Continuous and discontinuous opinion dynamics with bounded confidence

Ceragioli, Francesca; Frasca, Paolo

doi:10.1016/j.nonrwa.2011.10.002

Cited by 74 publications

(55 citation statements)

References 10 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This model, which is a continuous-time counterpart of the opinion dynamics studied by Hegselmann & Krause [34], has been proposed by [8] and further considered in [15]. Very similar models have been considered in [40,35,51,19,49].…”

Section: Discontinuities Generalized Solutions and (Dis)agreement Inmentioning

confidence: 99%

“…The structure of these equilibria is a set of separated clusters of individuals sharing the same opinion. In [8,15] it is proved that, due to robustness issues, one can expect the opinion values of different clusters to be approximately twice the threshold apart. The most recent results on this matter are probably those in [49].…”

Section: Theorem 8 (Sufficient Conditions For Consensus)mentioning

confidence: 99%

See 1 more Smart Citation

Discontinuities, Generalized Solutions, and (Dis)agreement in Opinion Dynamics

Ceragioli¹,

Frasca²

2018

Control Subject to Computational and Communication Constraints

View full text Add to dashboard Cite

Section: Discontinuities Generalized Solutions and (Dis)agreement Inmentioning

confidence: 99%

Section: Theorem 8 (Sufficient Conditions For Consensus)mentioning

confidence: 99%

Discontinuities, Generalized Solutions, and (Dis)agreement in Opinion Dynamics

Ceragioli¹,

Frasca²

2018

Control Subject to Computational and Communication Constraints

View full text Add to dashboard Cite

“…As the first contribution, we prove existence and completeness of Carathéodory solutions from every initial condition. This is a relevant fact because most discontinuous systems, including well-known models of opinion dynamics, do not have complete Carathéodory solutions [13]: even proving existence for most initial conditions can be a difficult task [7,6].…”

mentioning

confidence: 99%

Consensus and Disagreement: The Role of Quantized Behaviors in Opinion Dynamics

Ceragioli¹,

Frasca²

2018

SIAM J. Control Optim.

Self Cite

View full text Add to dashboard Cite

Abstract. This paper deals with continuous-time opinion dynamics that feature the interplay of continuous opinions and discrete behaviours. In our model, the opinion of one individual is only influenced by the behaviours of fellow individuals. The key technical difficulty in the study of these dynamics is that the right-hand sides of the equations are discontinuous and thus their solutions must be intended in some generalized sense: in our analysis, we consider both Carathéodory and Krasovskii solutions. We first prove existence and completeness of Carathéodory solutions from every initial condition and we highlight a pathological behavior of Carathéodory solutions, which can converge to points that are not (Carathéodory) equilibria. Notably, such points can be arbitrarily far from consensus and indeed simulations show that convergence to non-consensus configurations is common. In order to cope with these pathological attractors, we study Krasovskii solutions. We give an estimate of the asymptotic distance of all Krasovskii solutions from consensus and we prove its tightness by an example of equilibrium such that this distance is quadratic in the number of agents. This fact implies that quantization can drastically destroy consensus. However, consensus is guaranteed in some special cases, for instance when the communication among the individuals is described by either a complete or a complete bipartite graph.

show abstract

“…In the terminology of [5], proper initial conditions yield proper Carathéodory solutions of (6). It is shown in [5] that except for at most a set of Lebesgue measure zero all initial conditions are proper initial conditions.…”

Section: Bounded Confidencementioning

confidence: 99%

“…In continuous time, if the confidence range is delimited by a sharp threshold, then the right hand side of the resulting ODEs is discontinuous. Existence and uniqueness analysis of the corresponding solutions have been carried out in [5], [6]. In [6] approximations of the discontinuous dynamics are suggested.…”

Section: Introductionmentioning

confidence: 99%

A bounded confidence model that preserves the signs of the opinions

Ceragioli

Lindmark

Veiback

et al. 2016

2016 European Control Conference (ECC)

Self Cite

View full text Add to dashboard Cite

Abstract-The aim of this paper is to suggest a modification to the usual bounded confidence model of opinion dynamics, so that "changes of opinion" (intended as changes of the sign of the initial state) of an agent are never induced by the dynamics. In order to do so, a bipartite consensus model is used, endowing it with a confidence range. The resulting signed bounded confidence model has a state-dependent connectivity and a behavior similar to its standard counterpart, but in addition it preserves the sign of the opinions by "repelling away" opinions localized near the origin but on different sides with respect to 0.

show abstract

Continuous and discontinuous opinion dynamics with bounded confidence

Cited by 74 publications

References 10 publications

Discontinuities, Generalized Solutions, and (Dis)agreement in Opinion Dynamics

Discontinuities, Generalized Solutions, and (Dis)agreement in Opinion Dynamics

Consensus and Disagreement: The Role of Quantized Behaviors in Opinion Dynamics

A bounded confidence model that preserves the signs of the opinions

Contact Info

Product

Resources

About