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Voter and majority dynamics with biased and stubborn agents
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Mukhopadhyay, Arpan, Mazumdar, Ravi R. and Roy, Rahul (2020) Voter and majority dynamics with biased and stubborn agents. Journal of Statistical Physics, 181 . pp. 1239-1265. doi:10.1007/s10955-020-02625-w ISSN 0022-4715.
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Official URL: https://doi.org/10.1007/s10955-020-02625-w
Abstract
We study binary opinion dynamics in a fully connected network of interacting agents. The agents are assumed to interact according to one of the following rules: (1) Voter rule: An updating agent simply copies the opinion of another randomly sampled agent; (2) Majority rule: An updating agent samples multiple agents and adopts the majority opinion in the selected group. We focus on the scenario where the agents are biased towards one of the opinions called the preferred opinion. Using suitably constructed branching processes, we show that under both rules the mean time to reach consensus is Θ(logN), where N is the number of agents in the network. Furthermore, under the majority rule model, we show that consensus can be achieved on the preferred opinion with high probability even if it is initially the opinion of the minority. We also study the majority rule model when stubborn agents with fixed opinions are present. We find that the stationary distribution of opinions in the network in the large system limit using mean field techniques.
| Item Type: | Journal Article | ||||||||
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| Subjects: | Q Science > QA Mathematics Q Science > QA Mathematics > QA76 Electronic computers. Computer science. Computer software |
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| Divisions: | Faculty of Science, Engineering and Medicine > Science > Computer Science | ||||||||
| Library of Congress Subject Headings (LCSH): | Random walks (Mathematics) , Intelligent agents (Computer software) | ||||||||
| Journal or Publication Title: | Journal of Statistical Physics | ||||||||
| Publisher: | Springer New York LLC | ||||||||
| ISSN: | 0022-4715 | ||||||||
| Official Date: | November 2020 | ||||||||
| Dates: |
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| Volume: | 181 | ||||||||
| Page Range: | pp. 1239-1265 | ||||||||
| DOI: | 10.1007/s10955-020-02625-w | ||||||||
| Status: | Peer Reviewed | ||||||||
| Publication Status: | Published | ||||||||
| Reuse Statement (publisher, data, author rights): | This is a post-peer-review, pre-copyedit version of an article published in Journal of Statistical Physics. The final authenticated version is available online at: http://dx.doi.org/[insert DOI]. | ||||||||
| Access rights to Published version: | Open Access (Creative Commons) | ||||||||
| Date of first compliant deposit: | 12 August 2020 | ||||||||
| Date of first compliant Open Access: | 9 March 2021 | ||||||||
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