Asynchronous opinion dynamics on the &lt;tex&gt;$k$&lt;/tex&gt;-nearest-neighbors graph

Rossi, Wilbert Samuel; Frasca, Paolo

doi:10.1109/cdc.2018.8619285

Cited by 8 publications

(5 citation statements)

References 19 publications

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“…If k = 2, then each agent averages her opinion with the closest agent apart himself. For general k, this dynamics was studied in [24]. In this case, there exist non-clustered configurations that are equilibria, see [24] for two examples (one using the tie break rule and one not).…”

Section: Lemma 1 (Clustered Configurations): a Configuration Is Clustered If And Only Ifmentioning

confidence: 99%

“…For general k, this dynamics was studied in [24]. In this case, there exist non-clustered configurations that are equilibria, see [24] for two examples (one using the tie break rule and one not). Instead, for m < n, the following result shows that all equilibria are clustered configurations.…”

Section: Lemma 1 (Clustered Configurations): a Configuration Is Clustered If And Only Ifmentioning

confidence: 99%

“…In the control community, [22] has recently used Petri nets to define a class of models where interactions depend on the opinions of multiple agents: despite some similarity, our model does not belong to this class. Closely related papers are also [23], where the authors define a dynamics in which each agent is influenced by a fixed number of neighbors, and our recent paper [24], which deals the case m = n: this special case is simpler to study and does not exhibit metastable states. Instead, the paper [25] introduces random sampling in the metric bounded confidence model.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Lemma 1 (Clustered Configurations): a Configuration Is Clustered If And Only Ifmentioning

confidence: 99%

Section: Lemma 1 (Clustered Configurations): a Configuration Is Clustered If And Only Ifmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Opinion Dynamics With Topological Gossiping: Asynchronous Updates Under Limited Attention

Rossi

Frasca

2020

IEEE Control Syst. Lett.

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“…Among first order "opinion" models, [1] has recently used Petri nets to define a class of models where interactions depend on the opinions of multiple agents: despite some similarities, our model does not belong to this class. In our recent papers [29,28], we have studied two dynamics with asynchronous updates (with and without sub-sampling, respectively) that are discrete-time counterparts of the model we propose here. Finally, our contribution here differs from the one of [2] as the latter focuses on specific properties of the equilibria, such as the distribution of their clusters' sizes, studied by extensive simulations, whereas we are interested in analytical results about dynamical properties like convergence to the equilibria and about their robustness to perturbations.…”

Section: Introductionmentioning

confidence: 99%

Modeling limited attention in opinion dynamics by topological interactions

Ceragioli¹,

Frasca²,

Rossi³

2020

Preprint

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This work explores models of opinion dynamics with opiniondependent connectivity. Our starting point is that individuals have limited capabilities to engage in interactions with their peers. Motivated by this observation, we propose a continuous-time opinion dynamics model such that interactions take place with a limited number of peers: we refer to these interactions as topological, as opposed to metric interactions that are postulated in classical bounded-confidence models. We observe that topological interactions produce equilibria that are very robust to disruptions.

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“…Touri et al [16] and Etesami et al [17] both considered an asynchronous HK model, in which only one agent is communicating at each time. Rossi et al studied an opinion dynamics on the k-nearest-neighbors graph, which is essentially an asynchronous model [19]. Ding et al considered an asynchronous opinion scenario with online and offline interactions [18].…”

Section: Introductionmentioning

confidence: 99%

Quasi-synchronization of bounded confidence opinion dynamics with stochastic asynchronous rule

Su¹,

Wang²,

Chen³

et al. 2020

Preprint

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Recently the theory of noise-induced synchronization of Hegselmann-Krause (HK) dynamics has been well developed. As a typical opinion dynamics of bounded confidence, the HK model obeys a synchronous updating rule, i.e., all agents check and update their opinions at each time point. However, whether asynchronous bounded confidence models, including the famous Deffuant-Weisbuch (DW) model, can be synchronized by noise have not been theoretically proved. In this paper, we propose a generalized bounded confidence model which possesses a stochastic asynchronous rule. The model takes the DW model and the HK model as special cases and can significantly generalize the bounded confidence models to practical application. We discover that the asynchronous model possesses a different noise-based synchronization behavior compared to the synchronous HK model. Generally, the HK dynamics can achieve quasi-synchronization almost surely under the drive of noise. For the asynchronous dynamics, we prove that the model can achieve quasi-synchronization in mean, which is a new type of quasi-synchronization weaker than the "almost surely" sense. The results unify the theory of noise-induced synchronization of bounded confidence opinion dynamics and hence proves the noise-induced synchronization of DW model theoretically for the first time. Moreover, the results provide a theoretical foundation for developing noisebased control strategy of more complex social opinion systems with stochastic asynchronous rules.

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Asynchronous opinion dynamics on the <tex>$k$</tex>-nearest-neighbors graph

Cited by 8 publications

References 19 publications

Opinion Dynamics With Topological Gossiping: Asynchronous Updates Under Limited Attention

Opinion Dynamics With Topological Gossiping: Asynchronous Updates Under Limited Attention

Modeling limited attention in opinion dynamics by topological interactions

Quasi-synchronization of bounded confidence opinion dynamics with stochastic asynchronous rule

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