Graduation Year
2026
Document Type
Open Access Senior Thesis
Degree Name
Bachelor of Science
Department
Mathematics
Reader 1
Heather Z. Brooks
Reader 2
Christopher E. Miles
Terms of Use & License Information
Rights Information
© 2026 Madeline Reeve
Abstract
Models of opinion dynamics aim to describe the spread of opinions over time in a social network. However, many canonical models are deterministic and thus may fail to capture uncertainty present in social interactions. This work investigates the effect of adding noise into bounded-confidence models, a class of opinion dynamics models where agents are more likely to be influenced by opinions close to their own. In particular, we propose a noisy modification of the Deffuant–Weisbuch bounded-confidence model. We prove that in this model all agents eventually adopt the same opinion—that is, our model converges to consensus. In doing so, we delineate more general conditions under which noisy bounded-confidence models reach consensus and highlight other models that satisfy these criteria. We conclude with a preliminary analysis of the convergence time of our proposed noisy Deffuant–Weisbuch model.
Recommended Citation
Reeve, Madeline, "Toward Conditions for Consensus of Noisy Bounded-Confidence Models" (2026). HMC Senior Theses. 293.
https://scholarship.claremont.edu/hmc_theses/293
