Researcher ORCID Identifier


Graduation Year


Document Type

Open Access Senior Thesis

Degree Name

Bachelor of Science



Reader 1

Heather Z. Brooks

Reader 2

Vin de Silva

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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 Hegselmannā€“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 š¯›¾ and š¯›æ and recovers the Hegselmannā€“Krause model as š¯›¾ approaches infinity.
We analyze the effect of š¯›¾ and š¯›æ 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.