The papal election is also of interest to game-theory researchers because the conclave is a prime example of a qualified majority voting system. Since every cardinal is a well-known public figure, the conclave provides an excellent opportunity to study so-called convex voting. Researchers find the conclave particularly unique in terms of voting because, unlike typical electoral situations, cardinals do not form parties or factions. Although political preferences and presumed voting blocks may emerge within the papal electoral body, there is no official party structure, and each cardinal votes independently. 

Led by Kóczy Á. László, game theory research director at the HUN-REN KRTK Institute of Economics (KTI), and Sziklai R. Balázs, a researcher at the institute and associate professor at Budapest’s Corvinus University, the team examined the voting process of the papal election 12 years ago, when they predicted that Jorge Bergoglio, later Pope Francis, would rank among the top three candidates, even though he was not considered a front-runner at the time. 

The researchers have now updated the ranking. They believe that Pope Francis’s stance on poverty and church reforms will be decisive in the upcoming election. Therefore, the ranking method was developed based on the GDP of the candidate’s home country and the progressiveness of the cardinals. At the top of the list is Michael Czerny, a Canadian Jesuit priest of Czech origin, with 13.2%. 

American Cardinal Kevin Farrell did not make the top ten, securing only 8.6%. German cardinals Reinhard Marx (7.7%, 13th place), Gerhard Ludwig Müller (7.5%, 16th place), and Kurt Koch (7.4%, 17th place) also have strong chances. Among African cardinals, Dieudonné Nzapalainga from the Central African Republic ranked the highest with 7.6%, securing 14th place. Cardinal Péter Erdő from Hungary holds 65th place with 3.5%. 

The research suggests that the combination of all 90 cardinals is unlikely to be uniform, as there are distinct differences in preferences. They hypothesize that a candidate who is acceptable to both progressive and conservative cardinals will likely be acceptable to moderates as well. Since Pope Francis appointed many cardinals from outside Europe, the composition of the papal electorate has changed significantly over the past 12 years, with Europe now accounting for only about a third of the electors and more progressive cardinals being present. The classification of cardinals based on their progressiveness was done using artificial intelligence. 

In their analysis, the researchers disregarded changing preferences and potential strategic plays, instead identifying the most influential cardinals based on their positions. The analysis assumes that the chosen pope will resemble these influential figures, who are also likely to be potential candidates. The study is based on measuring a priori voting influence, assuming that those who could swing the election will have greater influence during the vote. 

The researchers acknowledge that the metrics they used are far from perfect but still provide a solid approach. In addition to examining the unique voting system of the papal election, the researchers highlight that science deals with real situations based on data, which helps in understanding power dynamics and events much better than the flood of superficial impressions and opinions found on social media. The researchers believe that even in complex situations like the papal election, they can provide the best possible predictions. 

The new pope will be elected by the College of Cardinals, composed of cardinals under 80, with a two-thirds majority. When Pope Francis was elected, there were 115 cardinals; now, 133 will vote. The election rules are complex, with several rounds of voting possible, and the cardinals’ positions may shift throughout the process. 

Source: HUN-REN KRTK Institute of Economics press release