Researcher ORCID Identifier
Open Access Senior Thesis
Bachelor of Science
Heather Z. Brooks
Vin de Silva
© 2022 Solomon Valore-Caplan
We present and analyze a model for how opinions might spread throughout a network of people sharing information. Our model is called the smoothed bounded-confidence model and is inspired by the bounded-confidence model of opinion dynamics proposed by Hegselmann and Krause. In the Hegselmann–Krause model, agents move towards the average opinion of their neighbors. However, an agent only factors a neighbor into the average if their opinions are sufficiently similar. In our model, we replace this binary threshold with a logarithmic weighting function that rewards neighbors with similar opinions and minimizes the effect of dissimilar ones. This weighting function can be tuned with parameters 𝛾 and 𝛿 and recovers the Hegselmann–Krause model as 𝛾 approaches infinity.
We analyze the effect of 𝛾 and 𝛿 on some of the stationary states of the smoothed bounded-confidence model on the complete graph. In particular, we analyze the stationary states with consensus and those with two distinct opinions.
Valore-Caplan, Solomon, "Smoothed Bounded-Confidence Opinion Dynamics on the Complete Graph" (2022). HMC Senior Theses. 261.