A Multi-Agent Model for Opinion Evolution under Cognitive Biases
CoRR(2024)
摘要
We generalize the DeGroot model for opinion dynamics to better capture
realistic social scenarios. We introduce a model where each agent has their own
individual cognitive biases. Society is represented as a directed graph whose
edges indicate how much agents influence one another. Biases are represented as
the functions in the square region [-1,1]^2 and categorized into four
sub-regions based on the potential reactions they may elicit in an agent during
instances of opinion disagreement. Under the assumption that each bias of every
agent is a continuous function within the region of receptive but resistant
reactions (𝐑), we show that the society converges to a consensus if
the graph is strongly connected. Under the same assumption, we also establish
that the entire society converges to a unanimous opinion if and only if the
source components of the graph-namely, strongly connected components with no
external influence-converge to that opinion. We illustrate that convergence is
not guaranteed for strongly connected graphs when biases are either
discontinuous functions in 𝐑 or not included in 𝐑. We
showcase our model through a series of examples and simulations, offering
insights into how opinions form in social networks under cognitive biases.
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