MMM Workshop September 2023

Polarisation in the bounded confidence model: A revised view

Rainer Hegselmann
Frankfurt School of Finance & Management

15 Sep 2023, 11:45–12:10

Presentation Slides (PDF)


The bounded confidence model (BC model) is a very simple model: Period by period, all agents average over all opinions that are no further away from their actual opinion than a given distance epsilon, their ‘bounded confidence’. It was introduced by Hegselmann and Krause in [2002].

According to the analysis at that time, it appeared that BC processes monotonically lead to a decreasing number of final clusters as the confidence interval (given by epsilon) increases. At a certain size of the confidence interval, a polarisation phase appeared. Furthermore, it was shown that the polarisation effect becomes stronger for non-symmetrical confidence intervals (leftists listen more to the left, rightists listen more to the right).

However, our approach at the time (random starting distributions, repeated runs, then some statistics) obscured the fact that the transition from plurality to polarisation to consensus is by no means monotonic.

In retrospect, it is very clear that we completely missed a crucial feature of our model back in [2002]: For increasing values of epsilon, our analysis then suggested smooth transitions in the model’s behaviour. In fact, the transitions are wild, chaotic and non-monotonic - as discovered and described by Jan Lorenz in [2006]. The most dramatic example of such effects is a consensus that breaks down for larger values of epsilon.

My talk will present a rather fundamental new approach to analysing the BC model. The new approach makes the non-monotonicities in the polarisation/consensus transition of the BC model unmissible.

Relevant publications

Polarization and Radicalization in the Bounded Confidence Model: A Computer-Aided Speculation

Bounded Confidence Revisited: What We Overlooked, Underestimated, And Got Wrong