Category: Statistics

Summary: Measuring how consensus time and finite-size scaling behave near the critical confidence threshold in the Hegselmann-Krause opinion model.

In the Hegselmann-Krause model, agents repeatedly average with nearby opinions and can either reach consensus or split into multiple clusters. This experiment focuses on the slowing-down region near the critical confidence threshold, where consensus times appear to diverge and finite-size effects become especially important.

The simulation sweeps both agent number and confidence threshold, recording time to consensus and the number of final opinion clusters. Those measurements are then used to estimate a divergence exponent and a finite-size scaling collapse, rather than only reporting whether consensus eventually occurs.

That matters because much of the existing literature uses modest system sizes. The project aims to turn a familiar opinion-dynamics transition into a cleaner scaling problem with enough statistics to distinguish the critical exponents governing slowdown and size dependence.

Method: Repeated Hegselmann-Krause simulations across system sizes and confidence thresholds, estimating consensus times and finite-size scaling exponents near the critical point.

What is measured: Consensus time, critical divergence exponent, finite-size scaling exponents, and number of final opinion clusters.