Asynchronous Opinion Dynamics in Social Networks Article Swipe

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Petra Berenbrink , Martin Hoefer , Dominik Kaaser , Pascal Lenzner , Malin Rau , Daniel Schmand ·

YOU? · · 2022 · Open Access · · DOI: https://doi.org/10.48550/arxiv.2201.12923

Opinion spreading in a society decides the fate of elections, the success of products, and the impact of political or social movements. The model by Hegselmann and Krause is a well-known theoretical model to study such opinion formation processes in social networks. In contrast to many other theoretical models, it does not converge towards a situation where all agents agree on the same opinion. Instead, it assumes that people find an opinion reasonable if and only if it is close to their own. The system converges towards a stable situation where agents sharing the same opinion form a cluster, and agents in different clusters do not \mbox{influence each other.} We focus on the social variant of the Hegselmann-Krause model where agents are connected by a social network and their opinions evolve in an iterative process. When activated, an agent adopts the average of the opinions of its neighbors having a similar opinion. By this, the set of influencing neighbors of an agent may change over time. To the best of our knowledge, social Hegselmann-Krause systems with asynchronous opinion updates have only been studied with the complete graph as social network. We show that such opinion dynamics with random agent activation are guaranteed to converge for any social network. We provide an upper bound of $\mathcal{O}(n|E|^2 (\varepsilon/δ)^2)$ on the expected number of opinion updates until convergence, where $|E|$ is the number of edges of the social network. For the complete social network we show a bound of $\mathcal{O}(n^3(n^2 + (\varepsilon/δ)^2))$ that represents a major improvement over the previously best upper bound of $\mathcal{O}(n^9 (\varepsilon/δ)^2)$. Our bounds are complemented by simulations that indicate asymptotically matching lower bounds.

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Social network (sociolinguistics) Convergence (economics) Asynchronous communication Computer science Public opinion Opinion leadership Mathematical economics Mathematics Politics Social media Political science Economics Public relations Law World Wide Web Economic growth Computer network

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Type: preprint
Language: en
Landing Page: http://arxiv.org/abs/2201.12923
PDF: https://arxiv.org/pdf/2201.12923
OA Status: green
Cited By: 4
Related Works: 10
OpenAlex ID: https://openalex.org/W4225858618

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DOI: https://doi.org/10.48550/arxiv.2201.12923

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Title: Asynchronous Opinion Dynamics in Social Networks

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Type: preprint

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Language: en

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Publication year: 2022

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Publication date: 2022-01-30

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Authors: Petra Berenbrink, Martin Hoefer, Dominik Kaaser, Pascal Lenzner, Malin Rau, Daniel Schmand

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Landing page: https://arxiv.org/abs/2201.12923

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PDF URL: https://arxiv.org/pdf/2201.12923

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Concepts: Social network (sociolinguistics), Convergence (economics), Asynchronous communication, Computer science, Public opinion, Opinion leadership, Mathematical economics, Mathematics, Politics, Social media, Political science, Economics, Public relations, Law, World Wide Web, Economic growth, Computer network

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Cited by: 4

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Citations by year (recent): 2024: 1, 2023: 2, 2022: 1

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abstract_inverted_index.network.	189, 207, 235
abstract_inverted_index.opinion.	63, 151
abstract_inverted_index.opinions	129, 144
abstract_inverted_index.process.	134
abstract_inverted_index.connected	122
abstract_inverted_index.converges	85
abstract_inverted_index.different	102
abstract_inverted_index.formation	37
abstract_inverted_index.iterative	133
abstract_inverted_index.neighbors	147, 158
abstract_inverted_index.networks.	41
abstract_inverted_index.political	18
abstract_inverted_index.processes	38
abstract_inverted_index.products,	13
abstract_inverted_index.situation	55, 89
abstract_inverted_index.spreading	1
abstract_inverted_index.Hegselmann	25
abstract_inverted_index.activated,	136
abstract_inverted_index.activation	199
abstract_inverted_index.elections,	9
abstract_inverted_index.guaranteed	201
abstract_inverted_index.knowledge,	171
abstract_inverted_index.movements.	21
abstract_inverted_index.previously	256
abstract_inverted_index.reasonable	72
abstract_inverted_index.represents	250
abstract_inverted_index.well-known	30
abstract_inverted_index.improvement	253
abstract_inverted_index.influencing	157
abstract_inverted_index.simulations	268
abstract_inverted_index.theoretical	31, 47
abstract_inverted_index.asynchronous	176
abstract_inverted_index.complemented	266
abstract_inverted_index.convergence,	224
abstract_inverted_index.asymptotically	271
abstract_inverted_index.\mbox{influence	106
abstract_inverted_index.$\mathcal{O}(n^9	261
abstract_inverted_index.Hegselmann-Krause	117, 173
abstract_inverted_index.$\mathcal{O}(n\|E\|^2	214
abstract_inverted_index.$\mathcal{O}(n^3(n^2	246
abstract_inverted_index.(\varepsilon/δ)^2)$	215
abstract_inverted_index.(\varepsilon/δ)^2)$.	262
abstract_inverted_index.(\varepsilon/δ)^2))$	248
cited_by_percentile_year
countries_distinct_count	0
institutions_distinct_count	6
sustainable_development_goals[0].id	https://metadata.un.org/sdg/10
sustainable_development_goals[0].score	0.5199999809265137
sustainable_development_goals[0].display_name	Reduced inequalities
citation_normalized_percentile