Dijk, Linda van (2025) Modeling Opinion Dynamics: Biased Agents in Voter and Majority Rule Models. Bachelor's Thesis, Mathematics.
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Abstract
Opinion dynamics in social networks studies the interplay between individual beliefs and collective behaviour. This thesis investigates binary opinion dynamics within connected social networks influenced by biased agents, as studied by Mukhopadhyay et al. (“Voter and majority dynamics with biased and stubborn agents,” Journal of Statistical Physics, vol. 181, pp. 1239–1265, 2020). Biased agents have a preference for a specified opinion, the preferred opinion. Two updating rules are analysed; the voter and the majority rule. The voter rule stipulates that agents update their opinion by randomly sampling the opinion of another agent, whereas in the majority rule model, agents take a sample of 2K agents and adopt the majority opinion of this random sample. It is of interest to study whether consensus is reached, that is, when all agents hold the same opinion. The voter model analysis will demonstrate that the exit probability, the probability that consensus is achieved on the preferred opinion, converges to 1 as the network size increases to infinity. The analysis of the majority rule model will show that a phase transition exists in the exit probability. Moreover, the mean consensus time for both models is characterised to be Θ(log N ), where N is the network size.
| Item Type: | Thesis (Bachelor's Thesis) |
|---|---|
| Supervisor name: | Szabo, R. and Trapman, J.P. |
| Degree programme: | Mathematics |
| Thesis type: | Bachelor's Thesis |
| Language: | English |
| Date Deposited: | 06 Mar 2025 10:00 |
| Last Modified: | 06 Mar 2025 10:00 |
| URI: | https://fse.studenttheses.ub.rug.nl/id/eprint/34838 |
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