🧮 Holy Numbers: The Mathematical Miracle Behind Predicting the Pope
How three data scientists cracked the Vatican's sacred code and predicted who would wear the papal crown
😽 Keepin’ It Simple Summary for Younger Readers
👧🏾✊🏾👦🏾
🔬🗺️ Scientists created a special kind of map 🗺️ that doesn't show places 🌍, but instead shows who knows who 👥 and who works with who 🤝 among the Catholic Church's important leaders called cardinals.
They figured out which cardinals had the most friends 👬, which ones talked to lots of different groups 🗣️, and which ones were good at getting people to work together 🤝. Using math 📊 and these special maps 🗺️, they could tell who would likely become the next Pope ⛪ before the actual vote 🗳️ happened!
This shows that even things that seem mysterious 🕵️♂️, like picking a new Pope, follow patterns 📈 that math can help us understand.
🗝️ Takeaways
🔍 Researchers from Bocconi University accurately predicted the papal election using network science and mathematical analysis.
🕸️ The study mapped three critical dimensions of cardinal power: status (connections to influential peers), information control (bridging between groups), and coalition-building ability.
🧪 By analyzing official co-memberships, episcopal consecration lines, and informal relationships, researchers created the first comprehensive map of Vatican power networks.
🏆 The winning papal candidate scored highest in "status" as measured by eigenvector centrality, confirming the model's predictive power.
🌍 These same network analysis methods could be applied to understand power dynamics in governments, corporations, and other institutions that impact marginalized communities.
Divine Algorithms: How Network Science Predicted the Next Pope
When the sacred and statistical collide, even the Holy Spirit might appreciate a good algorithm.
The white smoke has risen from the Sistine Chapel, signaling to the world that a new Pope has been elected. But long before the cardinals entered the conclave on May 7th, a team of Italian researchers had already run the numbers and mapped the invisible pathways of power that would likely determine who would wear the papal crown.
While millions watched for smoke signals, these data scientists were studying something else entirely: the complex web of relationships binding the College of Cardinals together.
Talk about your heavenly networks!
What is Network Theory? Understanding the Science of Connections
Before diving into how mathematicians predicted the papal election, let's take a moment to understand the powerful tool they used: network theory.
At its most basic, network theory is the study of how things connect to each other. Imagine a spider web, where each intersection represents a person (or "node" in network-speak) and each strand of silk represents a relationship or connection (called an "edge" or "tie"). Network theory provides the mathematical tools to analyze these webs of connection.
We all intuitively understand networks. Your social circle is a network. The internet is a network. The electrical grid powering your home is a network. However, network theory enables us to quantify and visualize these connections in ways that reveal hidden patterns.
Think about your own social circles for a moment. Some people are "connectors" who know everyone across different groups, while others are tightly embedded within a single, close-knit community. Additionally, some have connections to particularly influential or powerful people. Network theory provides precise mathematical methods to identify and measure these different positions.
Here are some key concepts that even non-mathematicians can understand:
Centrality: How important or influential a node is within the network
Clustering: How tightly interconnected groups form within the larger network
Bridges: People who connect otherwise separate groups
Density: How interconnected the overall network is
Through mathematical formulas with intimidating names like "eigenvector centrality," network scientists can identify who holds various types of power in any social system. The person with the most direct connections isn't necessarily the most influential—sometimes it's the individual who is linked to other well-connected people, or the one who bridges different clusters.
If this sounds like office politics or high school social dynamics, that's because it is—just quantified and mapped with mathematical precision.
In the borderlands, we observe these networks manifest across communities, governments, and international relations. The mayor who knows the right people in Washington. The community organizer who connects different neighborhood groups. The businessperson linked to influencers on both sides of the border.
Network theory provides us with the tools to perceive and comprehend these invisible architectures of influence.
Sacred Statistics: Where Math Meets Mystery
For those of us in the borderlands who've watched powerful institutions come and go across centuries—from Spanish missionaries to copper barons to border patrol—there's something darkly amusing about seeing the Vatican's power structure laid bare through mathematics.
The most secretive election process in the world, supposedly guided by divine inspiration, turns out to be as mappable as your Facebook friends list.
A remarkable study conducted by Bocconi University scholars Giuseppe Soda, Alessandro Iorio, and Leonardo Rizzo has demonstrated that even the Vatican's closed doors can't keep out the analytical eye of network science.1
These researchers weren't making wild guesses or reading celestial tea leaves—they were calculating probabilities based on hard data about who knows whom, who works with whom, and who ordained whom in the labyrinthine world of Catholic hierarchy.
