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

We propose and analyze agent-based models to investigate consensus formation under qualified majority constraints, motivated by the dynamics of papal conclaves. The framework incorporates social imitation, strategic adaptation based on candidate viability and ideological alignment among agents. We consider both a baseline model without explicit ideological structure and an extended version with competing ideological blocs. Numerical simulations show that ideological polarization tends to delay consensus, while increased strategic responsiveness can significantly accelerate convergence. The interplay between social influence and strategic behavior leads to nontrivial collective dynamics, with strong sensitivity of convergence times to model parameters. We further validate the model by comparing its predictions with historical data from papal conclaves held between 1939 and 2025, finding good agreement across a wide range of scenarios. The rapid outcome of the 2025 conclave suggests that informal consensus-building mechanisms may play a key role in accelerating coordination. Beyond this specific application, the proposed framework captures general features of collective decision-making in structured populations and provides a simple platform to study nonlinear consensus dynamics. Our results indicate that small behavioral changes may produce large-scale effects, consistent with phenomena analogous to continuous phase transitions.