**Conflict of interest**

**4. Conclusions**

**polarisation**

**Acknowledgements**

**36**

views, which becomes too difficult to change.

slightly more likely to become dominant in the long run).

further waves of propaganda and keep updating their opinion.

Social models are a simplification of very complex processes which happen at an individual level but might be able to capture some collective emergent aspects. In terms of opinion dynamics, modelling individual views as a number, simplifying external forces such as propaganda, simulating interactions and a process of opinion updating let us detect emergent patterns, including an increase in the global levels of polarisation and the frequency of homophilic interactions between individuals. The network structure plays a significant role, as the emergence of homophilic clusters which reinforce their opinions is detected, particularly on a network where

there is a large distance between nodes, such as a proximity network.

*Theory of Complexity - Definitions, Models, and Applications*

very different states. For some regions in the parameter space, there is unpredictability in the state in which society will be after propaganda.

connected society is more prone to the creation of homophilic clusters.

**4.1 What is different between a highly polarised society and one with little**

On a highly polarised society, individuals become "immune" to propaganda which does not support their views and dismiss it easily, whereas propaganda which supports their views is confirmation of their beliefs and takes individuals into even more extreme and plarised views. On a polarised society, even with little levels of homophily (meaning that individuals are likely to be exposed to both types of propaganda), individuals are eventually too biased in favour of any of the extreme

On a society with little levels of polarisation, views could either have a consensus

However, the most frequently observed consensus is one in which barely anyone

This chapter was completed with support from the PEAK Urban programme, funded by UKRI's Global Challenge Research Fund, Grant Ref: ES/P011055/1.

on one of the two extremes, in which case, propaganda in favour of any of the opinions has little impact. This case happens when one of the two views becomes dominant at early stages, in which case, individuals also become "immune" to propaganda (and since the first propaganda they are exposed is þ1, that view is

has extreme views, propaganda in favour of the two views flows between most individuals and they update their opinion accordingly, but not enough to reject

The observed results in terms of the trajectories and the observed levels of polarisation and homophily after many rounds of propaganda show that there might be a high sensitivity concerning the parameters. Two simulations under the same network structure and even the same initial opinions and parameters might follow different trajectories and end with substantially distinct levels of homophily and polarisation. The model initially exposes 1% of the population to some propaganda and depending on who is exposed, the dynamic changes and eventually reach

In the simulated networks, the average degree is 7.6 for the proximity network and 10 for the small-world and the scale-free network. The intensity of interactions, measured as the degree of the nodes, accelerates or frictions the diffusion of propaganda, and thus, accelerates of frictions polarisation and homophily as well. A lessThe author declare no conflict of interest.
