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Phase transitions in biased opinion dynamics with 2-choices rule
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Mukhopadhyay, Arpan (2023) Phase transitions in biased opinion dynamics with 2-choices rule. Probability in Engineering and Informational Sciences . pp. 1-18. doi:10.1017/S0269964823000098 (In Press)
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Official URL: https://doi.org/10.1017/S0269964823000098
Abstract
We consider a model of binary opinion dynamics where one opinion is inherently `superior' than the other and social agents exhibit a `bias' towards the superior alternative. Specifically, it is assumed that an agent updates its choice to the superior alternative with probability $\alpha >0$ irrespective of its current opinion and the opinions of the other agents. With probability $1-\alpha$ it adopts the majority opinion among two randomly sampled neighbours and itself. We are interested in the time it takes for the network to converge to a consensus on the superior alternative. In a complete graph of size $n$, we show that irrespective of the initial configuration of the network, the average time to reach consensus scales as $\Theta(n \log n)$ when the bias parameter $\alpha$ is sufficiently high, i.e., $\alpha > \alpha_c$ where $\alpha_c$ is a threshold parameter that is uniquely characterised. When the bias is low, i.e., when $\alpha \in (0,\alpha_c]$, we show that the same rate of convergence can only be achieved if the initial proportion of agents with the superior opinion is above certain threshold $p_c(\alpha)$. If this is not the case, then we show that the network takes $\Omega(\exp(\Theta(n)))$ time on average to reach consensus.
Item Type: | Journal Article | ||||||
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Subjects: | Q Science > QA Mathematics Q Science > QA Mathematics > QA76 Electronic computers. Computer science. Computer software Q Science > QC Physics T Technology > TA Engineering (General). Civil engineering (General) |
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Computer Science | ||||||
Library of Congress Subject Headings (LCSH): | Phase transformations (Statistical physics), Phase transformations (Statistical physics) -- Computer simulations, Intelligent agents (Computer software), Graph theory, Artificial intelligence, Computer programming | ||||||
Journal or Publication Title: | Probability in Engineering and Informational Sciences | ||||||
Publisher: | Cambridge University Press | ||||||
Official Date: | 10 March 2023 | ||||||
Dates: |
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Page Range: | pp. 1-18 | ||||||
DOI: | 10.1017/S0269964823000098 | ||||||
Status: | Peer Reviewed | ||||||
Publication Status: | In Press | ||||||
Reuse Statement (publisher, data, author rights): | This article has been published in a revised form in Probability in Engineering and Informational Sciences https://doi.org/10.1017/S0269964823000098. This version is free to view and download for private research and study only. Not for re-distribution or re-use. © The Author(s), 2023. Published by Cambridge University Press. | ||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||
Date of first compliant deposit: | 29 August 2023 | ||||||
Date of first compliant Open Access: | 10 September 2023 |
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