Asynchronous Opinion Dynamics in Social Networks
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 theoret...
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Main Authors | , , , , , |
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Format | Journal Article |
Language | English |
Published |
30.01.2022
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Subjects | |
Online Access | Get full text |
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Summary: | 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 $\mathcal{O}(n|E|^2
(\varepsilon/\delta)^2)$ 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 $\mathcal{O}(n^3(n^2 +
(\varepsilon/\delta)^2))$ that represents a major improvement over the
previously best upper bound of $\mathcal{O}(n^9 (\varepsilon/\delta)^2)$. Our
bounds are complemented by simulations that indicate asymptotically matching
lower bounds. |
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DOI: | 10.48550/arxiv.2201.12923 |