The Holy Algorithm
What makes this study groundbreaking isn't just its subject matter but its methodology. The research team reconstructed what they called a "multilevel model of the Vatican network" using three primary sources of data:
Official co-memberships - Who works together in the Roman Curia dicasteries, commissions, councils, and academies
Lines of episcopal consecration - The "spiritual genealogies" of who ordained whom
Informal relationships - Mapped through journalistic sources, including ideological alignments and patronage networks
From this data, they developed three key metrics to determine a Cardinal's "prominence" in the ecclesiastical network:
Status (measured by 'eigenvector centrality') - Rewards cardinals connected to influential peers
Information control (measured by 'betweenness centrality') - Identifies bridges between different groups
Coalition-building ability - A composite index measuring a cardinal's ability to form alliances
They even factored in the optimal age range based on historical data from papal elections since 1800. No stone left unturned, no variable left behind.
Let's break down these metrics in more understandable terms:
Status (Eigenvector Centrality): This isn't just about how many connections a cardinal has, but the quality of those connections. A cardinal scores high if they're connected to other highly connected cardinals. Think of it as the "popular kid who's friends with all the other popular kids" metric. In the Vatican context, this means cardinals who are close to other influential cardinals carry more weight.
Information Control (Betweenness Centrality): This identifies cardinals who serve as bridges between different groups or factions. These individuals often control the flow of information and can translate between different perspectives. In any organization, people in these positions frequently have an outsized influence because they can form a consensus between otherwise disconnected groups.
Coalition-Building Ability: This composite measure looks at a cardinal's ability to form alliances and build support blocks. It measures both how embedded they are in their own tight-knit group (clustering) and how many direct connections they have overall (degree centrality).
The mathematics behind these metrics is complex, but the intuition is remarkably common-sense: influence comes not just from who you know, but from strategic position in the overall network.
The Cardinals in the Network
According to their analysis, the top contenders in each category were:
Top 5 by Status:
Robert Prevost (moderate, US)
Lazzaro You Heung-sik (soft liberal, South Korea)
Arthur Roche (liberal, UK)
Jean-Marc Aveline (soft liberal, France)
Claudio Gugerotti (soft liberal, Italy)
Top 5 for Information Control:
Anders Arborelius (soft conservative, Sweden)
Pietro Parolin (liberal, Italy)
Víctor Fernández (liberal, Argentina)
Gérald Lacroix (moderate, Canada)
Joseph Tobin (liberal, USA)
Top 5 for Coalition Building Capacity:
Luis Antonio Tagle (soft liberal, Philippines)
Ángel Fernández Artime (soft liberal, Spain)
Gérald Lacroix (moderate, Canada)
Fridolin Besungu (soft conservative, Congo)
Sérgio da Rocha (soft liberal, Brazil)
And lo and behold—according to Leonardo Rizzo, "The elected Pope scored first in our metrics of Status (eigenvector centrality)." The researchers didn't explicitly state they were trying to predict the outcome, but their model proved remarkably accurate.
The white smoke essentially validated their equations.
The Power of Networks
What's fascinating is how this approach reveals the true nature of power within seemingly opaque institutions. As someone from the borderlands, where we've witnessed power played out across cultures and centuries, there's something eerily familiar about these dynamics.
Whether it's tribal councils, city governments, multinational corporations, or, apparently, the College of Cardinals, the same principles apply: connections matter. Being connected to influential people matters even more. And being positioned as a bridge between different groups? That's power gold.
As the researchers themselves put it:
"Even in the Church, as in any human organization, relationships matter. The more connected, listened to, and central an individual is in the flow of information, the more likely they are to become a unifying figure."
Implications Beyond the Vatican
What makes this study so valuable isn't just its ability to predict a papal election—it's what it teaches us about how power works everywhere.
The same methods could be applied to predict leadership transitions in governments, corporations, or any organization where relationships form the invisible architecture of influence. It strips away the mystique and reveals the mathematical reality underneath.
For marginalized communities who have often found themselves outside these networks of power—whether Indigenous peoples, immigrants, or others on society's periphery—understanding these dynamics offers a crucial window into how decisions that affect our lives are really made.
Those of us in the borderlands know all too well how power networks—from Washington D.C. to state capitals to local governments—create policies that shape our daily existence, often without any input from the people most affected.
