Brugts, Britt (2026) Convergence and Consensus in the Adaptive Deffuant-Weisbuch Model. Bachelor's Thesis, Applied Mathematics.
|
Text
BScThesisBritts4757238July2026.pdf Download (3MB) | Preview |
Abstract
This thesis explores the adaptive version of the Deffuant-Weisbuch model, that is, instead of a constant threshold our threshold is a function of the agent's opinions. The motivation is that agent's willingness to listen to others can be different; some are more stubborn than others. We refer to this function as the confidence bound function. We prove that if eventually only symmetric updates occur, the model converges to a limit state. Under the additional condition that the confidence bound function is always above 0.5, we derive a lower bound on the probability of consensus that depends on the initial opinion distribution. We furthermore prove that on the complete graph we have almost sure convergence, and if our confidence bound function is monotone then we have convergence to a limit state for given edge choices. To complement these theoretical results, we provide simulations for two kinds of confidence bound functions: one that is symmetric and one that is monotone. We do this on the complete graph, the Erdös-Rényi graph and the cycle, and for the uniform initial opinion distribution and a polarized initial opinion distribution. These simulations show that if our symmetric confidence bound is tight we more likely have fragmentation, and for the monotone confidence bound we likely have at most two opinion clusters, which are persistent to all three graph topologies.
| Item Type: | Thesis (Bachelor's Thesis) |
|---|---|
| Supervisor name: | Szabo, R. and Grzegorczyk, M.A. |
| Degree programme: | Applied Mathematics |
| Thesis type: | Bachelor's Thesis |
| Language: | English |
| Date Deposited: | 16 Jul 2026 15:01 |
| Last Modified: | 16 Jul 2026 15:01 |
| URI: | https://fse.studenttheses.ub.rug.nl/id/eprint/37444 |
Actions (login required)
 |
View Item |