Summary
Since the turn of the century, extremism has become an increasingly visible and influential force. While major terrorist events have brought urgency to the topic, extreme behaviour is not limited to politics or religion; it appears in sports rivalries, celebrity culture, brand loyalty, and online communities. In many ways, it is a natural by-product of how groups form, interact, and evolve.
Given its prevalence, it is perhaps surprising how little we understand how extremist viewpoints emerge, particularly in populations that begin as largely moderate. This question sits at the heart of my research: what drives groups toward polarisation, and under what conditions can extreme views take hold or even dominate?
This work belongs to the field of Opinion Dynamics, an interdisciplinary area spanning sociology, mathematics, and physics. These models aim to describe how individual opinions evolve through interaction, and how complex collective behaviours emerge from relatively simple rules. My focus was on understanding how extremist populations form, and on developing a model that captures these dynamics in a simpler and more complete way.
To build intuition, consider a room full of experts. Each person expresses their opinion, listens to others, and updates their view accordingly. Repeating this process eventually leads to consensus, provided individuals are willing to adjust toward the majority [1] . While useful, this is clearly an idealised scenario.
A more realistic approach introduces uncertainty. Individuals are only willing to consider opinions within a certain range. As this range increases, so too does openness to influence. This leads to the Bounded Confidence (BC) model [2] , where consensus is no longer guaranteed and populations instead settle into clusters of agreement.
The Relative Agreement (RA) model builds on this idea by introducing pairwise interactions and weighting influence toward those with more similar opinions [3] . These seemingly small changes produce dramatically different outcomes.
Depending on initial conditions, populations may converge to a central consensus (Central Convergence), split into opposing camps (Bipolar Convergence), or, more surprisingly, shift almost entirely toward a single extreme viewpoint (Single Extreme Convergence). These behaviours closely resemble real-world patterns.
The interactive model below (Figure 1) allows you to explore these dynamics for yourself. Try adjusting uncertainty or the proportion of extremists and observe how the population evolves over time.
Parameters
Figure 1: The position of a line on the y-axis shows the opinion of that expert, while the x-axis shows the progression of time. The colour of the line highlights the expert's uncertainty; red showing a confident expert and green being completely unsure. As can be seen by their red colouring, the extremists are highly confident in their opinion.
However, a key limitation remains: these models assume the presence of extremists from the outset. They do not explain where those initial extreme viewpoints come from.
To address this, I drew on Social Judgement Theory [4] , which suggests that strong disagreement does not simply reduce influence, but can actively push individuals further apart.
Incorporating this into the model leads to the Relative Disagreement (RD) model. This small but important addition removes the need for pre-existing extremists; extreme viewpoints can emerge naturally from interactions within an initially moderate population.
The second interactive model (Figure 2) allows you to explore this effect. Try increasing disagreement influence and observe how quickly instability and polarisation can emerge.
Parameters
Figure 2: The position of a line on the y-axis shows the opinion of that expert, while the x-axis shows the progression of time. The colour of the line highlights the expert's uncertainty; red showing a confident expert and green being completely unsure.
Together, these models provide a clearer and more realistic explanation of how extremism can arise, spread, and sometimes dominate. Given the connection between these dynamics and major social and humanitarian challenges, improving our understanding of them is not only of academic interest, but of real-world importance.
Publications
MEADOWS, M. and Cliff, D. (2012). Reexamining the Relative Agreement Model of Opinion Dynamics. Journal of Artificial Societies and Social Simulation , 15(4):4, http://jasss.soc.surrey.ac.uk/15/4/4.html
MEADOWS, M. and Cliff, D. (2013). The Relative Agreement Model of Opinion Dynamics in Populations with Complex Social Network Structure. Complex Networks IV: Proceedings of COMPLENET (pp. 71-79). Springer Berlin Heidelberg.
MEADOWS, M. and Cliff, D. (2013). The Relative Disagreement model of opinion dynamics - Where do extremists come from? Proceedings of IWSOS 2013 .
MEADOWS, M. (2013). Examining the Relative Disagreement model of Opinion Dynamics with Klemm-Equíluz social network topologies. Proceedings of DHSS 2013 .
Links
Chess
The British Universities' Chess Association organises national university chess tournaments across the UK. I took over its website in 2012, and in 2018 built a new site to showcase the association's 79-year history, its events, results, and the community around them.
I joined Downend & Fishponds chess club after my time at the University of Bristol and built their website in 2013. What started as a simple club site has grown into an online community for its members, with league tables, results, and club news.
Winner of the English Chess Federation's website of the year 2017 award.
A coaching site for a London-based chess coach and close friend. I built the site to reflect the quality of his teaching: clean, focused, and easy for prospective students to find what they need.
Projects
A side project born from running score prediction leagues with friends. I wanted a way to make the experience more engaging and competitive, so I built a platform to handle scoring, leaderboards, and league management.