Polar Opinion Dynamics in Social Networks

Amelkin, Victor; Bullo, Francesco; Singh, Ambuj K.

doi:10.1109/tac.2017.2694341

Cited by 120 publications

(80 citation statements)

References 63 publications

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“…Remark 4: It should be noted that Theorem 2 does not consider the case where there exist i, j ∈ [n] such that x i (0) > 0 and x j (0) < 0. It has been shown in [33] that for this case, the continuous-time model has lim t→∞ x(t) = 0. However, this is not always the case for the discrete-time model with stubborn neutrals, as we will show shortly, since in discrete-time, the opinion of an agent i can jump from x i (t) > 0 to x i (t + 1) < 0, but this is not possible in the continuous-time case.…”

Section: B Stubborn Neutralsmentioning

confidence: 99%

“…Specifically, the consensus will be reached at −1 if and only if x(0) = −1, and at 1 if and only if x(0) 1 does not hold. Remark 2: The discrete-time model with stubborn positives has the same limiting behavior as the continuous-time model considered in [33]. We consider the general timevarying case whereas only the time-invariant case was studied in [33].…”

Section: A Stubborn Positivesmentioning

confidence: 99%

“…opinions (which change with time), then necessarily the interpersonal influences are state-dependent, and thus timevarying. In a recent paper [33], a continuous-time model has been proposed for fixed social network topology which considers, separately, three different cognitive processes to drive the influence change. In [33], the term "polar opinion dynamics" relates to the fact that the level of influence is dependent on how extreme, i.e.…”

Section: Introductionmentioning

confidence: 99%

“…We first propose a general model, show it can be considered as a generalization of both the DeGroot model and the Friedkin-Johnsen model [29], [30], and establish some general properties of the model. We then investigate discrete-time versions of two of the three cognitive process introduced in [33], bearing in mind that discrete-time models are more appropriate to describe opinion dynamics, at least from the point that individuals change their minds from time to time, instead of continuously. In addition, we provide social examples from existing literature to motivate these susceptibility functions.…”

Section: Introductionmentioning

confidence: 99%

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Discrete-Time Polar Opinion Dynamics with Heterogeneous Individuals

Liu¹,

Anderson

et al. 2018

2018 IEEE Conference on Decision and Control (CDC)

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This paper considers a discrete-time opinion dynamics model in which each individual's susceptibility to being influenced by others is dependent on her current opinion. We assume that the social network has time-varying topology and that the opinions are scalars on a continuous interval. We first propose a general opinion dynamics model based on the DeGroot model, with a general function to describe the functional dependence of each individual's susceptibility on her own opinion, and show that this general model is analogous to the Friedkin-Johnsen model, which assumes a constant susceptibility for each individual. We then consider two specific functions in which the individual's susceptibility depends on the polarity of her opinion, and provide motivating social examples. First, we consider stubborn positives, who have reduced susceptibility if their opinions are at one end of the interval and increased susceptibility if their opinions are at the opposite end. A court jury is used as a motivating example. Second, we consider stubborn neutrals, who have reduced susceptibility when their opinions are in the middle of the spectrum, and our motivating examples are social networks discussing established social norms or institutionalized behavior. For each specific susceptibility model, we establish the initial and graph topology conditions in which consensus is reached, and develop necessary and sufficient conditions on the initial conditions for the final consensus value to be at either extreme of the opinion interval. Simulations are provided to show the effects of the susceptibility function when compared to the DeGroot model.

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Section: B Stubborn Neutralsmentioning

confidence: 99%

Section: A Stubborn Positivesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Discrete-Time Polar Opinion Dynamics with Heterogeneous Individuals

Liu¹,

Anderson

et al. 2018

2018 IEEE Conference on Decision and Control (CDC)

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“…Remark 1: For some models, each individual has a parameter describing her susceptibility to external influence (the parameter is constant in [14] and opinion-dependent in [4]). However, both models share the same property; when an individual i is exposed to two equal pieces of opinions from either end of the spectrum, the opinion furthest from opinion x i is more attractive.…”

Section: A Exploring the Bias Parameter's Effectmentioning

confidence: 99%

Stability Analysis of a Nonlinear Opinion Dynamics Model for Biased Assimilation

Xia

Liu

Cao

et al. 2018

2018 IEEE Conference on Decision and Control (CDC)

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This paper analyzes a nonlinear opinion dynamics model which generalizes the DeGroot model by introducing a bias parameter for each individual. The original DeGroot model is recovered when the bias parameter is equal to zero. The magnitude of this parameter reflects an individual's degree of bias when assimilating new opinions, and depending on the magnitude, an individual is said to have weak, intermediate, and strong bias. The opinions of the individuals lie between 0 and 1. It is shown that for strongly connected networks, the equilibria with all elements equal identically to the extreme value 0 or 1 is locally exponentially stable, while the equilibrium with all elements equal to the neutral consensus value of 1 2 is unstable. Regions of attraction for the extreme consensus equilibria are given. For the equilibrium consisting of both extreme values 0 and 1, which corresponds to opinion polarization according to the model, it is shown that the equilibrium is unstable for all strongly connected networks if individuals all have weak bias, becomes locally exponentially stable for complete and two-island networks if individuals all have strong bias, and its stability heavily depends on the network topology when individuals have intermediate bias.Analysis on star graphs and simulations show that additional equilibria may exist where individuals form clusters.

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