The difference between us and the Vatican? We don't even get the courtesy of some white smoke to let us know when decisions have been made.
Network Theory Applied: Real-World Examples
The Vatican study isn't an isolated case. Network theory has been successfully applied to understand and predict outcomes in many contexts:
Business Leadership Succession: Researchers have used similar network analysis to predict who is likely to become the next CEO at major corporations. Studies show that executives with high "betweenness centrality" (those who bridge between different departments or divisions) are often more likely to ascend to leadership positions than those who are highly connected but only within a single silo.
Academic Influence: Citation networks reveal which researchers and papers have the most influence in a field, not just by counting direct citations but by measuring their position in the overall network of scientific knowledge.
Pandemic Spread: Network theory helped predict how COVID-19 would spread through communities based on social connection patterns, identifying super-spreader events before they happened.
Political Power: Congressional voting patterns can be analyzed as networks, revealing the hidden power brokers who influence legislation—often not the most publicly visible politicians.
Here in the borderlands, network analysis could help us understand how decisions about immigration policy, water rights, or economic development really get made. By mapping the networks of influence that connect local officials to state and federal power brokers, we might better understand where to focus advocacy efforts for meaningful change.
The beauty of network theory is that it doesn't just describe the world as it is—it can help us reimagine more equitable networks. By identifying structural holes where connections are missing, we can build strategic bridges to ensure that marginalized voices have pathways to influence.
When Data Meets Divinity
There's something both comforting and disquieting about applying network science to a process traditionally viewed as guided by the Holy Spirit. Comforting because it suggests that even the most powerful and secretive institutions operate according to predictable human patterns. Disquieting because it strips away some of the mystery.
But perhaps this is a false dichotomy. Maybe the divine works through these human networks rather than despite them. After all, if you believe in a Creator who designed the mathematical underpinnings of the universe, shouldn't that same Creator be comfortable working within the social mathematics of human connection?
The spirit moves in mysterious ways—but apparently those ways can be mapped with a good algorithm.
A Hope for Transparency
Understanding how power networks function offers hope for greater transparency and inclusivity in the future. If we can map these invisible structures—whether in religious institutions, governments, or corporations—we can begin to see where change is needed.
For those of us living in the borderlands, where decisions made in distant capitals profoundly impact our communities, this kind of analysis offers a powerful tool. It helps us understand not just who holds power, but how power flows, where the pressure points are, and how networks might be reconfigured to include more diverse voices.
The Bocconi researchers weren't trying to demystify the conclave or challenge its spiritual significance. Rather, as Rizzo explained, their aim was "to show that a robust methodology, grounded in sound theory, can illuminate even the most obscure corners of human behavior and organizational dynamics."
In that illumination lies hope—hope that by understanding how power works, we can work toward systems where power is more equitably distributed.
Network Science as Community Empowerment
For communities that have historically been excluded from power networks, network theory offers not just insight but potential strategies for change. When we understand how networks function, we can be more strategic about forming connections that amplify marginalized voices.
Consider these practical applications:
Network Mapping: Community organizations can map their own networks to identify key influencers, potential allies, and strategic gaps. Who connects your community to decision-makers? Where are bridges missing?
Strategic Connection-Building: Rather than trying to connect with everyone, network theory suggests focusing on building relationships with those who have high betweenness centrality—people who bridge between different worlds.
Coalition Formation: By identifying groups with complementary strengths and shared goals, communities can form more effective coalitions based on network principles.
Identifying Leverage Points: Network analysis can reveal surprising sources of influence that aren't immediately obvious from organizational charts or formal power structures.
Here in the borderlands, our communities have long developed intuitive strategies for navigating complex power structures across cultures, languages, and national boundaries. Network theory gives us a language and framework to make this tacit knowledge explicit, shareable, and systematically improvable.
The tools that predicted a pope can help predict—and shape—the future of our own communities.
Stay Connected
If you found this analysis valuable, consider supporting Three Sonorans Substack to help us continue revealing these insights. At the intersection of mathematics, power, and culture, we're working to understand the invisible forces that shape our world.
And if you're interested in learning more about network science and its applications in understanding power structures that affect our communities, drop a comment below. How might these same analytical tools be applied to understand power dynamics in border politics? What other seemingly divine processes might yield to mathematical analysis?
After all, in the ever-shifting landscape of the borderlands, we need all the predictive power we can get—even if it comes in the form of eigenvector centrality.
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