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Opinion Dynamics with Random Actions and a Stubborn Agent

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Olle Abrahamsson, Danyo Danev, Erik G. Larsson

Social and Information Networks · Submitted 9 Dec 2019

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We then consider a recent extension of the DeGroot model in which the opinion of each agent is a random Bernoulli distributed variable, and by leveraging on the first result we establish that this model also leads to consensus, in the sense of convergence in probability, in the presence of a stubborn agent.

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arXiv ID1912.04183 (version 1)
Pith IDORMTXR5H, Pith's permanent record of this paper and its review
CitationDanyo Danev, Erik G. Larsson, Olle Abrahamsson. "Opinion Dynamics with Random Actions and a Stubborn Agent." arXiv:1912.04183 (2019). https://pith.science/paper/ORMTXR5H
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The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,249 input tokens.

What the abstract itself states, as probabilities: claims first 0.06 · states limitation 0.08 · human participants 0.04 · controlled comparison 0.05 · randomized assignment 0.03 · states quantitative result 0.06 · compares with prior results 0.94 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

We study opinion dynamics in a social network with stubborn agents who influence their neighbors but who themselves always stick to their initial opinion. We consider first the well-known DeGroot model. While it is known in the literature that this model can lead to consensus even in the presence of a stubborn agent, we show that the same result holds under weaker assumptions than has been previously reported. We then consider a recent extension of the DeGroot model in which the opinion of each agent is a random Bernoulli distributed variable, and by leveraging on the first result we establish that this model also leads to consensus, in the sense of convergence in probability, in the presence of a stubborn agent. Moreover, all agents' opinions converge to that of the stubborn agent.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We study opinion dynamics in a social network with stubborn agents who influence their neighbors but who themselves always stick to their initial opinion. background 0.61 0.34 0.05 asserted 0.90
s1 We consider first the well-known DeGroot model. method 0.67 0.24 0.02 asserted 0.66
s2 While it is known in the literature that this model can lead to consensus even in the presence of a stubborn agent, we show that the same result holds under weaker assumptions than has been previously reported. contribution 0.53 0.86 0.20 asserted 1.00
s3 We then consider a recent extension of the DeGroot model in which the opinion of each agent is a random Bernoulli distributed variable, and by leveraging on the first result we establish that this model also leads to consensus, in the sense of convergence in probability, in the presence of a stubborn agent. result 0.63 0.92 0.33 asserted 1.00
s4 Moreover, all agents' opinions converge to that of the stubborn agent. result 1.00 0.86 0.31 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

What was examined, and what was not

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  • references and citing sentences
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  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

We study opinion dynamics in a social network with stubborn agents who influence their neighbors but who themselves always stick to their initial opinion. We consider first the well-known DeGroot model. While it is known in the literature that this model can lead to consensus even in the presence of a stubborn agent, we show that the same result holds under weaker assumptions than has been previously reported. We then consider a recent extension of the DeGroot model in which the opinion of each agent is a random Bernoulli distributed variable, and by leveraging on the first result we establish that this model also leads to consensus, in the sense of convergence in probability, in the presence of a stubborn agent. Moreover, all agents' opinions converge to that of the stubborn agent.

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How the literature uses it

1 arXiv paper cite this in 2 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers whose main result relates to this one's

Found among the papers closest to this one by title and main claim. Pith's classifier compared each pair's main results and a second model family confirmed the relation; checked against two further families, shown conflicts agreed 118 times in 120 and shown same results 218 times in 239. The quoted sentence is the other paper's main claim.

States the same result 1 paper
  • We then consider a recent extension of the DeGroot model in which the opinion of each agent is a random Bernoulli distributed variable, and by leveraging on the first result we establish that this model also leads to consensus, in the sense of convergence in probability, in the presence of a stubborn agent.

    On the Impact of Random Actions on Opinion Dynamics · 0.93

What it cites

Cites as background 1 paper
  • Another class of models incorporates randomness, for example in terms of random interactions [ref] or as in [ref] , where at each time \(n\) a randomly selected agent communicates a random opinion to its neighbors.

    Optimizing Opinions with Stubborn Agents · Introduction · 0.99

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