A Weighted-Median Model of Opinion Dynamics on Networks
arxiv(2024)
Abstract
Social interactions influence people's opinions. In some situations, these
interactions result in a consensus opinion; in others, they result in opinion
fragmentation and the formation of different opinion groups in the form of
"echo chambers". Consider a social network of individuals, who hold
continuous-valued scalar opinions and change their opinions when they interact
with each other. In such an opinion model, it is common for an opinion-update
rule to depend on the mean opinion of interacting individuals. However, we
consider an alternative update rule - which may be more realistic in some
situations - that instead depends on a weighted median opinion of interacting
individuals. Through numerical simulations of our opinion model, we investigate
how the limit opinion distribution depends on network structure. For
configuration-model networks, we also derive a mean-field approximation for the
asymptotic dynamics of the opinion distribution when there are infinitely many
individuals in a network.
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