A Multi-Agent Model for Opinion Evolution under Cognitive Biases
<|reference_start|>A Multi-Agent Model for Opinion Evolution under Cognitive Biases: 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 ($\mathbf{R}$), 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 $\mathbf{R}$ or not included in $\mathbf{R}$. We showcase our model through a series of examples and simulations, offering insights into how opinions form in social networks under cognitive biases.<|reference_end|>
@article{alvim2024a,
    title={A Multi-Agent Model for Opinion Evolution under Cognitive Biases},
    author={M'ario S. Alvim, Artur Gaspar da Silva, Sophia Knight, and Frank
  Valencia},
    journal={arXiv preprint arXiv:2402.17615},
    year={2024},
    archivePrefix={arXiv},
    eprint={2402.17615},
    primaryClass={cs.MA cs.SI}
}