This article dives into how a classic network science method, eigenvector centrality, was used to accurately predict Pope Leo XIV’s election by analyzing cardinal relationships, highlighting its unexpected success over sophisticated AI and prediction markets and its broader implications for complex system analysis.
When Pope Francis passed away in April, the world braced for a centuries-old tradition cloaked in intense secrecy: the papal conclave. Two weeks later, 133 cardinal electors gathered in the Sistine Chapel, tasked with selecting the next pontiff. Outside the Vatican’s walls, a diverse array of prognosticators, from seasoned pundits and bookmakers to crowdsourced prediction markets and even cutting-edge artificial intelligence models, attempted to forecast the outcome. Yet, almost universally, they failed to anticipate the election of Robert Prevost, now known as Pope Leo XIV.
Amidst the widespread misses, a team of researchers from Bocconi University in Milan, Italy, unearthed a powerful insight using a decades-old mathematical technique. This method, strikingly, is a distant cousin of the algorithm that propelled Google into a household name, demonstrating that sometimes, the most profound insights come from foundational principles rather than the latest technological marvels.
The Conclave’s Challenge: Secrecy and Complexity
Predicting traditional political elections is inherently difficult, even with the wealth of polling data, primary results, and historical trends at our disposal. Papal elections, by contrast, present a unique set of challenges. They are infrequent, and the cardinals involved are bound by a solemn oath of secrecy, making traditional data collection virtually impossible. This environment of limited information and high stakes makes forecasting a true test of any predictive model.
Network Science to the Rescue: An “Ecclesiastic LinkedIn”
To navigate these complex circumstances, Giuseppe Soda, Alessandro Iorio, and Leonardo Rizzo from Bocconi University’s School of Management turned to social networks. Their approach involved meticulously mapping out the personal and professional relationships among the College of Cardinals, the senior clergy who serve as both voters and potential candidates. One could envision this intricate web of connections as an “ecclesiastic LinkedIn” profile for the Vatican’s inner circle.
The researchers compiled data from publicly available records, identifying connections based on shared work in Vatican departments, ordination relationships (who ordained whom), and personal friendships. Once this network was established, they applied techniques from network science to evaluate cardinals based on three key measures of influence within this elaborate structure:
- Status: How central and well-regarded a cardinal is within the network, reflecting the influence of their connections.
- Mediation Power: A cardinal’s ability to bridge disparate parts of the network, connecting otherwise unconnected groups.
- Coalition Building: How effectively a cardinal can foster large alliances and bring together diverse factions.
Remarkably, Robert Prevost, widely considered an underdog by conventional analysts, ranked number one in the “status” measure. While he did not feature in the top five for the other two metrics, his preeminent “status” proved to be the decisive indicator, a finding the Bocconi team initially presented as a demonstration of network-based analysis rather than an explicit prediction. Their success, however, lends significant credence to the method’s potential. The original paper outlining their methodology can be found through a hint from Bocconi University researchers.
Understanding “Status”: The Core of Eigenvector Centrality
To quantify “status” rigorously, mathematicians delve beyond simple counts. A basic approach, degree centrality, merely counts the number of connections a person has. While easy to compute, this method falls short by treating all links equally, failing to account for the qualitative difference between knowing many ordinary people and knowing a few highly influential individuals. The analogy holds: there’s a world of difference between knowing everyone at your local coffee shop and being on a first-name basis with a handful of senators.
This is where eigenvector centrality enters the picture. This mathematical measure captures the recursive nature of influence. Instead of just summing connections, it assigns each person a score that is proportional to the sum of the scores of their connections within the network. In essence, your influence is boosted if your friends are influential, and their influence, in turn, depends on the influence of *their* friends, and so on. This elegant, circular definition requires sophisticated mathematical finesse to compute, often involving iterative processes until the scores converge. An in-depth explanation of eigenvector centrality can be found in academic resources.
Google’s PageRank: A Familiar Cousin
The concept of eigenvector centrality isn’t just for academic circles or papal predictions; it forms the bedrock of one of the internet’s most critical algorithms: Google’s PageRank. When you type a query into Google, its algorithm doesn’t just find relevant sites; it ranks them. Founders Larry Page and Sergey Brin recognized that a link from a highly influential site like Scientific American carries far more weight than a link from a personal blog. PageRank, a variant of eigenvector centrality, assigns importance to web pages based on the importance of the pages linking to them. This not only ensures high-quality search results but also thwarts attempts at “search-engine cheating” by artificially inflating link counts from low-status pages.
Beyond Papal Predictions: Real-World Applications
The utility of eigenvector centrality and its related measures extends far beyond papal conclaves and search engine rankings. Researchers across diverse fields leverage these tools to understand influence in complex networks. For instance, epidemiologists utilize it to pinpoint “superspreaders” in disease networks, identifying individuals whose high connectivity makes them critical in controlling outbreaks. Neuroscientists, too, apply it to brain imaging data to decode neural connectivity patterns, shedding light on how different parts of the brain communicate and influence each other. This demonstrates the broad applicability of network science as a field.
AI’s Misses vs. Math’s Precision
The success of the Bocconi team stands in stark contrast to the failures of cutting-edge AI models and prediction markets in this specific instance. While AI continues to evolve rapidly, its predictive power can sometimes be limited by data availability, the quality of its training sets, and its inability to fully grasp nuanced, human-centric systems. Recent incidents, such as Google’s own AI chatbot, Gemini, drawing criticism for generating historically inaccurate images of “diverse” founding fathers, popes, and Vikings, underscore the challenges AI faces in accurately reflecting complex historical and social contexts. The ability of the network science approach to cut through this complexity, focusing on the underlying structure of relationships, proved superior.
It’s a poetic twist that the new Pope, Leo XIV (Robert Prevost), reportedly studied mathematics as an undergraduate. As white smoke billowed from the Sistine Chapel, signaling the election of a new pontiff, it confirmed that the complex social dynamics of influence could be unraveled not by advanced AI, but by the enduring wisdom of a piece of mathematical theory: influence isn’t just about who you know, but crucially, who *they* know.
