When cardinals strategize: An agent-based model of influence and ideology for the papal conclave

Physicist Nuno Crokidakis has published a paper on arXiv proposing two agent-based models that simulate papal conclave dynamics, focusing on how social influence, strategic voting, and ideological alignment impact the time needed to elect a pope. The first model has cardinals interact via imitation of peers (with probability p) and shifting support to the most voted candidate from the previous round (with probability q). Strategic behavior is introduced through 'useful voting,' where agents abandon their preferred candidate if they fall below a vote threshold, switching to the most viable alternative. A candidate needs a two-thirds qualified majority to win.

The second model extends this by adding ideological blocs—progressives and conservatives—with 20% conservative cardinals reflecting current appointments. Simulations reveal that ideological polarization increases voting rounds, delaying elections. However, higher strategic responsiveness (q) restores efficiency even under polarization. The model was validated against historical conclave data from 1939 to 2025, reproducing observed convergence times. The rapid 2025 conclave outcome, despite divisions, suggests informal pre-vote consensus-building as a key accelerator. The paper will appear in Chaos, Solitons & Fractals.