On November 19, 2025, Ph.D. candidate Federico Capannoli defended his thesis at Leiden University, revealing new insights into how opinions form and evolve within large groups. His research, which explores the dynamics of opinion change, utilizes mathematical models to represent complex networks, providing a unique perspective on societal behavior.
Modeling Opinions in Complex Networks
Capannoli’s work focuses on the idea that many real-life processes are too intricate for direct analysis. Instead, he employs mathematical frameworks to simplify and understand these phenomena. “We can represent complex processes, such as how opinions shift in social networks or how diseases spread, using similar mathematical structures,” he explains.
During his studies, Capannoli visualized individuals as nodes in a network, where each person’s opinion is indicated by the color of their node. Connections between nodes represent friendships, illustrating how opinions can be influenced over time. This model serves as a foundation for his exploration of opinion dynamics.
Insights from Recent Elections
Capannoli cites recent elections as a pertinent example of his research in action. “Everyone has a preferred political party, which corresponds to the color of their node. In the lead-up to elections, conversations and interactions can lead to shifts in these opinions,” he notes. His models suggest that, eventually, consensus can be reached among the group.
The time taken to achieve consensus is influenced by various factors. “The number of individuals involved and the connections between them are crucial,” Capannoli states. “If a few individuals are highly connected, consensus can be reached much faster.” This highlights the significant impact that influential figures, particularly on social media, can have on public opinion.
Capannoli also examined the effect of bias on opinion formation, particularly during political campaigns. He explains, “If two people converse, there’s a chance one may adopt an opinion influenced by propaganda.” His modeling indicates that a high level of bias can drastically reduce the time it takes to reach a consensus.
The Complexity of Social Dynamics
However, real-life social dynamics are more complicated than the models suggest. “Differences in opinion can lead to the breakdown of friendships or the formation of new connections,” Capannoli adds. This phenomenon of co-evolution, where opinions and relationships influence one another, presents a challenge for researchers.
Leiden University is at the forefront of this research area, particularly within the groups led by Frank den Hollander and Rajat Subhra Hazra. Capannoli emphasizes the importance of understanding this co-evolution, as it can result in the polarization of opinions, leading to the fragmentation of social networks.
“It’s quite alarming when you consider the implications,” he reflects. “Social media can reinforce existing beliefs, creating echo chambers. It’s essential to engage with differing viewpoints to prevent isolation within ideologically homogeneous groups.”
Capannoli’s research not only contributes to the field of mathematics but also offers valuable insights into the mechanisms driving societal change. As the world grapples with increasing polarization, understanding the dynamics of opinion formation becomes ever more critical.
