuations in Signed Social Networks

Opinion Dynamics With Topological Gossiping: Asynchronous Updates Under Limited Attention

Structural Balance and Interpersonal Appraisals Dynamics: Beyond All-to-All and Two-Faction Networks

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