An Assimilation Anomaly: Averaging-Induced Reversal of Overall Opinion in Two Interacting Societies

Assimilation – the tendency for individuals to adjust their opinions to more closely align with those around them – is one of the central components of computational social-influence and opinion-dynamics models that seek to elucidate how large-scale societal trends can emerge from local social interactions among small groups of individuals. Although assimilation processes have been well studied using increasingly sophisticated assimilative schemes like bounded confidence, nonlinear opinion-averaging methodologies, time-varying social network structures, etc., we show there is a surprising, previously unrecognized phenomenon lurking in even the simplest of assimilation models. We consider here two societies that start out on opposite sides of some opinion spectrum, for instance, one initially very conservative society and the other very liberal. We assume small groups of individuals from these societies can meet and interact, and that during an interaction each person’s opinion simply moves closer to the average opinion of the group. One might anticipate that this barebones assimilation process – which involves nothing more than simple numerical averaging of opinions during each encounter – will invariably lead to a steady (and rather uninteresting) convergence of overall opinion among the two societies wherein the initial intersocietal differences are straightforwardly washed away. We show instead that a counterintuitive, large-scale demographic reversal can sometimes emerge – i.e., the two societies can potentially end up swapping their relative positions on the opinion spectrum, with the initially conservative society ending up more liberal, on the whole, than the formerly liberal society. This finding (dubbed an “assimilation anomaly†) shows how the process of repeatedly taking simple averages on a local level can induce an overall reversal of average opinion on a global level. Using a heat diffusion model from physics, we reveal the origins of this curious phenomenon. This dynamical effect involving two interacting societies is wholly distinct from other interesting social-influence phenomena described in the opinion-dynamics literature (e.g., polarization, fragmentation, phase transitions, bifurcations, etc.).