标题： 当红衣主教们运筹帷幄时：教皇选举团中关于影响和意识形态的基于代理的模型 显示英文标题

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

摘要： 我们提出了两种基于代理的模型来研究教皇选举会议（papal conclaves）的动力学，重点分析社会影响、策略性投票和意识形态一致性如何影响选出教皇所需的时间。 在第一个模型中，红衣主教通过两种机制进行互动：以概率$p$模仿随机选择的同伴的选择，以概率$q$转向上一轮获得最多票数的候选人。 此外，通过“实用投票”的方式引入了策略行为，即如果候选人的得票数低于某一阈值比例，则代理人会放弃自己首选的候选人，转而支持最可行的替代者。 候选人必须获得三分之二的多数票才能当选。 然后，我们通过引入意识形态阵营扩展了框架，将每位红衣主教和候选人分配到两个群体之一（例如进步派和保守派）。 红衣主教最初会投票给自己群体内的候选人，但可能因战略原因跨过意识形态界限。 我们用 $20\%$名保守派红衣主教初始化选民，反映当前由教皇任命所塑造的构成。 数值模拟表明，意识形态极化往往会通过增加所需的投票轮次数量来延迟选举。 然而，更高的策略响应度$q$值可以在极化情况下恢复效率。 我们进一步通过校准参数到 1939 年至 2025 年间举行的教皇选举会议的历史数据来验证模型。 该模型再现了观察到的收敛时间，并且与实际数据有很好的一致性，这表明它在不同制度背景下的解释能力。 尽管存在意识形态分歧，2025 年教皇选举会议的结果迅速得出，这表明非正式共识建设的重要性，可能是投票之前的关键机制，可以加速收敛。 显示英文摘要

摘要： We propose and analyze two agent-based models to investigate the dynamics of papal conclaves, focusing on how social influence, strategic voting, and ideological alignment affect the time required to elect a pope. In the first model, cardinals interact through two mechanisms: with probability $p$, they imitate the choice of a randomly selected peer, and with probability $q$, they shift support to the most voted candidate from the previous round. Additionally, strategic behavior is introduced via ``useful voting'', where agents abandon their preferred candidate if he receives less than a threshold fraction of the votes, switching instead to the most viable alternative. A candidate must secure a qualified majority of two-thirds to be elected. We then extend the framework by incorporating ideological blocs, assigning each cardinal and candidate to one of two groups (e.g., progressives and conservatives). Cardinals initially vote for candidates from their own group but may cross ideological lines for strategic reasons. We initialize the electorate with $20\%$ conservative cardinals, reflecting the current composition shaped by papal appointments. Numerical simulations show that ideological polarization tends to delay the election by increasing the number of voting rounds required. However, higher values of strategic responsiveness $q$ can restore efficiency even under polarization. We further validate the model by calibrating parameters to historical data from conclaves held between 1939 and 2025. The model reproduces observed convergence times with good agreement, supporting its explanatory power across institutional contexts. The rapid outcome of the 2025 conclave, despite ideological divisions, suggests the importance of informal consensus-building, possibly prior to voting, as a key mechanism for accelerating convergence.