 A number of models further refine the “bounded confidence” mechanisms of the Hegselmann Krause model. Deffuant et al., for example, replace the sharp cutoff of influence in Hegselmann-Krause with continuous influence values (Deffuant et al. 2002; Deffuant 2006; Meadows &amp; Cliff 2012). Agents are again assigned both opinion values and threshold (“uncertainty”) ranges, but the extent to which the opinion of agent i is influential on agent j is proportional to the ratio of the overlap of their ranges (opinion plus or minus threshold) over i’s range. Opinion centers and threshold ranges are updated accordingly, resulting in the possibility of individuals with narrower and wider ranges. Given the updating algorithm, influence may also be asymmetric: individuals with a narrower range of tolerance, which Deffuant et al. interpret as higher confidence or lower uncertainty, will be more influential on individuals with a wider range than vice versa. The influence on polarization of “stubborn” individuals who do not change, and of agents on extremes, has also been studied, showing a clear impact on the dynamics of belief change in the  group.[5]